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BEGIN:VEVENT
SUMMARY:Bei Wang (University of Utah - USA)
DTSTART:20210820T150000Z
DTEND:20210820T160000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/1
DESCRIPTION:Title: Sheaf-Theoretic Stratification Learning From Geometric and Topolog
ical Perspectives\nby Bei Wang (University of Utah - USA) as part of G
EOTOP-A seminar\n\n\nAbstract\nWe investigate a sheaf-theoretic interpreta
tion of stratification learning from geometric and topological perspective
s. Our main result is the construction of stratification learning algorith
ms framed in terms of a sheaf on a partially ordered set with the Alexandr
off topology. We prove that the resulting decomposition is the unique mini
mal stratification for which the strata are homogeneous and the given shea
f is constructible. In particular\, when we choose to work with the local
homology sheaf\, our algorithm gives an alternative to the local homology
transfer algorithm given in Bendich et al. (2012)\, and the cohomology str
atification algorithm given in Nanda (2020). Additionally\, we give exampl
es of stratifications based on the geometric techniques of Breiding et al.
(2018)\, illustrating how the sheaf-theoretic approach can be used to stu
dy stratifications from both topological and geometric perspectives. This
approach also points toward future applications of sheaf theory in the stu
dy of topological data analysis by illustrating the utility of the languag
e of sheaf theory generalizing existing algorithms. This is joint work wit
h Adam Brown.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yusu Wang (UC San Diego - USA)
DTSTART:20210903T150000Z
DTEND:20210903T160000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/2
DESCRIPTION:Title: Persistent Laplacian: properties and algorithms\nby Yusu Wang
(UC San Diego - USA) as part of GEOTOP-A seminar\n\n\nAbstract\nThe combin
atorial graph Laplacian\, as an operator on functions defined on the verte
x set of a graph\, is a fundamental object in the analysis of and optimiza
tion on graphs. There is also an algebraic topology view of the graph Lapl
acian which arises through considering boundary operators and specific inn
er products defined on simplicial (co)chain groups. This permits extending
the graph Laplacian to a more general operator\, the q-th combinatorial L
aplacian to a given simplicial complex. An extension of this combinatorial
Laplacian to the setting of pairs (or more generally\, a sequence of) sim
plicial complexes was recently introduced by (R.) Wang\, Nguyen and Wei. I
n this talk\, I will present serveral results (including a persistent vers
ion of the Cheeger inequality) from our recent study of the theoretical pr
operties for the persistence Laplacian\, as well as efficient algorithms t
o compute it. This is joint work with Facundo Memoli and Zhengchao Wan.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Enzo Orlandini (Physics U. Padova - Italy)
DTSTART:20210917T150000Z
DTEND:20210917T160000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/3
DESCRIPTION:Title: Getting interlocked circular chains through the needle’s eye
\nby Enzo Orlandini (Physics U. Padova - Italy) as part of GEOTOP-A semina
r\n\n\nAbstract\nThe process of driven translocation of polymer chains thr
ough a narrow pore can be severely hindered by the presence of self and mu
tual entanglement. In circular chains this entanglement is trapped in the
form of knots and links that may act as potential obstruction at the pore
affecting the translocation dynamics. Here we present theoretical results
mainly based on extensive Langevin simulations on the driven translocation
dynamics of topologically linked rings. We highlight the role of link com
plexity\, pore size and driving force field on the translocation process
and suggest how to extend nanopore sensing techniques to probe the topolog
ical properties of these systems and\, for instance\, to distinguish knott
ed from linked states and two component to multicomponent links.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lynn Zechiedrich (Baylor College of Medicine - USA)
DTSTART:20211001T150000Z
DTEND:20211001T160000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/4
DESCRIPTION:Title: Cooperativity of looping- and supercoiling-mediated base-pair disr
uption among distant sites modulates the 3-D structure of DNA to control i
ts activity\nby Lynn Zechiedrich (Baylor College of Medicine - USA) as
part of GEOTOP-A seminar\n\n\nAbstract\nJonathan M. Fogg and Lynn Zechied
rich\n\nBaylor College of Medicine\n\nDNA in cells is supercoiled and cons
trained into loops. Despite the ubiquity and importance of supercoiling in
regulating nearly every aspect of DNA activity\, relatively little is kno
wn about how. To determine how supercoiling influenced DNA shape\, we dete
rmined the 3-D structures of individual 336 bp DNA minicircles over a wide
range of supercoiling from s = -0.019 to +0.085 (Irobalieva et al. 2015).
Supercoiled DNA forms far more bent and contorted shapes than predicted.
We sought to understand how DNA formed these shapes using coarse-grained m
olecular dynamics simulations (Wang et al. 2017)\, which predicted that si
te-specific disruptions to base pairing may explain otherwise energeticall
y unfavorable sharp DNA bends. Likewise\, bending strain at the apices of
highly writhed DNA circles leads to broken base pairs. Probing for and map
ping where base-pair disruptions occur\, we discovered that negative super
coiling transmits mechanical stress along the DNA backbone to disrupt base
pairing at specific distant sites (Fogg et al. 2021). This unprecedented
base-pair disruption cooperativity among distant sites localizes certain s
equences to superhelical apices to facilitate DNA writhing and relieve tor
sional strain\, likely preventing more extensive denaturation that can cau
se genomic instability. We also discovered how cells may exploit DNA loopi
ng to position DNA nicks to facilitate repair. Our data explain how DNA ca
n form short loops through base-pair disruption and reveal a complex inter
play between looping- and supercoiling-mediated site-specific disruptions
to base pairing and the 3-D conformation of DNA\, which influence how geno
mes are stored\, replicated\, transcribed\, repaired\, and likely other as
pects of DNA activity. We hope to harness these looping- and supercoiling-
mediated site-specific denaturation and mechanical correlations to design
novel DNA shapes for nanotechnology.\n\nIrobalieva\, R.N.*\, Fogg\, J.M.*\
, Catanese\, D.J.\, Sutthibutpong\, T.\, Chen\, M.\, Barker\, A.K.\, Ludtk
e\, S.J.\, Harris\, S.A.\, Schmid\, M.F.\, Chiu\, W.\, and Zechiedrich\, L
. (2015) Structural diversity of supercoiled DNA. Nature Comm. Oct 12\;6:8
440 PMC4608029 (*equal contribution)\n\nWang\, Q.\, Irobalieva\, R. N.\, C
hiu\, W.\, Schmid\, M. F.\, Fogg\, J. M.\, Zechiedrich\, L.\, and Pettitt\
, B.M. (2017) DNA sequence determines conformational distribution of minic
ircles under torsional stress. Nucleic Acids Res. 45\, 7633–7642 PMC5737
869\n\nFogg\, J.M.\, Judge\, A.K.\, Stricker\, E.\, Chan\, H.L.\, and Zech
iedrich\, L. Supercoiling and looping promote DNA base accessibility and c
oordination among distant sites. Nature Comm. in press.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Janet M. Thornton (EMBL-EBI - UK)
DTSTART:20211015T150000Z
DTEND:20211015T160000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/5
DESCRIPTION:Title: The Wonderful World of Protein Structures\nby Janet M. Thornto
n (EMBL-EBI - UK) as part of GEOTOP-A seminar\n\n\nAbstract\nThis talk wil
l aim to present an overview of the three dimensional structures of protei
ns. These large and intricate molecules perform the vast majority of the b
iological functions of life and the structures of over 170\,000 proteins h
ave been determined and are stored in the Protein Databank. A detailed und
erstanding of their structures has gradually emerged over the last 50 year
s. Chirality within protein structures is observed at all 'levels' of stru
cture\, starting with the basic stereochemistry of the polypeptide chain\,
through local chain folding\, to the 'tertiary' structure of the whole ch
ain and even to chirality of large complexes.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fazle Hussain and Jie Yao (Texas Tech University - USA)
DTSTART:20211029T150000Z
DTEND:20211029T160000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/6
DESCRIPTION:Title: Dynamics of viscous vortex knots and links\nby Fazle Hussain a
nd Jie Yao (Texas Tech University - USA) as part of GEOTOP-A seminar\n\n\n
Abstract\nReconnection is the process by which two approaching vortices cu
t and connect to each other. As a topologically changing event\, it has be
en a subject of considerable fundamental interest for decades – not only
in (classical) viscous flows but also in quantum fluids\, as well as in n
umerous other fields\, such as plasmas\, polymers\, DNAs\, and so on. For
viscous fluid flows\, reconnection is believed to play a significant role
in various important phenomena\, such as turbulence cascade\, fine-scale m
ixing\, and aerodynamic noise generation. We first delineate the underlyin
g mechanism involved in vortex reconnection and its apparent role in turbu
lence cascade. Then we address the helicity dynamics involved in viscous r
econnection occurring in evolutions of a trefoil knotted vortex and a Hopf
-link. For both cases\, we find that the global helicity H graduall
y decreases before reconnection but sharply increases during reconnection
– this effect increases with increasing vortex Reynolds number (Re≡
circulation/viscousity). This suggests that H for viscous flows
is not conserved as Re→∞. Both positive and negative helical s
tructures are simultaneously generated before and during reconnection\, an
d their different decay rates due to asymmetric reconnection appears to ca
use such an increase of H during reconnection. By examining the top
ological aspects of the helicity dynamics\, we find that different from H\, the sum of linking and writhing numbers (i.e.\, Lk+Wr) con
tinuously drop during reconnection. Our results suggest that the twist\, w
hich increases with Re\, plays a more important role in helicity dy
namics than recognized before\, particularly at high Re.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paweł Dłotko (Dioscuri Center - Poland)
DTSTART:20211112T160000Z
DTEND:20211112T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/7
DESCRIPTION:Title: Data\, their relations and shape - topology in action\nby Pawe
ł Dłotko (Dioscuri Center - Poland) as part of GEOTOP-A seminar\n\n\nAbs
tract\nTopological data analysis is a rapidly developing area of mathemati
cs with applications in data science. In addition to revealing the shape o
f data we develop tools for visualizing high dimensional scalar and vector
valued functions. As an example\, we explore relations between various kn
ot invariants\, and extrapolate how presented tools may help to compare va
rious\, high-dimensional descriptors of fixed datasets. In particular\, we
show how these ideas can be used to compare different mapper-type graphs
of the same dataset. This is a joint work with Davide Gurnari\, Anna Jurek
\, Simon Rudkin and Radmila Sazdanovic.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antonio Rieser (CIMAT - Mexico)
DTSTART:20211119T160000Z
DTEND:20211119T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/8
DESCRIPTION:Title: Applied topology from the classical point of view\nby Antonio
Rieser (CIMAT - Mexico) as part of GEOTOP-A seminar\n\n\nAbstract\nWe gene
ralize several basic notions in algebraic topology to categories which con
tain both topological spaces classically treated by classical homotopy the
ory as well as more discrete and combinatorial spaces of interest in appli
cations\, such as graphs and point clouds. The advantage of doing so is th
at there are now non-trivial 'continuous' maps from paracompact Hausdorff
spaces to finite spaces (given the appropriate structure)\, and one may th
en compare the resulting topological invariants on each side functorially.
We find that there are a number of possible such categories\, each with i
ts own particular homotopy theory and associated homologies\, and\, additi
onally\, that there is a generalization of the coarse category which allow
s finite sets to be non-trivial (i.e. not 'coarsely' equivalent to a point
). We will give an overview of these theories and several applications\, s
how how they are related to familiar objects in applied topology\, such as
the Vietoris-Rips homology\, and discuss the advantages and disadvantages
of each. We finish by describing a recent construction of sheaf theory in
the category of Cech closure spaces\, a strict generalization of the cate
gory of topological spaces.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacob Leygonie (University of Oxford - UK)
DTSTART:20211203T160000Z
DTEND:20211203T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/9
DESCRIPTION:Title: Inverse Problems for Persistent Homology\nby Jacob Leygonie (U
niversity of Oxford - UK) as part of GEOTOP-A seminar\n\n\nAbstract\nPersi
stent Homology (PH) is a widely used topological descriptor for data. In o
rder to get a systematic understanding of the data science scenarios where
PH is successful\, it is crucial to know about its discriminative power\,
i.e. the ability to identify and disambiguate patterns in the data\, or i
n other words it is crucial to know about the information loss and the inv
ariances of PH. Formally these interrogations translate into the following
inverse problem: Given an element in the image of PH\, a so-called barcod
e D\, what is the fiber (pre-image) of PH over D? There are several ways o
f defining PH: for point clouds in a metric space\, for filter functions o
n a simplicial complex and for continuous functions on an arbitrary space\
, to name a few. Hence there are as many inverse problems to address. In t
his talk I will review the simplicial situation as well as that of Morse f
unctions on a smooth manifold\, with the aim of showing some geometrically
surprising fibers and transmitting my interest for these intricate invers
e problems.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Kahle (Ohio State University - USA)
DTSTART:20211210T160000Z
DTEND:20211210T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/10
DESCRIPTION:Title: Configurations spaces of particles: homological solid\, liquid\,
and gas\nby Matthew Kahle (Ohio State University - USA) as part of GEO
TOP-A seminar\n\n\nAbstract\nConfiguration spaces of points in the plane a
re well studied and the topology of such spaces is well understood. But wh
at if you replace points by particles with some positive thickness\, and p
ut them in a container with boundaries? It seems like not much is known. T
o mathematicians\, this is a natural generalization of the configuration s
pace of points\, perhaps interesting for its own sake. But is also importa
nt from the point of view of physics––physicists might call such a spa
ce the "phase space" or "energy landscape" for a hard-spheres system. Sinc
e hard-spheres systems are observed experimentally to undergo phase transi
tions (analogous to water changing into ice)\, it would be quite interesti
ng to understand topological underpinnings of such transitions.\n\nWe have
just started to understand the homology of these configuration spaces\, a
nd based on our results so far we suggest working definitions of "homologi
cal solid\, liquid\, and gas". This is joint work with a number of collabo
rators\, including Hannah Alpert\, Ulrich Bauer\, Robert MacPherson\, and
Kelly Spendlove.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tudor Ratiu (EPFL & Shanghai Jiao Tong University - Switzerland an
d China)
DTSTART:20220121T160000Z
DTEND:20220121T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/11
DESCRIPTION:Title: The Geometry of Fluid Dynamics\nby Tudor Ratiu (EPFL & Shangh
ai Jiao Tong University - Switzerland and China) as part of GEOTOP-A semin
ar\n\n\nAbstract\nFluid motion has a remarkable geometric structure genera
ted by Poisson structures on the Hamiltonian and variational structures on
the Lagrangian side. I will briefly review the standard results for ideal
incompressible homogeneous flows and then show how this is extended to fl
uids with advected quantities. A much more elaborate extension happens for
the Eringen model of liquid crystals because these fluids have internal s
tructure. Then I will introduce a momentum map with values in differential
characters that captures topological information\, something the classica
l momentum map cannot do. This has consequences in hydrodynamics\, specifi
cally for Clebsch variables\, since it permits to deal with solutions whos
e helicity is integer valued.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jesús Rodríguez-Viorato (CIMAT - México)
DTSTART:20220204T160000Z
DTEND:20220204T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/12
DESCRIPTION:Title: Topological Analysis from Latent Semantic Analysis\nby Jesús
Rodríguez-Viorato (CIMAT - México) as part of GEOTOP-A seminar\n\n\nAbs
tract\nLatent Semantic Analysis is one of the most widely used and accepte
d techniques in natural language processing. A better understanding of the
topology of Latent Spaces could lead to better applications. We applied d
ifferent topological techniques such as Ballmapper and persistent homology
to the Latent Semantic representation of hundreds of thousands of abstrac
ts and titles from the ArXiv database. We will present a comprehensible sy
nthesis of our computations\, comparing results between different time fra
mes and ArXiv categories.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Tulio Angulo (UNAM - México)
DTSTART:20220218T160000Z
DTEND:20220218T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/13
DESCRIPTION:Title: Coexistence holes in ecological systems\nby Marco Tulio Angul
o (UNAM - México) as part of GEOTOP-A seminar\n\n\nAbstract\nA central ch
allenge of Ecology is to explain the enormous biodiversity of species that
we find on Earth\, from the diversity of plant and animal species that st
ably coexist in tropical forests to the variety of microbial species that
coexist in our gut. Ecologists have focused on characterizing the "limits"
of species coexistence ---that is\, the maximum number of different speci
es that can coexist under given constraints. Yet\, little is known about t
he structure of species coexistence below such limits. Namely\, is it poss
ible to assemble an ecological system by adding one species at a time unti
l reaching the coexistence limits? Or is it possible to find obstructions
where species coexistence abruptly breaks before reaching the limits? To a
ddress these questions\, we built a novel formalism based on hypergraphs a
nd Algebraic Topology to show that\, below its limits\, species coexistenc
e in ecological systems has ubiquitous obstructions that we call "coexiste
nce holes". A coexistence hole occurs during an assembly process when a sp
ecies collection does not coexist\, although we can assemble it from sub-c
ollections that coexist. Using theoretical and experimental ecological sys
tems\, we provide direct evidence showing that coexistence holes obey regu
larities. Namely\, their diversity is constrained by the internal structur
e of species interactions\, while their frequency can be explained by exte
rnal factors acting on these systems. Overall\, our work provides one of t
he first applications of Algebraic Topology to Ecology\, unveiling how bio
diversity is a discontinuous process driven by internal design constraints
.\n\nThis is joint work with Aaron Kelley (IM-UNAM)\, Luis Montejano (IM-U
NAM)\, Chuliang Song (McGill/Toronto University) and Serguei Saavedra (MIT
).\n\nReferences:\n[1] Angulo\, Marco Tulio\, et al. "Coexistence holes ch
aracterize the assembly and disassembly of multispecies systems." Nature E
cology & Evolution (2021): 1-11.\n[2] Letten\, A. D. (2021). "Coexistence
holes fill a gap in community assembly theory." Nature Ecology & Evolution
\, 1-2.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin Knudson (University of Florida - USA)
DTSTART:20220311T160000Z
DTEND:20220311T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/14
DESCRIPTION:Title: Discrete Stratified Morse Theory\nby Kevin Knudson (Universit
y of Florida - USA) as part of GEOTOP-A seminar\n\n\nAbstract\nIn this tal
k I will describe a discrete version of stratified Morse theory and give s
everal examples of the utility of theory. This is joint work with Bei Wang
.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Randall Kamien (University of Pennsylvania - USA)
DTSTART:20220318T160000Z
DTEND:20220318T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/15
DESCRIPTION:Title: A New Classification of Topological Defects\nby Randall Kamie
n (University of Pennsylvania - USA) as part of GEOTOP-A seminar\n\n\nAbst
ract\nSmectic liquid crystals are layered systems that abound in nature. I
will introduce these materials and show how the long-lived\, topologicall
y protected excitations defy simple classification. I will describe our at
tempts.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carina Curto (The Pennsylvania State University - USA)
DTSTART:20220401T160000Z
DTEND:20220401T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/16
DESCRIPTION:Title: Dynamically relevant motifs in inhibition-dominated networks\
nby Carina Curto (The Pennsylvania State University - USA) as part of GEOT
OP-A seminar\n\n\nAbstract\nMany networks in the brain possess an abundanc
e of inhibition\, which serves to shape and stabilize neural dynamics. The
neurons in such networks exhibit intricate patterns of connectivity whose
structure controls the allowed patterns of neural activity. In this work\
, we examine inhibitory threshold-linear networks (TLNs) whose dynamics ar
e constrained by an underlying directed graph. We develop a set of paramet
er-independent graph rules that enable us to predict features of the dynam
ics\, such as emergent sequences and dynamic attractors\, from properties
of the graph. These rules provide a direct link between the structure and
function of inhibition-dominated networks\, yielding new insights into how
connectivity shapes dynamics in real neural circuits. Recently\, we have
used these ideas to classify dynamic attractors in a two-parameter family
of TLNs spanning all 9608 directed graphs of size n=5. Remarkably\, we fin
d a striking modularity in the dynamic attractors\, with identical or near
-identical attractors arising in networks that are otherwise dynamically i
nequivalent. This suggests that\, just as one can store multiple static pa
tterns as stable fixed points in a Hopfield model\, a variety of dynamic a
ttractors can also be embedded in TLNs in a modular fashion.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yang-Hui He (London Institute for Mathematical Science & Merton Co
llege\, Oxford University)
DTSTART:20220422T150000Z
DTEND:20220422T160000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/17
DESCRIPTION:Title: Universes as Bigdata: Physics\, Geometry and Machine-Learning\nby Yang-Hui He (London Institute for Mathematical Science & Merton Coll
ege\, Oxford University) as part of GEOTOP-A seminar\n\n\nAbstract\nThe se
arch for the Theory of Everything has led to superstring theory\, which th
en led physics\, first to algebraic/differential geometry/topology\, and t
hen to computational geometry\, and now to data science.\nWith a concrete
playground of the geometric landscape\, accumulated by the collaboration o
f physicists\, mathematicians and computer scientists over the last 4 deca
des\, we show how the latest techniques in machine-learning can help explo
re problems of interest to theoretical physics and to pure mathematics.\nA
t the core of our programme is the question: how can AI help us with mathe
matics?\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Grosberg (NYU - USA)
DTSTART:20220506T150000Z
DTEND:20220506T160000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/18
DESCRIPTION:Title: Is Trivial Knot Really So Trivial?\nby Alexander Grosberg (NY
U - USA) as part of GEOTOP-A seminar\n\n\nAbstract\nWhile topological idea
s are widely popular in physics\, topology of classical linear threads of
polymers presents steep mathematical and conceptual challenges\, with appl
ications in both biopolymers and materials. I will concentrate on the sim
plest case of polymer unknots and review what is known about fluctuations
and statistical mechanics of such objects based mostly on simulations\, ex
periments\, and hand-waving theoretical arguments. Continuing with increa
singly sophisticated models and phenomena\, I will review several more rec
ent theoretical and experimental achievements\, and conclude with the disc
ussion of a controversial concept of “topological glass”.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claudia Landi (Università di Modena e Reggio Emilia - Italy)
DTSTART:20220520T150000Z
DTEND:20220520T160000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/19
DESCRIPTION:Title: Multi-parameter persistence from the viewpoint of discrete Morse
theory.\nby Claudia Landi (Università di Modena e Reggio Emilia - Ita
ly) as part of GEOTOP-A seminar\n\n\nAbstract\nAlthough there is no doubt
that multi-parameter persistent homology is a useful tool for the topologi
cal analysis of multivariate data\, a complete understanding of these modu
les is still lacking. Issues such as computation\, visualization\, and int
erpretation of the output remain difficult to solve. In this talk\, I will
show how discrete Morse theory may enhance our understanding of multi-par
ameter persistence by connecting the combinatorial properties of the criti
cal cells of multi-filtered data to the algebraic properties of their pers
istence modules.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiao-Gang Wen (MIT - USA)
DTSTART:20220603T150000Z
DTEND:20220603T160000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/20
DESCRIPTION:Title: From topological order to origin of elementary particles (from al
gebra to geometry)\nby Xiao-Gang Wen (MIT - USA) as part of GEOTOP-A s
eminar\n\n\nAbstract\nI will discuss the world of many-body long range ent
anglement. It turns out that both topological quantum matter and elementar
y particles arise from many-body long range entanglement.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lisbeth Fajstrup (Aalborg University - Denmark)
DTSTART:20220819T150000Z
DTEND:20220819T160000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/21
DESCRIPTION:Title: Collapsing in directed topology\nby Lisbeth Fajstrup (Aalborg
University - Denmark) as part of GEOTOP-A seminar\n\n\nAbstract\nIn a sim
plicial complex\, a pair of simplices are a collapsing pair\, if one is a
unique maximal coface of the other which is then a free face. Such a pair
can be collapsed by removal of the two simplices and all simplices betwee
n them – think about an edge in a solid tetrahedron\; collapsing means r
emoving the edge\, the interior of the tetrahedron and the interior of the
two faces containing that edge. This leads to a homotopy equivalence. The
re is a similar notion for cubical complexes. A sequence of collapses lead
s to a simpler (fewer simplices/cubes) space.\nFor a directed space\, whic
h is a topological space with a selected set of paths\, the directed paths
\, directed homotopy equivalence is a very strong requirement\, and not wh
at should be the basis of collapsing.\nWe study the following setting: A E
uclidean Cubical Complex\, an ECC\, is a subset of R^n which is a union of
elementary cubes. An elementary cube is a product of n intervals [ai\,ai+
e]\, where e is either 0 or 1. A directed path in an ECC is continuous and
non-decreasing in all coordinates.\nWe define a notion of collapse with t
he aim of preserving various properties of spaces of directed paths.\nThis
is joint work with the WiT\, Women in Topology\, group R. Belton\, R. Bro
oks\, S.Ebli\, L.F.\, B.T.Fasy\, N.Sanderson\, E. Vidaurre.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martina Scolamiero (KTH Royal Institute of Technology - Sweden)
DTSTART:20220902T150000Z
DTEND:20220902T160000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/22
DESCRIPTION:Title: Stable and interpretable topological feature maps\nby Martina
Scolamiero (KTH Royal Institute of Technology - Sweden) as part of GEOTOP
-A seminar\n\n\nAbstract\nPersistent homology\, a popular method in TDA\,
can be used to define feature maps encoding geometrical properties of data
. In this talk I will present a method\, developed by the TDA group at KTH
\, which allows to construct feature maps with learnable parameters\, stab
le with respect to distances on persistence modules. The feature maps are
in fact defined starting from distances between persistence modules rather
than on the barcode decomposition\, making the method suitable for genera
lisations. Particular focus will be on understanding parametrised families
of such feature maps\, such as those stable with respect to p-Wasserstein
distance. The use of Wasserstein stable features will be illustrated on r
eal world and artificial datasets.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandru Baltag (Universiteit van Amsterdam - Netherlands)
DTSTART:20220923T150000Z
DTEND:20220923T160000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/23
DESCRIPTION:Title: The Topology of Knowing (Or How to Avoid Unexpected Exams)\n
by Alexandru Baltag (Universiteit van Amsterdam - Netherlands) as part of
GEOTOP-A seminar\n\n\nAbstract\nIn this talk I will present applications o
f General Topology to Epistemic Logic (=the logical aspects of knowledge\,
knowabiity and belief) and Formal Learning Theory. I show that topologica
l methods can throw light on issues such as the value of simplicity as a l
earning strategy (cf. Ockham's Razor) and the analysis of epistemic parado
xes (e.g. the connection between the so-called Surprise Exam Paradox and t
he Cantor-Bendixson process of calculating the perfect core). Time-permitt
ing\, I may present some complete and decidable logical axiomatizations of
these notions and maybe even give a hint concerning the completeness proo
fs.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jérémy Ledent (University of Strathclyde - UK)
DTSTART:20220930T150000Z
DTEND:20220930T160000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/24
DESCRIPTION:Title: Knowledge and topology: a simplicial approach\nby Jérémy Le
dent (University of Strathclyde - UK) as part of GEOTOP-A seminar\n\n\nAbs
tract\nMulti-agent Epistemic Logic is a modal logic of knowledge. It allow
s to reason about a finite set of agents who may know facts about the worl
d\, and about each other. In this talk\, I will present a new semantics fo
r epistemic logic\, based on simplicial complexes. In this approach\, the
knowledge of the agents is modeled by a higher-dimensional space called a
simplicial model\; and the truth of an epistemic logic formula can be eval
uated by inspecting the various possible paths in this space. I will illus
trate these ideas using examples from the theory of distributed computing\
, where the agents correspond to individual processes who can exchange inf
ormation in order to solve a task. Both topological invariants and logical
invariants can be leveraged to prove that some distributed computing task
s are impossible to solve.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chad Giusti (University of Delaware - USA)
DTSTART:20221021T150000Z
DTEND:20221021T160000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/26
DESCRIPTION:Title: Tracking cycles in neural codes\nby Chad Giusti (University o
f Delaware - USA) as part of GEOTOP-A seminar\n\n\nAbstract\nCircular coor
dinate systems -- here\, cycles -- are ubiquitous in data encoded by the b
rain. Classical ideas from topology tell us that the structure of the enco
ded data must be reflected in the activity of the encoding neural populati
ons\, and methods from topological data analysis have been highly successf
ul at detecting signatures of such encodings. The next natural question we
might ask is how we assign meaning or semantics to observed cycles Here\,
we describe a new method for using a measure of cross-similarity to regis
ter\, or falsify the registration of\, cycles across populations. We demon
strate its use in simulated and experimental data\, and discuss ongoing wo
rk using these tools to investigate how feed-forward networks propagate cy
cles. This is joint work with Iris Yoon\, Niko Schonsheck\, and several ot
hers.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marc Lackenby (University of Oxford - UK)
DTSTART:20221104T160000Z
DTEND:20221104T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/27
DESCRIPTION:Title: Knot theory and machine learning\nby Marc Lackenby (Universit
y of Oxford - UK) as part of GEOTOP-A seminar\n\n\nAbstract\nKnot theory i
s divided into several subfields. One of these is hyperbolic knot theory\,
which is focused on the hyperbolic structure that exists on many knot com
plements. Another branch of knot theory is concerned with invariants that
have connections to 4-manifolds\, for example the knot signature and Heega
ard Floer homology. In my talk\, I will describe a new relationship betwee
n these two fields that was discovered with the aid of machine learning. S
pecifically\, we show that the knot signature can be estimated surprisingl
y accurately in terms of hyperbolic invariants. We introduce a new real-va
lued invariant called the natural slope of a hyperbolic knot in the 3-sphe
re\, which is defined in terms of its cusp geometry. Our main result is th
at twice the knot signature and the natural slope differ by at most a cons
tant times the hyperbolic volume divided by the cube of the injectivity ra
dius. This theorem has applications to Dehn surgery and to 4-ball genus. W
e will also present a refined version of the inequality where the upper bo
und is a linear function of the volume\, and the slope is corrected by ter
ms corresponding to short geodesics that have odd linking number with the
knot. My talk will outline the proofs of these results\, as well as descri
bing the role that machine learning played in their discovery.\n\nThis is
joint work with Alex Davies\, Andras Juhasz\, and Nenad Tomasev.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlo Barenghi (Newcastle University - UK)
DTSTART:20221118T160000Z
DTEND:20221118T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/28
DESCRIPTION:Title: Is turbulence knotted?\nby Carlo Barenghi (Newcastle Universi
ty - UK) as part of GEOTOP-A seminar\n\n\nAbstract\nVortex lines and strea
mlines in turbulent flows\, visualized in the experiments or in the numeri
cs\, appear chaotic\, twisted\, perhaps linked or knotted. The physical me
aning of this complexity and its relation to the dynamics is still obscure
. In this lecture I shall address this problem - the geometrical and topol
ogical complexity of turbulence - in the arguably simpler context of "quan
tum fluids".\n\nQuantum fluids (superfluid helium\, atomic Bose-Einstein c
ondensates\, etc)are studied in the laboratory at temperatures close to ab
solute zero. At these low temperatures the fundamental quantum properties
of matter are not masked by thermal disorder. In particular\, any rotatio
nal motion is constrained by quantum mechanics to individual vortex lines
of fixed strength (phase defects of a complex order parameter)\, unlike wh
at happens in ordinary fluids where vorticity is a continuous field. Quant
um turbulence\, created by stirring a quantum fluid\, is thus conceptually
simpler than ordinary turbulence\, consisting of a tangle of individual v
ortex lines rather than a disordered continuous vorticity field.\n\nAfter
describing some surprising similarities between quantum turbulence and ord
inary turbulence\, I shall show how the geometry and the topology of quant
um turbulence can be quantified in a relatively simple way\, hence demonst
rate that quantum turbulence is indeed knotted. Is ordinary turbulence kno
tted too?\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Di Giovanni (Twitter - UK)
DTSTART:20221209T160000Z
DTEND:20221209T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/30
DESCRIPTION:Title: Over-squashing and over-smoothing through the lenses of curvature
and multi-particle dynamics\nby Francesco Di Giovanni (Twitter - UK)
as part of GEOTOP-A seminar\n\n\nAbstract\nI am going to talk about two pr
oblems that Message Passing Neural Networks (MPNNs) have been shown to be
struggling from. The first one – known as over-squashing – is unavoida
ble in the MPNN class and concerns the input graph topology. This relates
to how information propagates in a graph. We show that discrete curvature
quantities (old and new) could help us understand where messages are being
lost and we can provably characterize the over-squashing phenomenon in te
rms of curvature. The second problem consists in analysing GNNs as multi-p
article dynamics using the lens of gradient flows of an energy. We investi
gate what happens when instead of learning the MPNN equations we learn an
energy and then let the equations follow the gradient flow of such energy.
This allows us to understand further the role of the channel-mixing matri
x that is ubiquitous in standard graph convolutional models as a bilinear
potential inducing both attraction and repulsion along edges via its posit
ive and negative eigenvalues respectively.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Baez (UC Riverside - USA)
DTSTART:20220909T150000Z
DTEND:20220909T160000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/31
DESCRIPTION:Title: Compositional Modeling with Decorated Cospans\nby John Baez (
UC Riverside - USA) as part of GEOTOP-A seminar\n\n\nAbstract\nOne goal of
applied category theory is to understand open systems: that is\, systems
with a boundary of some sort\, through which matter\, energy or informatio
n can flow in or out. We can describe a large class of open systems usin
g the mathematics of decorated cospans\, which we explain here. In variou
s examples these ideas have been implemented in software. An interesting
example comes from stock-flow diagrams\, which are widely used in epidemio
logy to model the dynamics of populations. Although tools already exist fo
r building these diagrams and simulating the systems they describe\, we ha
ve created a new package called StockFlow which uses decorated cospans to
overcome limitations of the existing tools. This is joint work with Xiaoy
an Li\, Sophie Libkind\, Nathaniel Osgood and Evan Patterson.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Bubenik (University of Florida - USA)
DTSTART:20221014T150000Z
DTEND:20221014T160000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/32
DESCRIPTION:Title: Topological Data Analysis for Biological Images and Video\nby
Peter Bubenik (University of Florida - USA) as part of GEOTOP-A seminar\n
\n\nAbstract\nI will present the results of two projects applying topologi
cal data analysis (TDA) and machine learning (ML) to biological data. In t
he first\, we have developed a new tool\, TDAExplore\, that combines TDA a
nd ML to both classify biological images and to provide a visualization th
at is biologically informative. In the second\, we use TDA and ML to class
ify quasi-periodic biological videos and we apply TDA to such a video to p
roduce synthetic periodic videos.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Érika Roldán (Max Planck Institute for Mathematics in the Scienc
es (MiS) Leipzig - Germany)
DTSTART:20230127T160000Z
DTEND:20230127T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/34
DESCRIPTION:Title: Topology of random 2-dimensional cubical complexes\nby Érika
Roldán (Max Planck Institute for Mathematics in the Sciences (MiS) Leipz
ig - Germany) as part of GEOTOP-A seminar\n\n\nAbstract\nWe study a natura
l model of random 2-dimensional cubical complexes which are subcomplexes o
f an n-dimensional cube\, and where every possible square (2-face) is incl
uded independently with probability p. Our main result exhibits a sharp th
reshold $p=1/2$ for homology vanishing as the dimension n goes to infinity
. This is a 2-dimensional analogue of the Burtin and Erdős-Spencer theore
ms characterizing the connectivity threshold for random graphs on the 1-sk
eleton of the n-dimensional cube. Our main result can also be seen as a cu
bical counterpart to the Linial-Meshulam theorem for random 2-dimensional
simplicial complexes. However\, the models exhibit strikingly different be
haviors. We show that if $p > 1 - √1/2 ≈ 0.2929$\, then with high prob
ability the fundamental group is a free group with one generator for every
maximal 1-dimensional face. As a corollary\, homology vanishing and simpl
e connectivity have the same threshold. This is joint work with Matthew Ka
hle and Elliot Paquette.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ingrid Membrillo Solís (University of Southampton - UK)
DTSTART:20230217T160000Z
DTEND:20230217T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/36
DESCRIPTION:Title: Spaces of discrete vector fields and their applications to comple
x systems dynamics\nby Ingrid Membrillo Solís (University of Southamp
ton - UK) as part of GEOTOP-A seminar\n\n\nAbstract\nA complex system is f
ormed by entities that\, through their interactions and dependencies\, giv
e rise to a unified whole with properties and behavior distinct from those
of its constituent parts. Examples of complex systems are the human brain
\, living cells\, the Earth's global climate\, organisms\, smart materials
\, ecosystems and the economy. Modelling complex systems dynamics is chall
enging due to the high dimensionality and variety of the non-linear phenom
ena that these systems exhibit\, such as network and pattern formation\, e
volution\, adaptation and self-organization. \n\nIn this talk\, we will pr
esent a data-driven approach to studying complex systems using spaces of d
iscrete vector fields. These spaces can be endowed with a family of metric
s that allow us to keep track of the dynamics of complex systems. We will
show that this geometric framework can be used for dimensionality reducti
on\, detection of stable and unstable global attractors\, and quantificati
on of physical properties. In particular\, we will show applications to th
e analysis of data obtained from simulations and experiments of soft matte
r materials\, and simulations of pattern formation on curved domains. This
is part of joint works with M. Van Rossem\, T. Orlova\, N. Podoliak\, T.
Madeleine\, H. Sohn\, I. Smalyukh\, G. D'Alessandro\, M. Kaczmarek and J.
Brodzki.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Armajac Raventós Pujol (Universidad Autónoma de Madrid - Spain)
DTSTART:20230303T160000Z
DTEND:20230303T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/37
DESCRIPTION:Title: Simplicial complexes and the index lemma: A pathway to reach agre
ements fairly\nby Armajac Raventós Pujol (Universidad Autónoma de Ma
drid - Spain) as part of GEOTOP-A seminar\n\n\nAbstract\nAggregating indiv
idual preferences is a fundamental problem in democracy:\nHow can we take
collective decisions fairly based on individual preferences? Arrow's impos
sibility theorem (1951) proves that it is not possible to do it when we as
sume some apparently mild conditions. Fortunately\, in some cases\, aggreg
ation is possible when the domain of individual preferences is restricted.
That is\, when voters can only report some preferences\, good aggregation
rules exist. However\, no theorem characterizes the domains in which aggr
egation is possible\, and the\nproblem remains open.\n\nDespite the Arrovi
an model being purely combinatorial\, Baryshnikov (1993) used simplicial c
omplexes and homology to prove Arrow's theorem and exposed a conjecture wh
ich characterized restricted domains through homology groups. The main dra
wback of using homology is that it is not affordable for most of the socia
l scientists. Therefore\, instead of homology\, we have used combinatorial
topology tools such as the Index Lemma (the combinatorial counterpart to
Poincare's Lemma) to tackle the problem. First\, we have proved the Arrow'
s impossibility theorem\, showing that combinatorial topology is helpful f
or our purposes.\n\nSecond\, we have characterized the domains allowing ag
gregation rules for the base case of two voters and three candidates. Our
characterization proves that homology groups are not enough to characteriz
e such domains. Our result gives us hope to obtain a general characterizat
ion of the good domains for aggregating preferences. Moreover\, it could b
e implemented computationally\, making it handled by practitioners in poli
tics and economics.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Darrick Lee (EPFL - Switzerland)
DTSTART:20230317T160000Z
DTEND:20230317T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/38
DESCRIPTION:Title: Mapping Space Signatures\nby Darrick Lee (EPFL - Switzerland)
as part of GEOTOP-A seminar\n\n\nAbstract\nThe path signature is a charac
terization of paths which has led to the development of rough paths in sto
chastic analysis\, and a powerful set of novel tools for time series data
in machine learning. In this talk\, we begin with some background on signa
ture methods in machine learning. We introduce the mapping space signature
\, a generalization of the path signature for maps from higher dimensional
cubical domains (such as images or videos)\, which is motivated by the to
pological/geometric perspective of iterated integrals of differential form
s by K. T. Chen. The mapping space signature shares many of the analytic a
nd algebraic properties of the path signature\, in particular it is univer
sal and characteristic. This is joint work with Chad Giusti\, Vidit Nanda\
, and Harald Oberhauser.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Koya Shimokawa (Ochanomizu University - Japan)
DTSTART:20230331T160000Z
DTEND:20230331T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/39
DESCRIPTION:Title: Applications of band surgery on knots and links\nby Koya Shim
okawa (Ochanomizu University - Japan) as part of GEOTOP-A seminar\n\n\nAbs
tract\nWe consider local moves of knots and links\, called band surgeries.
A band surgery usually changes the topology of knots and links. Signature
s\, Jones polynomials\, and other link invariants can be used to show the
absence of band surgery between a given pair of links. A band surgery has
been used for establishing mathematical models of DNA recombination and an
ti-parallel reconnection of vortex knots and links. In this talk\, we disc
uss applications of results of band surgeries to the unlinking of DNA link
s by site-specific recombination and to the untying of vortex knots by ant
i-parallel reconnection.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bastian Rieck (Institute of AI for Health and the Helmholtz Pionee
r Campus of Helmholtz Munich - Germany)
DTSTART:20230414T160000Z
DTEND:20230414T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/40
DESCRIPTION:Title: Curvature for Graph Learning\nby Bastian Rieck (Institute of
AI for Health and the Helmholtz Pioneer Campus of Helmholtz Munich - Germa
ny) as part of GEOTOP-A seminar\n\n\nAbstract\nCurvature bridges geometry
and topology\, using local\ninformation to derive global statements. While
well-known in a\ndifferential topology context\, it was recently extended
to the\ndomain of graphs. In fact\, graphs give rise to various notions\n
of curvature\, which differ in expressive power and purpose. We\nwill give
a brief overview of curvature in graphs\, define some relevant concepts\,
and show their utility for data science and machine learning applications
. In particular\, we shall discuss\ntwo applications: first\, the use of c
urvature to *distinguish*\nbetween different models for synthesising new g
raphs from some\nunknown distribution\; second\, a novel *framework* for d
efining curvature for hypergraphs\, whose structural properties require a
more generic setting. We will also describe new applications\nthat are spe
cifically geared towards a treatment by curvature\,\nthus underlining the
utility of this concept for data science.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xin Liu (Institute of Theoretical Physics\, Faculty of Science\, B
eijing University of Technology - China)
DTSTART:20230428T150000Z
DTEND:20230428T160000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/41
DESCRIPTION:Title: Role of topology in study of cascade evolutions of physical knot/
link complex systems\nby Xin Liu (Institute of Theoretical Physics\, F
aculty of Science\, Beijing University of Technology - China) as part of G
EOTOP-A seminar\n\n\nAbstract\nRecent laboratory and numerical experiments
in classical and quantum fluids and in recombinant DNA plasmids show that
physical knots/links are highly unstable\, decaying from a high-topologic
al complexity state to a low-complexity state through a series of reconnec
tion events. A possible theoretical picture for this phenomenon is that hi
erarchy of topological complexity is\nclosely related to spectrum of energ
y or other dynamical properties. For this study the following\nprogress wo
uld be reviewed: (i) ropelengths/crossing numbers of prime knots and links
versus the\ngroundstate energy spectrum\; (ii) adapted HOMFLYPT polynomia
l values used to quantify\ncomplexity of torus knots and links\; (iii) com
plexity degree of a knot defined in a Legendre\npolynomial basis in a suit
ably defined knot polynomial space. Some relevant undergoing\nnumerical si
mulation work is introduced as well. Our emphasis will be placed on the ro
le that\ntopologically non-conservative transitions play in the evolution
of a knot complex system\, in the\nhope of finding a scalar topological in
variant to manage energy or other spectrums.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mónica Clapp (Instituto de Matemáticas UNAM - Mexico)
DTSTART:20230519T160000Z
DTEND:20230519T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/43
DESCRIPTION:Title: Optimal partitions for the Yamabe equation\nby Mónica Clapp
(Instituto de Matemáticas UNAM - Mexico) as part of GEOTOP-A seminar\n\n\
nAbstract\nThe Yamabe equation on a Riemannian manifold $(M\, g)$ is of\nr
elevance in differential geometry. A positive solution to it gives rise to
a metric\non M which has constant scalar curvature and is conformally equ
ivalent to the\ngiven metric $g$.\nAn optimal $\\ell$-partition for the Ya
mabe equation is a cover of M by $\\ell$-pairwise\ndisjoint open subsets s
uch that the Yamabe equation with Dirichlet boundary\ncondition has a leas
t energy solution on each one of these sets\, and the sum of\nthe energies
of these solutions is minimal. Such a partition induces a generalized\nme
tric that vanishes on a set of measure zero and is conformally equivalent
to\n$g$ in the complement.\nI will present some results obtained in collab
oration with Angela Pistoia\n(La Sapienza Universit`a di Roma) and Hugo Ta
vares (Universidade de Lisboa)\nthat ensure the existence and establish qu
alitative properties of this type of\npartitions. To do this\, we use some
ideas from physics.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fernando Galaz-García (Durham University - UK)
DTSTART:20230602T160000Z
DTEND:20230602T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/44
DESCRIPTION:Title: Metric geometry of spaces of persistence diagrams\nby Fernand
o Galaz-García (Durham University - UK) as part of GEOTOP-A seminar\n\n\n
Abstract\nPersistence diagrams are central objects in topological data ana
lysis. They are pictorial representations of persistence homology modules
and describe topological features of a data set at different scales. In th
is talk\, I will discuss the geometry of spaces of persistence diagrams an
d connections with the theory of Alexandrov spaces\, which are metric gene
ralizations of complete Riemannian manifolds with sectional curvature boun
ded below. In particular\, I will discuss how one can assign to a metric p
air $(X\,A)$ a one-parameter family of pointed metric spaces of (generaliz
ed) persistence diagrams $D_p(X\,A)$ with points in $(X\,A)$ via a family
of functors $D_p$ with $p\\in [1\,\\infty]$. These spaces are equipped wit
h the p-Wasserstein distance when $p\\geq 1$ and the bottleneck distance w
hen $p=\\infty$. The functors $D_p$ preserve natural metric properties of
the space $X$\, including non-negative curvature in the triangle compariso
n sense when $p=2$. When $p=\\infty$\, the functor $D_\\infty$ is sequenti
ally continuous with respect to a suitable notion of Gromov–Hausdorff co
nvergence of metric pairs. When $(X\,A) = (\\mathbb{R}^2\,\\Delta)$\, wher
e $\\Delta$ is the diagonal of $\\mathbb{R}^2$\, one recovers previously k
nown properties of the usual spaces of persistence diagrams. This is joint
work with Mauricio Che\, Luis Guijarro\, Ingrid Membrillo Solis\, and Mot
iejus Valiunas.\n\nhttps://arxiv.org/abs/2109.14697\n\nhttps://arxiv.org/a
bs/2205.09718\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fred Chazal (INRIA Saclay - France)
DTSTART:20230113T160000Z
DTEND:20230113T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/45
DESCRIPTION:Title: Measure Vectorization for Automatic Topologically-Oriented Learni
ng with guarantees.\nby Fred Chazal (INRIA Saclay - France) as part of
GEOTOP-A seminar\n\n\nAbstract\nRobust topological information commonly c
omes in the form of a set of persistence diagrams that can be seen as disc
rete measures and are uneasy to use in generic machine learning frameworks
. \n\nIn this talk we will introduce a fast\, learnt\, unsupervised vecto
rization method\, named ATOL\, for measures in Euclidean spaces and use it
for reflecting underlying changes in topological behaviour in machine lea
rning contexts. The algorithm is simple and efficiently discriminates impo
rtant space regions where meaningful differences to the mean measure arise
. We will show that it is proven to be able to separate clusters of persis
tence diagrams. We will illustrate the strength and robustness of our appr
oach on a few synthetic and real data sets.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steve Oudot (INRIA Saclay - France.)
DTSTART:20230210T160000Z
DTEND:20230210T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/46
DESCRIPTION:Title: Signed rank decompositions for multi-parameter persistence: from
Moebius inversion to relative homological algebra\nby Steve Oudot (INR
IA Saclay - France.) as part of GEOTOP-A seminar\n\n\nAbstract\nA question
that comes up repeatedly in recent developments on\nmulti-parameter persi
stence is to define mathematically sound and\ncomputationally tractable no
tions of approximation for multi-parameter\npersistence modules. As $\\mat
hbb{R}^n$ is of wild representation type\, one\nseeks to approximate arbit
rary (say\, finitely presentable) modules by\nmodules coming from some sub
category that is easier to work with in\npractice. An obvious candidate su
bcategory is the one of\ninterval-decomposable modules\, whose summands ar
e indicator modules of\nintervals (i.e. convex\, connected subsets of $\\m
athbb{R}^n$\, equipped\nwith the product order). Indeed\, interval-decompo
sable modules are\nconvenient to work with\, since they are easy to encode
and manipulate on\na computer\, and to interpret visually. Several notion
s of module\napproximation using this subcategory have been proposed\, amo
ng which the\nmost common one seeks to preserve the rank invariant when sw
itching from\nthe original module to its interval-decomposable approximati
on. The\nmotivation is that\, the rank invariant being one of the weakest\
ninvariants available to us\, preserving it is considered to be a minimum.
\nAs it turns out\, this is not always possible\, however one can always\n
decompose the rank invariant of the module as a $\\mathbb{Z}$-linear\ncomb
ination of rank invariants of interval modules. Thus\, a weaker form\nof p
reservation of the rank invariant is possible\, in which the interval\nsum
mands are signed (hence the name "signed rank decomposition"). This\nfact
can be viewed as a consequence of the Moebius inversion formula\,\nbut mor
e fundamentally\, it can be obtained by working in the\nGrothendieck grou
p relative to an appropriate exact structure\, where the\nrank invariant o
f the module becomes equal to the alternating sum of the\nrank invariants
of the various terms in the module's minimal relative\nprojective resoluti
on. This alternative proof strategy offers some\nsignificant benefits: (1)
it links the coefficients in the decomposition\nto the structure of the m
odule\, as in the 1-parameter setting\; (2) it\nprovides a roadmap to stud
y their bottleneck stability\; (3) it connects\nmulti-parameter persistenc
e to relative homological algebra\, thereby\npaving the way towards the de
finition of more refined invariants for\nmulti-parameter persistence modul
es using larger classes of projectives.\nThe purpose of my talk will be to
tell this story.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Reidun Twarock (The University of York - UK)
DTSTART:20221216T160000Z
DTEND:20221216T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/47
DESCRIPTION:Title: Geometry in the Fight against Viral Infection\nby Reidun Twar
ock (The University of York - UK) as part of GEOTOP-A seminar\n\n\nAbstrac
t\nThe Covid-19 pandemic has highlighted the need for novel antiviral stra
tegies. In this talk\, I will demonstrate that insights into the geometric
principles underpinning virus architecture provide a key to uncovering th
e mechanisms by which viruses replicate and infect their hosts. Geometric
and topological descriptors of virus architecture\, combined with stochast
ic simulations\, reveal how viruses navigate the knife’s edge between st
ability and instability\, guaranteeing protection for their genetic cargo
while also enabling its timely release. Models of virus architecture also
provide a novel perspective on open problems in virus assembly. This inclu
des the origin and control\nof polymorphic particle assembly\, which arise
s\, amongst others\, when virus-derived protein containers are functionali
sed to present antigens for applications in vaccinology. They moreover pla
y an instrumental role in the discovery of genome-encoded virus assembly i
nstructions. These results shed new light on selective pressures on viral
evolution and pave the way for innovation in antiviral therapy and virus n
anotechnology.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yulia R. Gel (UT Dallas - USA)
DTSTART:20230818T160000Z
DTEND:20230818T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/48
DESCRIPTION:Title: Coupling Time-Aware Multipersistence Knowledge Representation wit
h Graph Convolutional Networks for Time Series Forecasting\nby Yulia R
. Gel (UT Dallas - USA) as part of GEOTOP-A seminar\n\n\nAbstract\nGraph N
eural Networks (GNNs) are proven to be a powerful machinery for learning c
omplex dependencies in multivariate spatio-temporal processes. However\, m
ost existing GNNs have inherently static architectures\, and as a result\,
do not explicitly account for time dependencies of the encoded knowledge
and are limited in their ability to simultaneously infer latent time-condi
tioned relations among entities. We postulate that such hidden time-condit
ioned properties may be captured by the tools of multipersistence\, i.e.\,
an emerging machinery in topological data analysis which allows us to qua
ntify dynamics of the data shape along multiple geometric dimensions. We p
ropose to summarize inherent time-conditioned topological properties of th
e data as time-aware multipersistence Euler-Poincaré surface and prove it
s stability. We then construct a supragraph convolution module which simul
taneously accounts for the extracted intra- and inter-dependencies in the
data. We illustrate the utility of the proposed approach in application to
forecasting highway traffic flow\, blockchain Ethereum token prices\, and
COVID-19 hospitalizations.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ran Levi (University of Aberdeen - UK)
DTSTART:20230901T160000Z
DTEND:20230901T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/49
DESCRIPTION:Title: Differential Calculus for Modules over Posets\nby Ran Levi (U
niversity of Aberdeen - UK) as part of GEOTOP-A seminar\n\n\nAbstract\nThe
concept of a persistence module was introduced in the context of topologi
cal data analysis. In its original incarnation a persistence module is def
ined to be a functor from the poset of nonnegative real numbers with theor
y natural order to the category of vector spaces and homomorphisms. These
are referred to as single parameter persistence modules and are a fundamen
tal and useful concept in topological data analysis when the source data d
epends on a single parameter. The concept naturally lends itself to genera
lisation\, and one may consider persistence modules as functors from an ar
bitrary poset (or more generally an arbitrary small category) to some abel
ian target category. In other words\, a persistence module is simply a rep
resentation of the source category in the target abelian category. As such
much research was dedicated to studying persistence modules in this conte
xt. Unsurprisingly\, it turns out that when the source category is more ge
neral than a linear order\, then its representation type is generally wild
. In particular\, keeping in mind that persistence module theory is suppos
ed to be applicable\, computability of general persistence modules is very
limited. In this talk I will describe the background and motivation for p
ersistence module theory and introduce a new set of ideas for local analys
is of persistence module by methods borrowed from spectral graph theory an
d multivariable calculus.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Petar Pavešić (University of Ljubljana - Slovenia)
DTSTART:20230908T160000Z
DTEND:20230908T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/50
DESCRIPTION:Title: Singularity-free motion planning for redundant parallel manipulat
ors\nby Petar Pavešić (University of Ljubljana - Slovenia) as part o
f GEOTOP-A seminar\n\n\nAbstract\nSome twenty years ago Michael Farber def
ined the topological complexity of robot motion\nplanning as a measure of
the difficulty to construct predictable motion plans for mechanical device
s\n(like robots) that are allowed to move in a given work space. More rece
ntly\, we defined the\ncomplexity of a kinematic map that takes into accou
nt the kinematic relation between the internal\nstates of a serial mechani
sm and its spatial poses. In our talk we will discuss a more general motio
n planning for parallel mechanisms. In particular\, we will consider mecha
nisms that are redundant in\nthe sense that the dimension of their joint s
pace is strictly bigger than the dimension of their work\nspace. The addit
ional degrees of freedom allow motion paths that avoid critical configurat
ions of\njoints\, and we will discuss how difficult it is to construct pre
dictable singularity-free motion plans that\nperform a given set of tasks.
This is joint work with Edward Haug and Adrian Peidro.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Isabel Darcy (University of Iowa - USA)
DTSTART:20230922T160000Z
DTEND:20230922T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/51
DESCRIPTION:Title: Modeling knotted proteins with tangles\nby Isabel Darcy (Univ
ersity of Iowa - USA) as part of GEOTOP-A seminar\n\n\nAbstract\nWe prove
using the mathematics of tangles that if a protein terminus passing throug
h a single loop results in a locally knotted protein\, then Taylor's twist
ed hairpin model is the most likely method for creating such knots. In thi
s case the knotted products will all be twist knots. If we assume a right-
handed chirality bias\, which is common in proteins\, then the majority o
f these twist knots will be right-handed trefoils ($+3_1$)\, followed by
left-handed trefoils ($-3_1$)\, achiral figure eight knots ($4_1$) and rig
ht-handed five crossing twist knots ($-5_2$). An alternative pathway has b
een observed computationally where a terminus passes through two loops. W
e use 3-string tangle analysis to model this pathway. This is joint work
with Garrett Jones and Puttipong Pongtanapaisan.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jens Eggers (Bristol\, UK)
DTSTART:20231006T150000Z
DTEND:20231006T160000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/52
DESCRIPTION:Title: Geometrical singularities and free surface cusps\nby Jens Egg
ers (Bristol\, UK) as part of GEOTOP-A seminar\n\n\nAbstract\nCusp shapes
are widely observed in nature\, most famously as the bright caustic lines
on the inside of a coffee cup. This can be understood from the fact that a
cusp arises from the smooth deformation of a parameterized curve. Remarka
bly\, the same generic cusp can be formed on the surface of a viscous flui
d with surface tension\, as demonstrated by Jeong and Moffatt [J. Fluid Me
ch. 241\, 1\, (1992)]\, using complex mapping techniques. However\, their
observation is limited to very specific and idealized geometries. Here we
demonstrate that cusps are indeed local solutions to the Stokes equation w
ith surface tension\, regardless of the global flow.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ximena Fernández (Durham University\, UK)
DTSTART:20231013T160000Z
DTEND:20231013T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/53
DESCRIPTION:Title: The Fermat principle in Riemannian geometry\nby Ximena Ferná
ndez (Durham University\, UK) as part of GEOTOP-A seminar\n\n\nAbstract\nI
n many situations in physics\, the path of light is determined not only by
spatial geometry but also by an underlying local density (e.g.\, mass con
centration in general relativity\, refractive index in optics). Consider a
scenario where a Riemannian manifold in Euclidean space is shaped by a de
nsity function\, with only a finite sample of points available. How can we
infer the original metric and determine the manifold's topology?\n\nThis
talk introduces a density-based method for estimating topological features
from data in high-dimensional Euclidean spaces\, assuming a manifold stru
cture. The key to our approach lies in the Fermat distance\, a sample metr
ic that robustly infers the deformed Riemannian metric. Theoretical conver
gence results and implications in the homology inference of the manifold w
ill be presented. Additionally\, I will show practical applications in tim
e series analysis with examples from real-world data.\n\nThis talk is base
d on the article: X. Fernandez\, E. Borghini\, G. Mindlin\, and P. Groisma
n. "Intrinsic Persistent Homology via Density-Based Metric Learning." Jour
nal of Machine Learning Research 24 (2023) 1-42.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Feichtner-Kozlov (University of Bremen - Germany)
DTSTART:20231020T160000Z
DTEND:20231020T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/54
DESCRIPTION:Title: Simplicial Methods in Distributed Computing\nby Dmitry Feicht
ner-Kozlov (University of Bremen - Germany) as part of GEOTOP-A seminar\n\
n\nAbstract\nWe will give a brief introduction to the subject. The survey
of main ideas and tools will be complemented with applications to specific
standard distributed tasks.\n\nWe will conclude with stating an open prob
lem in combinatorial topology which is related to the complexity of the We
ak Symmetry Breaking distributed task.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Allison Moore (Virginia Commonwealth University - USA)
DTSTART:20231103T160000Z
DTEND:20231103T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/55
DESCRIPTION:Title: Entanglement and invariants of theta-curves\nby Allison Moore
(Virginia Commonwealth University - USA) as part of GEOTOP-A seminar\n\n\
nAbstract\nA theta-curve is a spatial embedding of the unique graph with t
wo\nvertices joined by three parallel edges. Like knots and links\,\ntheta
-curves and their mathematical properties are relevant to the\nmathematica
l modeling of biopolymers. In this talk\, we will\ninvestigate unknotting
operations and define new invariants of\ntheta-curves. We will also genera
lize the statement that 'unknotting\nnumber one knots are prime' to theta-
curves. This is joint work with\nseveral sets of authors.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Clayton Shonkwiler (Colorado State - USA)
DTSTART:20231117T160000Z
DTEND:20231117T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/56
DESCRIPTION:Title: Geometric Approaches to Frame Theory\nby Clayton Shonkwiler (
Colorado State - USA) as part of GEOTOP-A seminar\n\n\nAbstract\nFrames ar
e overcomplete systems of vectors in Hilbert spaces. They were originally
introduced in the 1950s in the context of non-harmonic Fourier series\, an
d came to renewed prominence in the 1980s in signal processing application
s. More recently\, there has been burgeoning interest in frames in finite-
dimensional Hilbert spaces\, with applications to signal processing\, quan
tum information\, and compressed sensing.\nIn this talk\, I will describe
some ways in which tools from differential\, Riemannian\, and symplectic g
eometry can be applied to problems in frame theory. Some key tools that cr
op up are Hamiltonian actions\, the Cartan decomposition\, and geometric i
nvariant theory. This is joint work with Tom Needham and partially with Du
stin Mixon and Soledad Villar.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wojciech Chacholski (KTH - Sweden)
DTSTART:20231201T160000Z
DTEND:20231201T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/57
DESCRIPTION:Title: Data\, geometry\, and homology\nby Wojciech Chacholski (KTH -
Sweden) as part of GEOTOP-A seminar\n\n\nAbstract\nFor a successful analy
sis a suitable representation of data by objects amenable for statistical
methods is fundamental. There has been an explosion of applications in whi
ch homological representations of data played a significant role. I will p
resent one such representation called stable rank and introduce various no
vel ways of using it to encode geometry\, and then analyse\, data. I will
provide several illustrative examples of how to use stable ranks to find m
eaningful results.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alain Goriely (Oxford - UK)
DTSTART:20231215T160000Z
DTEND:20231215T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/58
DESCRIPTION:Title: The geometry and mechanics of chirality: from Maxwell's perversio
n to Feynman's obsession\nby Alain Goriely (Oxford - UK) as part of GE
OTOP-A seminar\n\n\nAbstract\nMany natural structures such as proteins\, c
limbing vines\, and seashells exhibit a well defined chirality\, some are
left-handed\, some are right-handed\, some are both. The ultimate origin o
f chirality is one of Nature's great mystery. However\, geometry and mecha
nics play a fundamental role in assigning chirality and carrying this info
rmation from microscopic to macroscopic scales. In this talk\, I will disc
uss the general problem of chirality\, chirality measure\, and chirality t
ransfer\, trace its history\, and use examples from chemistry and biology
to obtain general principles with some surprising twists.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gunnar Hornig (Dundee University - UK)
DTSTART:20230616T160000Z
DTEND:20230616T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/60
DESCRIPTION:Title: Magnetohydrodynamic relaxation\, helicity and minimum energy stat
es in magnetised plasmas\nby Gunnar Hornig (Dundee University - UK) as
part of GEOTOP-A seminar\n\n\nAbstract\nDuring the turbulent relaxation o
f a plasma with a high magnetic Reynolds number\, the magnetic energy is t
ypically dissipated faster than the magnetic helicity. Hence one can attem
pt to describe the result of such a relaxation as a state that minimises t
he energy while preserving the magnetic helicity. Mathematically the relat
ion between magnetic helicity and energy is defined by an inequality\, $|H
(B)| \\le (2/C) E(B)$\, a result that was first shown in a classical paper
by V.I. Arnold (1974) for simply connected domains. The formula shows how
a non-trivial magnetic field topology (a non-zero helicity) forms a lower
bound for the magnetic energy. The formula contains a constant C\, which
is the smallest possible eigenvalue of the curl operator in a magnetically
closed domain. The corresponding eigenfield is a state of maximum helicit
y for a given energy. We will discuss under which circumstances these maxi
mum helicity (minimum energy) states can be reached\, show how Arnold’s
formula can be applied to non-simply connected domains\, and how one can m
odify Arnold’s formula to find lower bounds for the energy even if $H(B)
=0$.\n\nReferences:\n\nArnold\, V.I.\, The asymptotic Hopf invariant and i
ts application\, Sel. Math. Sov.\, 5\, 327 (1986)\n\nCandelaresi\, S.\, Po
ntin\, D. I.\, Hornig\, G.\, & Podger\, B. Topological Constraints in the
reconnection of vortex braids\, Physics of Fluids\, (33)\, 056101 (2021)\n
\nYeates\, A.R.\, Hornig\, G. and Wilmot-Smith\, A.L. Topological Constrai
nts on Magnetic Relaxation\, Phys. Rev. Lett.\, 105\, 085002 (2010)\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anthea Monod (Imperial College - UK)
DTSTART:20240209T160000Z
DTEND:20240209T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/61
DESCRIPTION:Title: Tropical Geometry of Phylogenetic Tree Space\nby Anthea Monod
(Imperial College - UK) as part of GEOTOP-A seminar\n\n\nAbstract\nBHV sp
ace is a well-studied moduli space of phylogenetic trees that appears in m
any scientific disciplines\, including computational biology\, computer vi
sion\, combinatorics\, and category theory. Speyer and Sturmfels identify
a homeomorphism between BHV space and a version of the Grassmannian using
tropical geometry\, endowing the space of phylogenetic trees with a tropic
al structure\, which turns out to be advantageous for computational studie
s. In this talk\, I will present the coincidence between BHV space and the
tropical Grassmannian. I will then give an overview of some recent work I
have done that studies the tropical Grassmannian as a metric space and th
e practical implications of these results on probabilistic and statistical
studies on sets of phylogenetic trees.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitriy Morozov (Lawrence Berkeley National Laboratory - USA)
DTSTART:20240216T170000Z
DTEND:20240216T180000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/62
DESCRIPTION:Title: From Descriptive to Operational Topological Data Analysis\nby
Dmitriy Morozov (Lawrence Berkeley National Laboratory - USA) as part of
GEOTOP-A seminar\n\n\nAbstract\nTopological data analysis evolved over the
past two decades into a primarily descriptive field. Almost all applicati
ons aim to quantify the topology of data and use the resulting descriptors
to build a model for classification or regression. Recently\, a new line
of applications emerged\, one that uses topology to guide optimization and
thus modify the data or the model directly. After reviewing the descripti
ve view of TDA\, we will discuss the structure of the optimization problem
and demonstrate how understanding it leads to better optimization algorit
hms.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jörn Dunkel (Mathematics\, MIT - USA)
DTSTART:20240301T160000Z
DTEND:20240301T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/63
DESCRIPTION:Title: Topological packing statistics of living and non-living matter\nby Jörn Dunkel (Mathematics\, MIT - USA) as part of GEOTOP-A seminar\n
\n\nAbstract\nComplex disordered matter is of central importance to a wide
range of disciplines\, from bacterial colonies and embryonic tissues in b
iology to foams and granular media in materials science to stellar configu
rations in astrophysics. Because of the vast differences in composition an
d scale\, comparing structural features across such disparate systems rema
ins challenging. Here\, by using the statistical properties of Delaunay te
ssellations\, we introduce a mathematical framework for measuring topologi
cal distances between two- or three-dimensional point clouds. The resultin
g system-agnostic metric reveals subtle structural differences between bac
terial biofilms as well as between zebrafish brain regions\, and it recove
rs temporal ordering of embryonic development. We apply the metric to cons
truct a universal topological atlas encompassing bacterial biofilms\, snow
flake yeast\, plant shoots\, zebrafish brain matter\, organoids\, and embr
yonic tissues as well as foams\, colloidal packings\, glassy materials\, a
nd stellar configurations. Living systems localize within a bounded island
-like region of the atlas\, reflecting that biological growth mechanisms r
esult in characteristic topological properties.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Soteros (Mathematics U Saskatchewan - Canada)
DTSTART:20240315T160000Z
DTEND:20240315T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/64
DESCRIPTION:Title: Establishing that Knots and Links are Localized for Ring polymers
in nanochannels\nby Chris Soteros (Mathematics U Saskatchewan - Canad
a) as part of GEOTOP-A seminar\n\n\nAbstract\nLattice models have proved u
seful for studying the entanglement complexity of polymers. In 1988 Sumner
s and Whittington used a lattice model to prove that knotting is inevitabl
e for sufficiently long ring polymers and that knot complexity increases w
ith polymer length. In the lattice model\, a ring polymer is represented b
y a polygon on the simple cubic lattice. Subsequently\, Monte Carlo simula
tions of lattice polygons led to a 1996 conjecture consistent with the ide
a that knots occur in a localized way in fixed knot-type polygons. That is
\, the "knotted part" is expected to be small relative to the length of th
e polygon. Recently a first proof of this conjecture has been established
for the special case of polygons confined to an infinity x 2 x 1 lattice t
ube. The proof relies on a combination of novel knot theory and lattice co
mbinatorics\, and the results also extend to non-split links. Monte Carlo
simulations support that the conjecture also holds for larger lattice tube
s. Thus one expects that knots and links will also be localized for DNA in
nano channel experiments. A lattice tube model has also been used to stud
y the entanglement complexity of two polygons which both span the tube\, a
scenario for which it is known that linking is inevitable. In this case\,
evidence suggest that knots are still localized but the linked part is no
t. I will review some of the proofs and Monte Carlo results for these latt
ice tube models and highlight some of the remaining open questions.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Vaccarino (Politecnico di Torino - Italy)
DTSTART:20240405T160000Z
DTEND:20240405T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/65
DESCRIPTION:Title: Three easy pieces for Hodge Laplacian and higher order interactio
ns\nby Francesco Vaccarino (Politecnico di Torino - Italy) as part of
GEOTOP-A seminar\n\n\nAbstract\nFirstly\, we present a cross-order Laplaci
an renormalization group (X-LRG) scheme for arbitrary higher-order network
s. The renormalization group is a fundamental concept in the physics theor
y of scaling\, scale-invariance\, and universality. An RG scheme was recen
tly introduced for complex networks with dyadic interactions based on diff
usion dynamics. However\, we still lack a general RG scheme for higher-ord
er networks despite the mounting evidence of the importance of polyadic in
teractions. Our approach uses a diffusion process to group nodes or simpli
ces\, where information can flow between nodes and between simplices (high
er-order interactions).\n\nSecondly\, we discuss simplicial Kuramoto model
s\, which have emerged as a diverse and intriguing model that describes os
cillators on simplices rather than nodes. We present a unified framework t
o describe different variants of these models\, which are categorized into
three main groups: "simple" models\, "Hodge-coupled" models\, and "order-
coupled" (Dirac) models. We explore a potential application in reconstruct
ing brain functional connectivity from structural connectomes. We find tha
t simple edge-based Kuramoto models perform competitively or outperform co
mplex extensions of node-based models.\n\nLastly\, we consider associated
games in cooperative game theory\, which allows for the meaningful charact
erization of solution concepts. Moreover\, generalized values allow comput
ing each coalition's influence or power index in a game. We view associate
d games through the lens of game maps and graph Laplacian\, thus defining
the novel Hodge Generalized Value (HGV). We characterize HGV via an axioma
tic approach as a generalized value. Finally\, we show how HGV is linked t
o the solution of the Poisson equation derived from the Hodge decompositio
n of the direct graph associated with the poset of coalitions in the game.
\n\nReferences and coauthor list:\n\nNurisso\, M.\, Morandini\, M.\, Lucas
\, M.\, Vaccarino\, F.\, Gili\, T.\, & Petri\, G. (2024). Higher-order Lap
lacian Renormalization. arXiv preprint arXiv:2401.11298.\n\nNurisso\, M.\,
Arnaudon\, A.\, Lucas\, M.\, Peach\, R. L.\, Expert\, P.\, Vaccarino\, F.
\, & Petri\, G. (2023). A unified framework for Simplicial Kuramoto models
. arXiv e-prints\, arXiv-2305.\n\nMastropietro\, Antonio\, and Francesco V
accarino. "The Shapley-Hodge Associated Game." arXiv preprint arXiv:2303.1
7151(2023).\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iris Yoon (Wesleyan University - USA)
DTSTART:20240419T160000Z
DTEND:20240419T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/66
DESCRIPTION:Title: Topological tracing of encoded circular coordinates between neura
l populations\nby Iris Yoon (Wesleyan University - USA) as part of GEO
TOP-A seminar\n\n\nAbstract\nRecent developments in in vivo neuroimaging i
n animal models have made possible the study of information coding in larg
e populations of neurons and even how that coding evolves in different neu
ral systems. Topological methods\, in particular\, are effective at detect
ing periodic\, quasi-periodic\, or circular features in neural systems. On
ce we detect the presence of circular structures\, we face the problem of
assigning semantics: what do the circular structures in a neural populatio
n encode? Are they reflections of an underlying physiological activity\, o
r are they driven by an external stimulus? If so\, which specific features
of the stimulus are encoded by the neurons? To address this problem\, we
introduced the method of analogous bars (Yoon\, Ghrist\, Giusti 2023). Giv
en two related systems\, say a stimulus system and a neural population\, o
r two related neural populations\, we utilize the dissimilarity between th
e two systems and Dowker complexes to find shared features between the two
systems. We then leverage this information to identify related features b
etween the two systems. In this talk\, I will briefly explain the mathemat
ics underlying the analogous bars method. I will then present applications
of the method in studying neural population coding and propagation on sim
ulated and experimental datasets. This work is joint work with Gregory Hen
selman-Petrusek\, Lori Ziegelmeier\, Robert Ghrist\, Spencer Smith\, Yiyi
Yu\, and Chad Giusti.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pablo Suárez Serrato (UNAM - Mexico)
DTSTART:20240426T160000Z
DTEND:20240426T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/67
DESCRIPTION:Title: Topics in Geometric Learning\nby Pablo Suárez Serrato (UNAM
- Mexico) as part of GEOTOP-A seminar\n\n\nAbstract\nSimilarly to the grow
th of Applied Topology\, the uses and applications of Geometry are now exp
anding into scientific\, computational\, and engineering domains. First\,
we'll review the recent history of this expanding Applied Geometry area. I
'll mention several collaborations. Developing and implementing algorithms
inspired by the marked length spectrum that classifies complex networks (
with Eliassi-Rad and Torres) and analyzing digital images using a variant
of curve-shortening flow (with Velazquez Richards). As well as a definitio
n I proposed of a global convolution on manifolds of arbitrary topology\,
relevant for deep learning on manifolds. Furthermore\, I'll present our jo
int work with Evangelista and Ruiz Pantaleón on computational Poisson geo
metry. This work includes a practical application in learning symbolic exp
ressions of Hamiltonian systems. We've developed and released two Python p
ackages that are instrumental in this process. These packages enable symbo
lic and numerical computations of objects in Poisson geometry\, and they'r
e compatible with the deep learning frameworks NumPy\, TensorFlow\, and Py
Torch. We've utilized these packages to train neural networks\, particular
ly hybrids with CNN and LSTM components\, that learn symbolic expressions
of Hamiltonian vector fields. I'll present a tutorial on our computational
Poisson Geometry modules if time allows.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuanan Diao (UNC Charlote -USA)
DTSTART:20240503T160000Z
DTEND:20240503T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/68
DESCRIPTION:Title: Braid index and Ropelength of alternating knots\nby Yuanan Di
ao (UNC Charlote -USA) as part of GEOTOP-A seminar\n\n\nAbstract\nA long s
tanding conjecture states that the ropelength of any alternating link is a
t least proportional to its crossing number. That is\, there exists a cons
tant $b_0>0$ such that $R(K)\\ge b_0Cr(K)$ for any alternating link $K$\,
where $R(K)$ is the ropelength of $K$ and $Cr(K)$ is the crossing number o
f $K$. This conjecture has been recently proved affirmatively for the case
of alternating knots. In this talk I will present the main results/ideas
leading to the proof of this result\, where the braid index served as the
key bridge between the minimum crossing number and the ropelength of the k
not.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tamas Kalman (Mathematics\, Tokyo Institute of Technology - Japan)
DTSTART:20240517T150000Z
DTEND:20240517T160000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/69
DESCRIPTION:Title: Knotted and branching defects in ordered media\nby Tamas Kalm
an (Mathematics\, Tokyo Institute of Technology - Japan) as part of GEOTOP
-A seminar\n\n\nAbstract\nI will discuss a homotopy classification of the
global defect in ordered media\, with a particular emphasis on the example
of biaxial nematic liquid crystals. These are systems in which the order
parameter space is the quotient of the $3$-sphere $S^3$ by the quaternion
group $Q$\, and an important feature of them is that disclination lines ma
y branch and form graphs. Therefore as a model\, I will consider continuou
s maps from complements of spatial graphs to $S^3/Q$ modulo a certain equi
valence relation\, and find that the equivalence classes are enumerated by
the six subgroups of $Q$. Via monodromy around meridional loops\, the edg
es of our spatial graphs are marked by conjugacy classes of $Q$\; once one
passes to planar diagrams\, these labels can be refined to elements of $Q
$ associated to each arc. The same classification scheme applies not only
in the case of $Q$ but also to arbitrary groups. This research is joint wi
th Yuta Nozaki\, Yuya Koda\, and Masakazu Teragaito.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Goubault (Ecole Polytechnique - France)
DTSTART:20240531T160000Z
DTEND:20240531T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/70
DESCRIPTION:Title: Directed homology and persistence modules\nby Eric Goubault (
Ecole Polytechnique - France) as part of GEOTOP-A seminar\n\n\nAbstract\nI
n this talk\, I will give a self-contained account of a construction for a
directed homology theory based on modules over algebras\, linking it to b
oth persistence homology and natural homology.\n\nPersistence modules have
been introduced originally for topological data analysis\, where the data
set seen at different « resolutions » is organized as a filtration of s
paces. This has been further generalized to multidimensional persistence a
nd « generalized » persistence\, where a persistence module was defined
to be any functor from a partially ordered set\, or more generally a preor
dered set\, to an arbitrary category (in general\, a category of vector sp
aces).\n\nThis talk will be concerned with a more « classical » construc
tion of directed homology\, mostly for precubical sets here\, based on (bi
)modules over (path) algebras\, making it closer to classical homology wit
h value in modules over rings\, and of the techniques introduced for persi
stence modules. Still\, this construction retains the essential informatio
n that natural homology is unveiling. Of particular interest will be the r
ole of restriction and extension of scalars functors\, that will be centra
l to the discussion of Kunneth formulas\, Mayer-Vietoris and relative homo
logy sequences. If time permits as well\, we will discuss some « tameness
» issues\, for dealing with practical calculations.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis H Kauffman (University of Illinois at Chicago)
DTSTART:20240111T210000Z
DTEND:20240111T220000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/71
DESCRIPTION:Title: Reconnection Numbers of Knotted Vortices\nby Louis H Kauffman
(University of Illinois at Chicago) as part of GEOTOP-A seminar\n\n\nAbst
ract\nKnotted vortices such as those produced in water by Kleckner and Irv
ine tend to transform by reconnection to collections of unknotted and unli
nked circles. The reconnection number $R(K)$ of an oriented knot of link $
K$ is the least number of reconnections (oriented re-smoothings) needed to
unknot/unlink $K$. Putting this problem into the context of knot cobordis
m\, we show\, using Rasmussen's Invariant that the reconnection number of
a positive knot is equal to twice the genus of its Seifert spanning surfac
e. In particular an (a\,b) torus knot has $R=(a−1)(b−1)$. For an arbit
rary unsplittable positive knot or link $K$\, $R(K)=c(K)−s(K)+1$ where $
c(K)$ is the number of crossings of K and $s(K)$ is the number of Seifert
circles of $K$. Examples of vortex dynamics are illustrated in the talk.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cristian Micheletti (International School for Advanced Studies (SI
SSA))
DTSTART:20240108T210000Z
DTEND:20240108T220000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/72
DESCRIPTION:Title: Dynamics and mechanics of knotted DNA and RNAs: insights from mol
ecular dynamics simulations\nby Cristian Micheletti (International Sch
ool for Advanced Studies (SISSA)) as part of GEOTOP-A seminar\n\n\nAbstrac
t\nI will report on a series of studies where we used molecular dynamics s
imulations and various models to study how the properties of DNA and RNAs
are affected by the presence of knots and other forms of structural entang
lement[1]. I will first consider model DNA plasmids that are both knotted
and supercoiled\, and discuss how the simultaneous presence of knots and s
upercoiling creates long-lived multi-strand interlockings that might may b
e relevant for the simplifying action of topoisomerases. I next consider h
ow entangled nucleic acids behave when driven through narrow pores[2-4]\,
a setting that models translocation through the lumen of enzymes\, and dis
cuss the biological implication for a certain class of viral RNAs[4].\n\n
\n[1] L. Coronel\, A. Suma and C. Micheletti\, "Dynamics of supercoiled DN
A with complex knots"\, Nucleic Acids Res. (2018) 46 \, 7533 \n\n[2] A. Su
ma\, V. Carnevale and C. Micheletti\, Nonequilibrium thermodynamics of DNA
nanopore unzipping\, Phys. Rev. Lett.\, (2023)\, 130 048101\n\n[3] A. Sum
a\, A. Rosa and C. Micheletti\, Pore translocation of knotted polymer chai
ns: how friction depends on knot complexity\, ACS Macro Letters\, (2015)\,
4 \, 1420-1424\n\n[4] A. Suma\, L. Coronel\, G. Bussi and C. Micheletti\,
"Directional translocation resistance of Zika xrRNA” Nature Communicati
ons (2020)\, 11 \, art no. 3749\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuliy Baryshnikov (University of Illinois at Urbana-Champaign)
DTSTART:20240109T000000Z
DTEND:20240109T010000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/73
DESCRIPTION:Title: On Spaces of Coverings\nby Yuliy Baryshnikov (University of I
llinois at Urbana-Champaign) as part of GEOTOP-A seminar\n\n\nAbstract\nCo
nsider a relation $R\\subset X\\times Y$ between two topological spaces. A
finite collection $C=(x_1\,\\ldots\,x_n)\\in X^n$ is a covering if for an
y $y\\in Y$\, one has $(x_k\,y)\\in R$ for one of the points $x_k$ in $C
$. (For example\, if $X=Y$ is a metric space\, and $R$ is the relation of
being at the distance $<\\epsilon$\, then $C$ is a covering if the union o
f $\\epsilon$-balls around $x_k$'s cover $Y$.) The topology of the space o
f coverings $C_R(n)$ is important\, if unexplored\, topic in several appli
ed disciplines\, from multi-agent systems to sociology. In this talk we di
scuss some examples where the homotopy type of these spaces can be explici
tly computed.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ismar Volić (Wellesley College)
DTSTART:20240109T150000Z
DTEND:20240109T160000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/74
DESCRIPTION:Title: Simplicial complexes and political structures\nby Ismar Voli
ć (Wellesley College) as part of GEOTOP-A seminar\n\n\nAbstract\nSimplici
al complexes and their topology are a natural tool for modeling interactio
ns in a system and revealing its deeper underlying structures. We will dis
cuss how simplicial complexes can be used to study political systems in wh
ich coalitions are represented by simplices. Some basic topological constr
uctions can then easily be translated into political situations such as me
rging of parties\, introduction of mediators\, or delegation of power. The
topological point of view also supplies a refined point of view on game-t
heoretic notions like the Banzhaf and Shapley-Shubik power indices of agen
ts in a political system. We will also present a generalization to hypergr
aphs which captures an even richer collection of political dynamics concep
ts. Time permitting\, a recasting of some classical results from social ch
oice theory in topological and category-theoretic terms will also be menti
oned.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pablo Soberón (City University of New York)
DTSTART:20240109T210000Z
DTEND:20240109T220000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/75
DESCRIPTION:Title: New results on envy-free distributions\nby Pablo Soberón (Ci
ty University of New York) as part of GEOTOP-A seminar\n\n\nAbstract\nSimi
larly to the growth of Applied Topology\, the uses and applications of Geo
metry are now expanding into scientific\, computational\, and engineering
domains. First\, we'll review the recent history of this burgeoning Applie
d Geometry area. I'll mention a couple of collaborations\, developing and
implementing algorithms inspired by the marked length spectrum that classi
fy complex networks (with Eliassi-Rad and Torres) and analyzing digital i
mages using a variant of curve-shortening flow (with Velazquez Richards).
Then\, I'll present joint work with Evangelista and Ruiz Pantaleón on com
putational Poisson geometry and its applications to learning symbolic expr
essions of Hamiltonian systems. We developed and released two Python packa
ges that perform symbolic and numerical computation of objects in Poisson
geometry. We then used them to train neural networks (hybrids with CNN and
LSTM components) that learn symbolic expressions of Hamiltonian vector fi
elds. Finally\, I'll briefly mention the theoretical limitations of comput
ationally analyzing Hamiltonian dynamics. I recently constructed an exampl
e of a Hamiltonian flow on the 4-sphere that is Turing complete. Therefore
the most general cases of Hamiltonian learning problems are undecidable.\
n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Dranishnikov (University of Florida)
DTSTART:20240110T150000Z
DTEND:20240110T160000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/76
DESCRIPTION:Title: On some variations of TC and the LS-category\nby Alexander Dr
anishnikov (University of Florida) as part of GEOTOP-A seminar\n\n\nAbstra
ct\nDatasets can be viewed as mathematical objects (e.g.\, point clouds\,
matrices\, graphs\, images\, fields/functions) that have shape. This shape
can describe the space that data populates (e.g.\, data that lies on a ma
nifold) or can be used to understand the complex structures contained with
in data (e.g.\, the multi-scale organization of self-assembled materials).
Data shape can be exploited to improve the effectiveness of data analysis
methods or provide connections between complex materials and their physic
al and chemical properties. However\, quantifying shape is difficult to do
with common methods based on statistics\, signal processing\, or with the
use of machine learning. Topology and geometry are fields of mathematics
that provide tools for the characterization and quantification of the sha
pe of data directly.\n\nIn this talk I will discuss how data taken from in
dustrial processes\, such as time series and images\, can be represented a
s a shape and how that shape can be analyzed through topological and geome
trical methods such as the Euler characteristic (EC) and Riemannian manifo
ld geometry. I will provide a brief overview of these methods and illustra
te how exploiting the topology and geometry of data can provide improvemen
ts in data-centric tasks such as dimensionality reduction\, anomaly detect
ion\, and statistical process control in the context of textile production
\, chemical process systems\, and granular material manufacturing.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sophie Jackson (University of Cambridge)
DTSTART:20240111T150000Z
DTEND:20240111T160000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/77
DESCRIPTION:Title: The What\, Where\, How and Why of Topological Knots in Proteins\nby Sophie Jackson (University of Cambridge) as part of GEOTOP-A semina
r\n\n\nAbstract\nFor decades it was thought that topological knots would n
ever be formed by the polypeptide chain of any protein\, knotting being in
compatible with folding mechanisms. However\, we now know that many prote
ins fold and form three-dimensional structures in which the chain crosses
itself and threads through loop(s) to form knots. Proteins with very deep
knots\, i.e.\, a large part of the chain has passed through a knotting loo
p to form the knot have been identified\, and four different classes of kn
ots have been found embedded in protein strucutres: 3-1\, 4-1\, 5-2\, and
6-1 knots. In addition\, recently it has been established that a single p
olypeptide chain can contain more than one knot - several examples of tand
em trefoil knotted proteins have been characterised. With the advent of t
he machine-learning based protein structure algorithm AlphaFold\, several
new classes of knotted protein have been predicted although their knotted
structures have not yet been verified experimentally. Over twenty years\,
numerous experimental and computational studies on knotted proteins have
investigated how such structures might form\, in addition\, to the propert
ies of the knotted structure and whether they differ significantly or not
from unknotted proteins. In this talk\, I will review the field and expla
in 1) what knots are found in proteins and where they are within the folde
d structures\, 2) the mechanisms by which knotted may fold\, i.\, how the
knots get there\, and 3) why proteins may have evolved to form knotted str
uctures. The talk will provide background on twenty years of research as
well as discussing some state-of-the-art studies on designing proteins wit
h novel knotted folds\, as well as watching knotted proteins unfold and tr
anslocate through narrow pores.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mitchell Berger (University of Exeter)
DTSTART:20240108T150000Z
DTEND:20240108T160000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/78
DESCRIPTION:Title: Continuous topological measures: helicity\, winding\, and higher
order winding\nby Mitchell Berger (University of Exeter) as part of GE
OTOP-A seminar\n\n\nAbstract\nMany measures of topological complexity are
discrete: for example the linking number between two closed curves is an i
nteger. However\, some topological invariants can be continuous. The windi
ng number of two curves extending between parallel planes\, with fixed end
points provides a simple example. We will discuss how winding numbers wor
k in more complicated geometries such as spheres\, cubes\, and closed surf
aces in general. On the way\, we will need Gauss-Bonnet. Also we will touc
h on higher order winding related to the Borromean rings.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yusu Wang (UC San Diego)
DTSTART:20240112T150000Z
DTEND:20240112T160000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/79
DESCRIPTION:Title: Graph learning models: theoretical understanding\, limitations an
d enhancements\nby Yusu Wang (UC San Diego) as part of GEOTOP-A semina
r\n\n\nAbstract\nGraph data is ubiquitous in many application domains. The
rapid advancements in machine learning also lead to many new graph learni
ng frameworks\, such as message passing (graph) neural networks (MPNNs)\,
graph transformers and higher order variants. In this talk\, I will descri
be some of our recent journey in attempting to provide better (theoretical
) understanding of these graph learning models (e.g\, their representation
power and limitations in capturing long range interactions in graphs)\, t
he pros and cons of different models\, and ways to further enhance them in
practice. This talk is based on multiple pieces of work with various coll
aborators\, whom I will mention in the talk.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Radmila Sazdanovic (NC State University)
DTSTART:20240113T150000Z
DTEND:20240113T160000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/80
DESCRIPTION:Title: The shape of relations: knots and other stories\nby Radmila S
azdanovic (NC State University) as part of GEOTOP-A seminar\n\n\nAbstract\
nTopological Data Analysis provides tools for discovering relevant feature
s of data by analyzing the shape of a point cloud. In this context we deve
lop tools for visualizing maps between high dimensional spaces with the go
al of discovering relations between data sets with expected correlations.
Additionally we are adapting TDA tools to analyzing infinite data sets wh
ere representative sampling is impossible or impractical and using them in
synergy with ML techniques. Most of the examples will focus on analyzing
relations between knot invariants with additional examples in game theory
and cancer genomics.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pawel Dlotko (Dioscuri Centre in Topological Data Analysis\, Mathe
matical Institute\, Polish Academy of Sciences)
DTSTART:20240113T230000Z
DTEND:20240114T000000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/81
DESCRIPTION:Title: Data\, their shape\, and beyond\nby Pawel Dlotko (Dioscuri Ce
ntre in Topological Data Analysis\, Mathematical Institute\, Polish Academ
y of Sciences) as part of GEOTOP-A seminar\n\n\nAbstract\nIn contemporary
science we are exposed to vast amounts of data. Understanding them is ofte
n helpful\, sometimes essential\, to make considerable progress in the fie
ld. Mathematics\, and mathematical statistics\, offer a wealth of tools al
lowing for better understanding of data. Most tools concentrate on the qua
ntitative characterization of data\, rather than understanding their layou
t\, or shape. To fill in the gap\, in my Dioscuri Centre in Topological Da
ta Analysis\, we are developing new techniques to quantify the shape of da
ta and provide visualizations which\, in the next step\, deliver new knowl
edge. Our methods apply for a large variety of inputs\, including high dim
ensional samples\, time series\, images\, correlation patterns and more. I
n this talk\, I will give a brief and intuitive overview of our methods wi
th a hope that you may find them beneficial in your research. A showcase o
f the current usages of our methodology will provide both an important mot
ivation for\, and driving force to\, our research.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Natasha Jonoska (University of South Florida - USA)
DTSTART:20240823T160000Z
DTEND:20240823T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/82
DESCRIPTION:Title: Topological models for studying DNA self-assembly\nby Natasha
Jonoska (University of South Florida - USA) as part of GEOTOP-A seminar\n
\n\nAbstract\nThere is an increased necessity for mathematical study of se
lf-assembly of various phenomena ranging from nano-scale structures\, mate
rial design\, crystals and nano devices. We present a range of topological
questions associated with DNA self-assembly and three dimensional structu
res. The questions vary from topological graph theory related to DNA stran
d routing of a three-dimensional mesh\, to questions in knot theory relate
d to structural embeddings in 3D.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucile Vandembroucq (Universidade do Minho - Portugal)
DTSTART:20240906T160000Z
DTEND:20240906T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/83
DESCRIPTION:Title: On the (higher) topological complexity of manifolds with abelian
fundamental group\nby Lucile Vandembroucq (Universidade do Minho - Por
tugal) as part of GEOTOP-A seminar\n\n\nAbstract\nThe topological complexi
ty and its higher versions are homotopy invariants which were introduced b
y M. Farber and Y. Rudyak in order to give a topological measure of the co
mplexity of the motion planning problem. We will discuss some properties o
f these invariants for closed manifolds with abelian fundamental group. In
particular\, we will give sufficient conditions for the (higher) topologi
cal complexity of such a manifold to be non-maximal. This is based on join
t works with N. Cadavid\, D. Cohen\, J. González and S. Hughes.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claus Ernst (Western Kentucky University - USA)
DTSTART:20240913T160000Z
DTEND:20240913T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/84
DESCRIPTION:Title: On the braid index of knots and links\nby Claus Ernst (Wester
n Kentucky University - USA) as part of GEOTOP-A seminar\n\n\nAbstract\nWe
review a well-known method to compute the braid index. Using this method\
, we can give a compute the braid index of all alternating Montesinos knot
s and links and all non alternating pretzel knots and links. The method us
es just information that can be read of a minimal diagram of the knot or l
ink.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Uta Ziegler (Western Kentucky University - USA)
DTSTART:20240927T160000Z
DTEND:20240927T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/85
DESCRIPTION:Title: Random polygons in spherical confinement\nby Uta Ziegler (Wes
tern Kentucky University - USA) as part of GEOTOP-A seminar\n\n\nAbstract\
nIn this talk\, we provide a summary of the analysis of a large sample of
random equilateral polygons in spherical confinement. The analysis illustr
ates the dependence of the knot spectrum and of geometric properties of th
e polygons on the lengths of the polygons as well as the radius of confine
ment. The geometric properties are sometimes also influenced by the knotti
ng complexity. Since our polygons are rooted at the center of the confinem
ent sphere\, the presentation also addresses the question of what might ha
ppen for a confinement sphere with a radius less than 1. The generation pr
ocess for the spherical polygons is rigorous\, however\, the analysis are
only based on numerical results.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Max Lipton (MIT - USA)
DTSTART:20241011T160000Z
DTEND:20241011T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/86
DESCRIPTION:Title: Pseudodifferential Methods and the Mobius Knot Energy\nby Max
Lipton (MIT - USA) as part of GEOTOP-A seminar\n\n\nAbstract\nThe Mobius
energy of a knot is a useful analytic tool which can yield information abo
ut classical knot invariants. Freedman\, He\, and Wang proved the existenc
e of curves with a given prime knot type which minimizes the Mobius energy
\, and they also proved the minimizers are $C^{1\,1}$. Shortly after\, He
proved the minimizers are analytic using nonlocal techniques involving pse
udodifferential calculus. I will discuss these methods and how they may ap
ply to unresolved problems regarding the Mobius energy.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacek Brodzki (University of Southampton - United Kingdom)
DTSTART:20241018T160000Z
DTEND:20241018T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/87
DESCRIPTION:Title: Topological insights into physical phenomena\nby Jacek Brodzk
i (University of Southampton - United Kingdom) as part of GEOTOP-A seminar
\n\n\nAbstract\nMethods of Topological Data Analysis are now an important
part of modern data-driven scientific discovery. This talk will provide an
overview of recent results\, theoretical and experimental\, that arise fr
om the interactions between topology and physics. We will discuss topologi
cal characteristics that can be used to track the time evolution of physic
al system and to detect its phase transitions. We will then discuss a topo
logical quantification of disorder where it can be used to detect “suffi
ciently ordered systems” which\, although irregular\, still display inte
resting physical characteristics. We will end with a discussion of the use
s of topology in the design of physical systems.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hannah Santa Cruz (Vrije University Amsterdam - Netherlands)
DTSTART:20241101T160000Z
DTEND:20241101T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/88
DESCRIPTION:Title: Hodge Laplacians on Sequences\nby Hannah Santa Cruz (Vrije Un
iversity Amsterdam - Netherlands) as part of GEOTOP-A seminar\n\n\nAbstrac
t\nHodge Laplacians have been previously proposed as a natural tool for un
derstanding higher-order interactions in networks and directed graphs. In
this talk\, we will cover a Hodge-theoretic approach to spectral theory an
d dimensionality reduction for probability distributions on sequences and
simplicial complexes. We will introduce a feature space based on the Lapl
acian eigenvectors associated to a set of sequences\, and will see these
eigenvectors capture the underlying geometry of our data. Furthermore\, we
will show this Hodge theory has desirable properties with respect to natu
ral null-models\, where the underlying vertices are independent. Specifica
lly\, we will see the appropriate Hodge Laplacian has an integer spectrum
with high multiplicities\, and describe its eigenspaces. Finally\, we will
cover a simple proof showing the underlying cell complex of sequences has
trivial reduced homology.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mike Lesnick (SUNY Albany - USA)
DTSTART:20241115T160000Z
DTEND:20241115T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/89
DESCRIPTION:Title: Robustness and Computability of 2-Parameter Persistent Homology\nby Mike Lesnick (SUNY Albany - USA) as part of GEOTOP-A seminar\n\n\nA
bstract\nThe Vietoris-Rips filtration\, the standard filtration on metric
data in topological data analysis\, is notoriously sensitive to outliers a
nd can be insensitive to variations in density. A natural solution is to c
onsider 2-parameter persistence\, treating density and spatial scale as se
parate parameters. In this talk\, I will present results on the stability\
, robustness\, and computability of 2-parameter persistence. A main focus
will be Sheehy's subdivision-Rips bifiltration\, the only density-sensitiv
e bifiltration on metric data known to satisfy a strong robustness propert
y. This filtration is too large to compute directly\, but we will see that
it can be approximated by much smaller objects. Our results reveal an app
arent tension between robustness and computability for 2-parameter persist
ence\, which in spite of substantial progress\, is not yet fully understoo
d.\n\nThe talk will be based on three papers\, the first with Andrew Blumb
erg and the others with KenMcCabe: \n\n- https://link.springer.com/a
rticle/10.1007/s10208-022-09576-6
\n- https://arxiv.org/abs/2406.076
79
\n- https://arxiv.org/abs/2408.16716
\n
\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luis Vega (BCAM - Spain)
DTSTART:20241206T160000Z
DTEND:20241206T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/90
DESCRIPTION:Title: The binormal flow and the evolution of viscous vortex filaments\nby Luis Vega (BCAM - Spain) as part of GEOTOP-A seminar\n\n\nAbstract\
nI'll present the so called Localized Induction Approximation that describ
es the dynamics of a vortex filament according to the Binormal Curvature F
low (BF). I'll give a result about the desingularization of the Biot-Savar
t integral proved with Marco A. Fontelos within the framework of Navier-St
okes equations. Some particular examples regarding BF obtained with Valeri
a Banica will be also considered. These examples allow to connect BF with
the so called Riemann non-differentiable function and the Frisch-Parisi ap
proach to turbulence.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:María José Jiménez Rodríguez (Universidad de Sevilla - Spain)
DTSTART:20241122T160000Z
DTEND:20241122T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/91
DESCRIPTION:Title: Morse Theory for Chromatic Delaunay Triangulations\nby María
José Jiménez Rodríguez (Universidad de Sevilla - Spain) as part of GEO
TOP-A seminar\n\n\nAbstract\nThis talk is focused on new techniques for th
e topological data analysis (TDA) of labelled point cloud data.\nWell-esta
blished filtrations in TDA for a point cloud data include the Čech\, Viet
oris–Rips\, and alpha filtrations. Bauer and Edelsbrunner [BE16] demonst
rated that the Čech filtration can be simplicially collapsed onto the alp
ha filtration\, showing that they are homotopy equivalent.\nRecent techniq
ues in data collection across fields like cancer biology\, geospatial anal
ysis and ecology have produced chromatic (labeled) data that express inter
actions among points of different colors. In such cases\, it is crucial to
understand not only the overall spatial structure of the data but also th
e spatial relationships among subsets defined by their labels. The chromat
ic alpha filtration [Mon+24] is a generalization of the alpha filtration
that captures these relationships\, making it particularly useful for mult
i-species data in TDA.\nIn this talk we introduce the chromatic Delaunay
–Čech and chromatic Delaunay–Rips filtrations as computationally effi
cient alternatives to the chromatic alpha filtration. We use generalized d
iscrete Morse theory to demonstrate that the Čech\, chromatic Delaunay–
Čech\, and chromatic alpha filtrations are interconnected through simplic
ial collapses\, extending Bauer and Edelsbrunner’s results from non-chro
matic to chromatic contexts. \nOur findings offer theoretical support for
the application of chromatic Delaunay–Čech and chromatic Delaunay–Rip
s filtrations\, and we illustrate their computational advantages through n
umerical experiments.\n This is joint work with A. Natarajan\, T. Chaplin
and A. Brown from University of Oxford (arXiv:2405.19303).\n[BE16] Ulrich
Bauer and Herbert Edelsbrunner. “The Morse theory of Cech and Delaunay
complexes”. In: Transactions of the American Mathematical Society 369.5
(Dec. 27\, 2016)\, pp. 3741–3762. DOI:10.1090/tran/6991.\n[Mon+24] Seba
stiano Cultrera di Montesano et al. Chromatic Alpha Complexes. Feb. 7\, 20
24. arXiv: 2212.03128\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pablo Soberón (CUNY - USA)
DTSTART:20241213T160000Z
DTEND:20241213T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/92
DESCRIPTION:Title: Bisecting masses with hyperplane arrangements\nby Pablo Sober
ón (CUNY - USA) as part of GEOTOP-A seminar\n\n\nAbstract\nA hyperplane a
rrangement in $\\mathbb{R}^ d$ divides space into two sets via a chessboar
d coloring. Given a set of measures\, we can attempt to split each into tw
o equal parts using the chessboard coloring of a hyperplane arrangement. S
pecial cases of this problem include the classic ham sandwich theorem by B
anach or the necklace splitting theorem by Hobby and Rice. We present a ne
w common generalization of many mass partition results of this kind. Surpr
isingly\, the proof methods are not topological\, breaking a long traditio
n in the area. During this talk\, we will describe the results that can be
generalized this way and the reach of this new non-topological approach.\
nJoint work with Alfredo Hubard.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ciprian Manolescu (Stanford - USA)
DTSTART:20250117T160000Z
DTEND:20250117T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/93
DESCRIPTION:Title: Generalizations of Rasmussen's invariant\nby Ciprian Manolesc
u (Stanford - USA) as part of GEOTOP-A seminar\n\n\nAbstract\nOver the las
t 20 years\, the Rasmussen invariant of knots in $\\mathbb{S}^3$ has had a
number of interesting applications to questions about surfaces in $\\mat
hbb{B}^4$. In this talk I will survey some recent extensions of the invari
ant to knots in other three-manifolds: in connected sums of $\\mathbb{S}^
1$ x $\\mathbb{S}^2$ (joint work with Marengon\, Sarkar\, and Willis)\, i
n $\\mathbb{RP}^3$ (joint work with Willis\, and also separate work of Ch
en)\, and in a general setting (work by Morrison\, Walker and Wedrich\; an
d independently by Ren-Willis). I will describe how these invariants give
bounds on the genus of smooth surfaces in 4-manifolds\, and can even detec
t exotic 4-manifolds with boundary.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mathilde Papillon (UCSB - USA)
DTSTART:20250131T160000Z
DTEND:20250131T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/94
DESCRIPTION:Title: Make any GNN Go Topological with TopoTune\nby Mathilde Papill
on (UCSB - USA) as part of GEOTOP-A seminar\n\n\nAbstract\nGraph Neural Ne
tworks (GNNs) excel in learning from relational datasets\, processing node
and edge features in a way that preserves the symmetries of the graph dom
ain. However\, many complex systems--such as biological or social networks
--involve multiway complex interactions that are more naturally represente
d by higher-order topological spaces. The emerging field of Topological De
ep Learning (TDL) aims to accommodate and leverage these higher-order stru
ctures. Combinatorial Complex Neural Networks (CCNNs)\, fairly general TDL
models\, have been shown to be more expressive and better performing than
GNNs. However\, differently from the graph deep learning ecosystem\, TDL
lacks a principled and standardized framework for easily defining new arch
itectures\, restricting its accessibility and applicability. To address th
is issue\, we introduce in this talk Generalized CCNNs (GCCNs)\, a novel s
imple yet powerful family of TDL models that can be used to systematically
transform any (graph) neural network into its TDL counterpart. We show ho
w GCCNs generalize and subsume CCNNs\, and briefly describe extensive expe
riments on a diverse class of GCCNs. We show that these architectures cons
istently match or outperform CCNNs\, often with less model complexity. In
an effort to accelerate and democratize TDL\, we also introduce TopoTune\,
a lightweight software that allows practitioners to define\, build\, and
train GCCNs with unprecedented flexibility and ease.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steve Levene (UTD - USA)
DTSTART:20250214T160000Z
DTEND:20250214T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/95
DESCRIPTION:Title: Unmasking a hidden DNA-supercoil relaxation activity in a site-sp
ecific recombination system\nby Steve Levene (UTD - USA) as part of GE
OTOP-A seminar\n\n\nAbstract\nThe tyrosine superfamily of recombinases gen
erates knotted products when acting on inverted target sites in circular\,
supercoiled DNA. For the Cre/loxP system prime torus knots are formed exc
lusively even for strongly supercoiled DNA substrates. This is surprising
because models that are used to describe the recombination reaction predic
t the appearance of complex knot types over the course of repeated reactio
n cycles due to the release of mechanical energy stored in supercoiled DNA
. We solved this puzzle by revealing a hidden DNA-supercoil relaxation act
ivity that accompanies Cre/loxP recombination through a detailed kinetic a
nalysis of the joint distribution of DNA knot type and linking number. A b
iophysical model for the time evolution of topological states in circular
DNA generated by multiple reaction cycles of recombination shows that the
time-dependent knot distributions observed in experiments can only be quan
titatively explained by a model that includes DNA unwinding. Thus\, the de
tailed dynamics of transitions between topological states in knotted super
coiled DNA unravels an important aspect of the Cre/loxP recombination mech
anism that could not be discerned without probing the time dependence of t
he recombination mechanism.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Colin Adams (Williams College - USA)
DTSTART:20250228T160000Z
DTEND:20250228T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/96
DESCRIPTION:Title: Hyperbolicity for Knotoids\, Generalized Knotoids and Staked link
s\nby Colin Adams (Williams College - USA) as part of GEOTOP-A seminar
\n\n\nAbstract\nKnotoids are a useful variation on knots that can be used
to model proteins. We explain how one can apply hyperbolicity and hyperbol
ic volume as a powerful tool for distinguishing knotoids and a broad exten
sion of knotoids called generalized knotoids. Then\, we further consider s
taked knots\, a particular type of generalized knotoid where stakes are pl
aced around a projection of a knot\, restricting its motion and discuss hy
perbolicity in this context.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Agnese Barbensi (UQ - Australia)
DTSTART:20250314T140000Z
DTEND:20250314T150000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/97
DESCRIPTION:Title: Topologically steered simulations and the role of geometric const
raints in protein knotting\nby Agnese Barbensi (UQ - Australia) as par
t of GEOTOP-A seminar\n\n\nAbstract\nWe introduce a method to determine th
e optimal pathway by which a polymer may knot or unknot\, while subject to
a given set of physics\, and we investigate the effect of imposing geomet
ric constraints. We show that with protein-like geometric constraints\, th
e frequency of twist knots increases\, similar to the observed abundance o
f twist knots in protein structures. This is joint work with A.Klotz and D
.Goundaroulis.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oliver Gross (TU Berlin - Germany)
DTSTART:20250328T160000Z
DTEND:20250328T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/98
DESCRIPTION:Title: Conformal Geometry in Magnetic Relaxation\nby Oliver Gross (T
U Berlin - Germany) as part of GEOTOP-A seminar\n\n\nAbstract\nThe magneti
c relaxation problem studies the self-organization of magnetic field lines
in a perfectly conducting fluid to a steady state. In this talk I will di
scuss such a process from the perspective of conformal geometry. A key ins
ight is the conformal equivalence between force-free magnetic fields and s
o-called geodesible vector fields. Building on this insight\, I will discu
ss a computational approach to magnetic relaxation that is driven only by
local geometry optimization. The method is based on a structure-preserving
discretization for pressure-confined regions of an ideal plasma with free
boundary conditions\, which is represented by a collection of thickness c
urves interacting with each other. \nThis is joint work with Albert Chern
(UC San Diego\, CA\, USA)\, Ulrich Pinkall (TU Berlin\, Germany) and Peter
Schröder (Caltech\, Pasadena\, CA USA).\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Magnus Botnan (VU Amsterdam - Netherlands)
DTSTART:20250411T160000Z
DTEND:20250411T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/99
DESCRIPTION:Title: At the extremal points of filtered spaces\nby Magnus Botnan (
VU Amsterdam - Netherlands) as part of GEOTOP-A seminar\n\n\nAbstract\nIn
this talk\, I will present two recent projects exploring extremal properti
es of flag complexes and structural aspects of multiparameter persistence.
\n\nIn the first part (joint with Lies Beers\, accepted to SoCG '25)\, we
investigate fundamental yet surprisingly challenging questions about the V
ietoris–Rips barcode in degree k homology. Given a data set of N points\
, what is the maximum number of bars in its barcode? What is the maximal t
otal persistence? How long can the longest bar be? We establish tight boun
ds in many cases but also uncover intriguing open problems. I will place o
ur results in the context of earlier work by Kozlov and others\, highlight
ing key challenges that remain.\n\nThe second part (joint with U. Bauer\,
S. Oppermann\, and J. Steen) focuses on multiparameter persistence in homo
logy degree 0. It is well known that any diagram of vector spaces (over a
prime field) and linear maps can be realized via degree k homology applied
to a diagram of simplicial complexes. But what if we restrict to degree 0
? This is equivalent to studying diagrams of vector spaces and linear maps
arising from diagrams of sets and set maps—an inherently more difficult
setting. While our recent work develops a general theory\, I will focus o
n the specific case of grids which is closely related to clustering.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kathryn Lindsey (BC - USA)
DTSTART:20250425T160000Z
DTEND:20250425T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/100
DESCRIPTION:Title: Geometry and Topology of ReLU Neural Networks\nby Kathryn Li
ndsey (BC - USA) as part of GEOTOP-A seminar\n\n\nAbstract\nApplications o
f neural networks are rapidly transforming numerous fields\, yet a rigorou
s mathematical foundation for their behavior remains elusive. This talk wi
ll focus on feedforward networks with ReLU activations\, which correspond
precisely to the class of piecewise linear functions. I will explore how c
entral questions of interest to practitioners—such as expressivity\, gen
eralization\, and training dynamics—connect to ideas from geometry and t
opology. In particular\, I will discuss how these networks induce rich pol
yhedral and combinatorial structures on input space\, and how the space of
functions they compute can be viewed as a moduli space arising from quoti
enting parameter space by symmetries. I will highlight some recent progres
s and pose open problems. No prior familiarity with neural networks will
be assumed.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bernadette Stolz (MPIB - Germany)
DTSTART:20250509T160000Z
DTEND:20250509T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/101
DESCRIPTION:Title: Topological learning for spatial data\nby Bernadette Stolz (
MPIB - Germany) as part of GEOTOP-A seminar\n\n\nAbstract\nTopological dat
a analysis (TDA) has been successfully applied to study many biological ph
enomena. In this talk I will highlight two recent applications to spatial
data from oncology\, including synthetic and real-world data. The first ap
plication is a case study of topological model selection in tumour-induced
angiogenesis\, the process in which blood vessel networks are formed duri
ng tumour growth. While many mathematical models of tumour-induced angioge
nesis exist\, significant challenges persist in objectively evaluating and
comparing their outputs. We showcase a combination of TDA and approximate
Bayesian Computation for parameter inference and model selection. In the
second application I will present two techniques in relational TDA that we
develop to encode spatial heterogeneity of multispecies data. Our approac
hes are based on Dowker complexes and Witness complexes. We demonstrate th
at relational TDA features can extract biological insight\, including domi
nant immune cell phenotype (an important predictor of patient prognosis) a
nd parameter regimes in a data-generating model of tumour-immune cell inte
ractions. Our pipelines can be combined with graph neural networks (GNN)\,
a popular machine learning approach for spatial data. I will present how
we can incorporate local relational TDA into a GNN and significantly enhan
ce its performance on real-world data.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dante Chialvo (UNSAM - Argentina)
DTSTART:20250523T160000Z
DTEND:20250523T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/102
DESCRIPTION:Title: Life at the edge\nby Dante Chialvo (UNSAM - Argentina) as pa
rt of GEOTOP-A seminar\n\n\nAbstract\nWhy is life complex and — most imp
ortantly — what is the origin of the over abundance of complexity in nat
ure? This is a fundamental scientific question which\, paraphrasing the la
te Per Bak\, “is screaming to be answered but seldom is even being asked
”. We review recent attempts across several scales to link complexity wi
th scale invariance from the perspective of critical phenomena. This is a
nontechnical talk illustrating the approach discussing three cases\, namel
y the large-scale brain dynamics\, the characterization of spontaneous flu
ctuations of proteins\, and the physiological complexity of the cell mitoc
hondria network.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:María del Rocío González Díaz (Universidad de Sevilla - Spain)
DTSTART:20250606T160000Z
DTEND:20250606T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/103
DESCRIPTION:Title: Topology-based Optimization for Robot Fleet Behavior\nby Mar
ía del Rocío González Díaz (Universidad de Sevilla - Spain) as part of
GEOTOP-A seminar\n\n\nAbstract\nIn this talk\, I introduce novel topologi
cal methods for the analysis of robot fleet behaviors simulated using Navg
round software [1]. Our aim is to understand and improve the evolution of
robot fleet behaviors to\, for example\, reduce unintended behaviors such
as collisions and deadlocks. Understanding the robot fleet's dynamics will
allow us to predict safer and more efficient routes for robot displacemen
t. To achieve this\, we propose employing TDA techniques such as persisten
t homology\, block functions induced by persistence morphisms\, and persis
tent entropy. These methods leverage the geometric and topological structu
re of the data\, allowing us to capture high-level spatial and relational
patterns in agent behaviors and configurations. Unlike classical approache
s\, which often rely on predefined features or statistical assumptions\, T
DA provides an interpretable framework that can highlight qualitative diff
erences in the robot fleet's dynamics. While we do not claim definitive pe
rformance improvements over traditional methods\, the added interpretabili
ty and the ability to capture intrinsic spatial structures make these tech
niques particularly suitable for characterizing different agent behaviors
and ensuring safe and efficient simulations. This work is part of the Euro
pean Project 'REliable & eXplainable Swarm Intelligence for People with Re
duced mObility - REXASIPRO [2].//\n[1] https://idsia-robotics.github.io/na
vground/_build/html/index.html\n[2] https://cordis.europa.eu/project/id/10
1070028\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sophia Knight (UMD-USA)
DTSTART:20250221T160000Z
DTEND:20250221T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/104
DESCRIPTION:Title: Logical undefinability and Truth Set Algebras\nby Sophia Kni
ght (UMD-USA) as part of GEOTOP-A seminar\n\n\nAbstract\nI will describe t
ruth set algebras\, a new technique for proving the undefinability of logi
cal connectives through one another. I will illustrate the technique with
several examples. I will show new proofs of some existing results in logic
al undefinability\, and some new results proven using this technique.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ginestra Bianconi (QMUL - UK)
DTSTART:20250912T160000Z
DTEND:20250912T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/105
DESCRIPTION:Title: Topology shapes dynamics of higher-order networks and more\n
by Ginestra Bianconi (QMUL - UK) as part of GEOTOP-A seminar\n\n\nAbstract
\nComplex systems like the brain\, climate\, and next-generation artificia
l intelligence rely on higher-order interactions that extend beyond simple
pairwise relationships. These many-body interactions are captured by hig
her-order networks [1].\n\nBy integrating algebraic topology with non-line
ar dynamics\, theoretical physics and machine learning\, this talk reveals
the critical role of topology in shaping the dynamics of such systems [2]
.\n\nThe research highlights how topological signals\, dynamical variables
defined on nodes\, edges\, triangles\, and other higher-order structures\
, drive phenomena such as topological synchronization\, pattern formation\
, and triadic percolation. The surprising result that emerges from this re
search is that topological operators including the Topological Dirac opera
tor\, offer a common language for treating complexity\, AI algorithms\, an
d quantum physics. \n\nThese findings not only advance the understanding o
f the underlying mechanisms in neuroscience and climate science but also p
ave the way for transformative machine learning algorithms inspired by the
oretical physics.\n\nWe conclude the seminar discussing the role of geomet
ry in shaping dynamics. In particular we will provide an overview of the
emergent field of Statistical Mechanics of Geometry\, a promising new info
rmation theory framework for unifying quantum gravity captured by the Grav
ity from Entropy [3] approach\, complex systems and the theory of computat
ion.\n\n[1] Bianconi\, G.\, 2021. Higher-order networks: An introduction t
o Simplicial Complexes. Cambridge University Press.\n\n[2] Millán\, A.P.\
, Sun\, H.\, Giambagli\, L.\, Muolo\, R.\, Carletti\, T.\, Torres\, J.J.\,
Radicchi\, F.\, Kurths\, J. and Bianconi\, G.\, 2025. Topology shapes dyn
amics of higher-order networks. Nature Physics\, pp.1-9.\n\n[3] Bianconi\,
G.\, 2025. Gravity from entropy. Physical Review D\, 111(6)\, p.066001.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christine Heitsch (GT - USA)
DTSTART:20250919T160000Z
DTEND:20250919T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/106
DESCRIPTION:Title: On barrier height and other problems in RNA branching landscapes
\nby Christine Heitsch (GT - USA) as part of GEOTOP-A seminar\n\n\nAbs
tract\nUnderstanding the folding of RNA sequences into three-dimensional s
tructures is a fundamental challenge in molecular biology. A key aspect am
enable to mathematical analysis is characterizing the\nbranching of an RNA
secondary structure\, which is a critical molecular characteristic yet to
o often difficult to predict correctly. Using combinatorial models (i.e. p
lane trees/noncrossing perfect matchings) and methods (e.g. convex polytop
es and their normal fans)\, we give results that characterize different ty
pes of branching landscapes. Not only does this yield insights into RNA st
ructure formation\, but also suggests interesting new directions for furth
er mathematical analysis.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Gukov (CALTECH - USA)
DTSTART:20250926T160000Z
DTEND:20250926T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/107
DESCRIPTION:Title: A two-variable series for knot complements: recent developments
and applications\nby Sergei Gukov (CALTECH - USA) as part of GEOTOP-A
seminar\n\n\nAbstract\nIn this talk\, we review properties and application
s of quantum link invariants constructed from infinite-dimensional represe
ntations of quantum groups at generic values of $q$. When these invariants
were introduced by the speaker and Ciprian Manolescu approximately five y
ears ago\, they highlighted a new and surprising role of Spin$^c$ structur
es that was rather mysterious at the time and was not expected in complex
Chern-Simons theory. Since then\, the role of Spin$^c$ structures was unde
rstood thanks to many works --- including Akhmechet-Johnson-Krushkal\, Moo
re-Tarasca\, Harichurn-Nemethi-Svoboda\, among others --- and plays an imp
ortant part in connections to Heegaard Floer homology and categorification
of quantum $U_q (sl_2)$ invariants of 3-manifolds at generic $q$. This op
ens a new path from quantum topology to the study of exotic smooth structu
res on 4-manifolds.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benedikt Kolbe (UNI BONN - Germany)
DTSTART:20251010T160000Z
DTEND:20251010T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/108
DESCRIPTION:Title: Three-dimensional entangled graphs from mapping class groups and
approximate persistence computations\nby Benedikt Kolbe (UNI BONN - G
ermany) as part of GEOTOP-A seminar\n\n\nAbstract\nThis talk has two parts
. The first main part will discuss recent breakthroughs concerning an inhe
rently interdisciplinary project between mathematicians\, physicists\, che
mists\, and computer scientists that attempts to produce structures in thr
ee-dimensional Euclidean space from graph embeddings on triply-periodic mi
nimal surfaces. Exploring the different graphs embeddings naturally leads
to a new application\, relevant for materials science\, structure formatio
n\, and knot theory\, of the mapping class group (MCG) of a surface\, a pr
ominent object that has received considerable attention in pure mathematic
s. We explain how to apply the MCG to the construction of candidates for n
ew crystalline structures from graph embeddings on triply-periodic minimal
surfaces\, making use of the intrinsically hyperbolic nature of the surfa
ces for promising three-periodic structures. We then give an overview of n
ew results on MCGs that facilitates an enumeration of isotopy classes of g
raph embeddings with a given group of symmetries and conclude with a catal
ogue of three-dimensional structures that have resulted from the approach.
\n\nIn the second part of the talk\, we discuss ongoing work on analyzing
the resulting entangled structures using methods from topological data ana
lysis. We explain how the hyperbolic context has inspired novel results co
ncerning approximations of persistent homology computations of natural fil
trations for point sets of bounded doubling dimension.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juan Carlos Díaz Patiño (UNAM - México)
DTSTART:20251017T160000Z
DTEND:20251017T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/109
DESCRIPTION:Title: Applications of TDA to the study of the human brain connectome.<
/a>\nby Juan Carlos Díaz Patiño (UNAM - México) as part of GEOTOP-A sem
inar\n\n\nAbstract\nOne of the main scientific fields where TDA has been v
ery successfully applied has been in Neuroscience. In this talk\, we will
provide a brief introduction to functional magnetic resonance imaging\, in
cluding its various types of studies. Then we will present several results
obtained using TDA\, from both the Mapper algorithm and Persistent Homolo
gy perspectives.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicholas Beaton (UniMelb - Australia)
DTSTART:20251031T140000Z
DTEND:20251031T150000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/110
DESCRIPTION:Title: Lattice models of theta-shaped polymers and other branching stru
ctures\nby Nicholas Beaton (UniMelb - Australia) as part of GEOTOP-A s
eminar\n\n\nAbstract\nWe implement a new version of the BFACF algorithm co
mbined with the Wang-Landau method to sample lattice polymers with a theta
shape. The initial goal is to understand how the three "arms" scale in le
ngth\, and if this resembles the scaling of a large knotted polygon in dil
ute solution. Other shapes like "tadpoles" are also studied. These branchi
ng structures can potentially be used to model R-loops and other complex p
olymer molecules.\n\nThis is work in progress\, in collaboration with Alek
s Owczarek and James Gleeson.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boštjan Gabrovšek (UL\, Rudolfovo - Science and Technology Centr
e Novo mesto - Slovenia)
DTSTART:20251107T160000Z
DTEND:20251107T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/111
DESCRIPTION:Title: Topological analysis of knotted proteins\nby Boštjan Gabrov
šek (UL\, Rudolfovo - Science and Technology Centre Novo mesto - Slovenia
) as part of GEOTOP-A seminar\n\n\nAbstract\nWe present recent advances in
the topological analysis of protein structures\, combining mathematical i
nvariants\, persistent homology\, and machine learning. We explore how top
ological analysis captures subtle geometric features of folded chains\, en
abling efficient recognition of knots\, links\, θ-curves\, and lasso moti
fs inside proteins. Finally\, we show how integrating these tools\, rangin
g from combinatorial invariants to recurrent neural architectures\, reveal
s new insights into the organization\, dynamics\, and function of entangle
d proteins\, illustrating the deep interplay between topology and modern s
tructural biology.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lida Kanari (University of Oxford)
DTSTART:20251114T160000Z
DTEND:20251114T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/112
DESCRIPTION:Title: From Neurons to Networks: Exploring the Brain Through Algebraic
Topology\nby Lida Kanari (University of Oxford) as part of GEOTOP-A se
minar\n\n\nAbstract\nHow can mathematics help us understand the brain? In
recent years\, a field called topological data analysis (TDA) has offered
powerful new ways to study complex systems (from protein shapes to brain n
etworks) by capturing their underlying structure. In neuroscience\, these
tools help us uncover the hidden patterns that shape how brain cells conne
ct and communicate. The Topological Morphology Descriptor (TMD\, [1])\, tu
rns the branching shapes of neurons into mathematical “barcodes” that
summarize their structure. This approach allows us to classify\, cluster a
nd compare neurons across different types and species.\n\nIn this talk\, I
will present recent results in the topological representation of brain ce
lls\, focusing on neurons. I will then demonstrate how algebraic topology
provides insights into the relationships between single neurons and networ
ks\, allowing us to bridge different computational scales.\n\nA central qu
estion in neuroscience concerns the organizational principles that disting
uish the human brain from other species. Our findings [2] suggest that hum
an neurons are strikingly more complex than those in other animals. In par
ticular\, human pyramidal cells\, the most abundant cell type in the corte
x\, form denser\, more interconnected networks. This greater dendritic com
plexity\, a unique characteristic of human neurons\, may underlie the enha
nced computational power and cognitive flexibility of the human cortex.\n\
n[1] Kanari et al. 2018. A Topological representation of branching neurona
l morphologies\n\n[2] Kanari et al. 2025. Of mice and men: Dendritic archi
tecture differentiates human from mouse neuronal networks\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/112/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raymond Goldstein (CAM - UK)
DTSTART:20251128T160000Z
DTEND:20251128T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/113
DESCRIPTION:Title: The Geometry of Multicellular Life\nby Raymond Goldstein (CA
M - UK) as part of GEOTOP-A seminar\n\n\nAbstract\nOne of the most fundame
ntal issues in evolutionary biology is how unicellular life transitioned t
o multicellular life. How — and why — was it that the simplest single-
celled organisms that emerged from the primordial soup evolved into organi
sms with many cells and cell types dividing up life’s processes? This t
alk will describe recent experimental and theoretical advances in understa
nding the architecture of organisms that serve as models of this evolution
ary transition. I will discuss the shape-shifting properties of certain c
hoanoflagellates (the closest living relatives of animals)\, the recent di
scovery of common probability distributions of cellular neighborhood volum
es in yeast and alga\, as well as embryonic ‘inversion’ and the sponta
neous curling of the extracellular matrix of green algae. These studies t
ogether shed light on the fundamental question\, “How do cells produce s
tructures external to themselves in an accurate and robust manner?”\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/113/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Gilbert (UOE - UK)
DTSTART:20251205T160000Z
DTEND:20251205T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/114
DESCRIPTION:Title: The geometry of Lagrangian averaging in ideal fluid dynamics
\nby Andrew Gilbert (UOE - UK) as part of GEOTOP-A seminar\n\n\nAbstract\n
In seminal papers in the 1960s Vladimir Arnold introduced the idea that th
e motion of an ideal fluid can be considered as a geodesic in the space of
volume-preserving maps from the fluid domain to itself. This viewpoint pl
aces fluid dynamics\, on any Riemannian manifold\, in an abstract setting
which also incorporates Lie group structure. Although this theory is profo
und and beautiful\, at first sight it has little bearing for the everyday
applications of fluid dynamics. However it turns out that the process of
Lagrangian averaging (namely averaging over fluid parcels in an ensemble o
f fluid flows\, contrasted with Eulerian averaging at a fixed point)\, is
best understood using the ideas of pull-backs and Lie derivatives on a gen
eral manifold\, even though one ultimately applies these notions in ordina
ry three-dimensional space. \n\nThis talk will be very much aimed at fluid
dynamicists rather than professional geometers\, and will outline Arnold
’s ideas\, and applications to the Generalised Lagrangian Mean Theory pu
t forward by David Andrews and Michael McIntyre\, and subsequent related t
heories\, particularly of Andrew Soward and Paul Roberts.\n\nThis is joint
work with Jacques Vanneste (University of Edinburgh).\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/114/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Blumberg (CU - USA)
DTSTART:20251024T160000Z
DTEND:20251024T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/115
DESCRIPTION:Title: Curvature in geometric data analysis\nby Andrew Blumberg (CU
- USA) as part of GEOTOP-A seminar\n\n\nAbstract\nClassical manifold lear
ning relies on estimation of the tangent bundle of a manifold from a finit
e sample\, i.e.\, the first derivative. A natural next question to consid
er is second derivative information --- estimation and application of curv
ature from finite point clouds. This talk will survey the landscape on es
timating various kinds of curvature for point clouds and on applications o
f discrete curvature measures in geometric data analysis. The work discus
sed includes joint work with Hickok\, Saidi\, and Rieck.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/115/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Massa Shoura (Phinomics)
DTSTART:20260206T160000Z
DTEND:20260206T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/116
DESCRIPTION:Title: Genome Rewiring in Time and Space\nby Massa Shoura (Phinomic
s) as part of GEOTOP-A seminar\n\n\nAbstract\nGenomes are not static! They
are dynamic and modify their content and architecture in response to intr
insic and extrinsic signals. Genome dynamics have direct phenotypic conseq
uences in terms of cellular development\, programmed function\, and diseas
e. Although the genome is classically depicted as linear strings\, endogen
ous Extrachromosomal-circular DNA (eccDNA) comprises DNA products of "geno
me rewiring" in eukaryotic cells. By becoming physically unlinked from the
ir cognate linear chromosomes\, these elements become freed from the const
raints of linear linkage\, copy-number regulation\, and equal partitioning
to daughter cells. Thus\, these circular elements are direct contributors
to genomic diversity and cellular heterogeneity\; rendering this process
of their formation a remarkable vehicle for rapid cellular evolution. Yet\
, our understanding of genome rewiring via circular-DNA formation remains
a fragmentary aspect of the 4D genome. Using a new DNA-topology-centered g
enomics workflows (in conjunction with new informatics and AI/ML approache
s) to investigate eccDNA-mediated genetic diversity\, we have identified v
arious pathology-specific regions of rewired chromosomes in normal and can
cer backgrounds. In general\, this work resurrects and advances the eccDNA
field in addition to providing a missing key element for understanding on
cogenic heterogeneity\, consideration of which may drive novel diagnostics
and reevaluation of current therapies.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/116/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Smalyukh (University of Colorado and International Institute
for Sustainability with Knotted Chiral Meta Matter)
DTSTART:20260116T160000Z
DTEND:20260116T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/118
DESCRIPTION:Title: Artificial matter from knots: solitons and vortices in chiral me
dia\nby Ivan Smalyukh (University of Colorado and International Instit
ute for Sustainability with Knotted Chiral Meta Matter) as part of GEOTOP-
A seminar\n\n\nAbstract\nTopology is key for understanding properties of m
any natural material systems. Moreover\, topology can be used as an import
ant design principle to create artificial materials with properties not en
countered in nature. This lecture will discuss how stable solitonic and vo
rtex knots in chiral liquid crystals\, colloids and magnets can exhibit at
om-like behavior\, including fusion\, fission as well as self-assembly int
o various crystals and other forms of artificial matter [1-5]. The molecul
ar and host medium's chirality play important roles in enabling stability
of the spatially localized knotted solitons\, the hopfions\, and vortex st
ructures\, illustrating a hierarchical interplay of chirality effects. The
unusual crystals of self-assembled knots exhibit giant electrostriction\,
facile reconfigurability of lattice symmetries and other properties never
encountered in conventional forms of matter. These experimental demonstra
tions and theoretical/computational findings will let us revisit and admir
e the beautiful history of the early model of atoms by Kelvin\, Maxwell an
d Tait\, turning this model from a blunder to a new topological metamateri
al design approach. I will then show that these vortices interact with lig
ht similar to what was previously predicted for the elusive cosmic strings
\, with knots and crystalline arrays of vortices allowing to spatially loc
alize non-spreading laser beams into closed loops and knots\, potentially
paving the way to cosmology-inspired and knot-theory-guided optical engine
ering.\n\n[1] D. Hall\, J.-S. B. Tai\, L. Kauffman and I. I. Smalyukh. Nat
ure Physics doi.org/10.1038/s41567-025-03107-0 (2025).\n[2] J.-S. B. Tai
and I. I. Smalyukh. Science 365\, 1449-1453 (2019).\n[3] C. Meng\, J.-S. W
u\, and I. I. Smalyukh. Nature Materials 22\, 64–72 (2023).\n[3] H. Zhao
\, J.-S. B. Tai\, J.-S. Wu\, and I. I. Smalyukh. Nature Physics 19\, 451
–459 (2023).\n[4] R. Voinescu\, J.-S. B. Tai and I. I. Smalyukh. Phys Re
v Lett 125\, 057201 (2020).\n[5] P. J. Ackerman and I. I. Smalyukh. Nature
Mater 16\, 426-432 (2017).\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/118/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Patrizio Frosini (University of Pisa)
DTSTART:20260130T160000Z
DTEND:20260130T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/119
DESCRIPTION:Title: On the Role of Group Equivariant Non-Expansive Operators as a Br
idge between TDA and Machine Learning\nby Patrizio Frosini (University
of Pisa) as part of GEOTOP-A seminar\n\n\nAbstract\nGroup Equivariant Non
-Expansive Operators (GENEOs) were introduced ten years ago as a tool to r
educe and modulate the invariance of persistence diagrams (originally vali
d for every reparameterization of the signal domain) [1]. The computation
of persistence diagrams itself can be seen as an example of a GENEO. Subse
quently\, these operators have been independently studied and employed in
various applications in data analysis and machine learning [2-7]. In this
talk\, we will illustrate the definitions and basic properties of the main
concepts used in GENEO theory\, while also highlighting their promising a
pplications in TDA and Explainable Artificial Intelligence.\n\n[1] Patrizi
o Frosini\, Grzegorz Jabłoński\, Combining persistent homology and invar
iance groups for shape comparison\, Discrete & Computational Geometry\, vo
l. 55 (2016)\, n. 2\, pages 373-409. DOI:10.1007/s00454-016-9761-y.\n\n[2]
Mattia G. Bergomi\, Patrizio Frosini\, Daniela Giorgi\, Nicola Quercioli\
, Towards a topological-geometrical theory of group equivariant non-expans
ive operators for data analysis and machine learning\, Nature Machine Inte
lligence\, vol. 1\, n. 9\, pages 423 433 (2 September 2019). DOI:10.1038/s
42256-019-0087-3.\n\n[3] Giovanni Bocchi\, Stefano Botteghi\, Martina Bras
ini\, Patrizio Frosini\, Nicola Quercioli\,\nOn the finite representation
of linear group equivariant operators via permutant measures\,\nAnnals of
Mathematics and Artificial Intelligence\, vol. 91 (2023)\, n. 4\, 465 487.
DOI:10.1007/s10472-022-09830-1.\n\n[4] Giovanni Bocchi\, Patrizio Frosini
\, Massimo Ferri\,\nA novel approach to graph distinction through GENEOs a
nd permutants\,\nScientific Reports\, 15 (2025)\, 6259. DOI: 10.1038/s4159
8-025-90152-7.\n\n[5] Giovanni Bocchi\, Patrizio Frosini\, Alessandra Mich
eletti\, Alessandro Pedretti\, Gianluca Palermo\, Davide Gadioli\, Carmen
Gratteri\, Filippo Lunghini\, Akash Deep Biswas\, Pieter F.W. Stouten\, An
drea R. Beccari\, Anna Fava\, Carmine Talarico\, GENEOnet: A breakthrough
in protein binding pocket detection using group equivariant non-expansive
operators\, Scientific Reports\, 15 (2025)\, 34597. DOI:10.1038/s41598-025
-18132-5.\n\n[6] Raúl Felipe\, GENEOs with respect to the projective Hilb
ert metric\,\nThe Journal of Geometric Analysis\, vol. 35 (9) (2025)\, 264
. DOI: 10.1007/s12220-025-02102-4.\n\n[7] Diogo Lavado\, Alessandra Michel
etti\, Giovanni Bocchi\, Patrizio Frosini\, Cláudia Soares\,\nSCENE-Net:
Geometric induction for interpretable and low-resource 3D pole detection w
ith Group-Equivariant Non-Expansive Operators\, Computer Vision and Image
Understanding\, vol. 262 (2025)\, 104531. DOI: 10.1016/j.cviu.2025.104531.
\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/119/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniela Egas (MPI-CBG)
DTSTART:20260213T160000Z
DTEND:20260213T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/120
DESCRIPTION:Title: From neuron morphology to connectivity motifs that support funct
ion\nby Daniela Egas (MPI-CBG) as part of GEOTOP-A seminar\n\n\nAbstra
ct\nA central hypothesis in neuroscience is that many aspects of brain fun
ction are determined by the “map of the brain”\, and that its computat
ional power relies on its connectivity architecture. Impressive scientific
and engineering advances in recent years have produced a plethora of larg
e-scale\, cellular-resolution brain network reconstructions with incredibl
y complex architectures.\n\nA central feature of the architecture is its i
nherent directionality\, which reflects the flow of information. Evidence
shows that in biological neural networks reciprocal connections and highe
r-order motifs\, such as directed cliques\, emerge preferentially rather t
han at random. This raises fundamental questions in both mathematics and c
omputational neuroscience. \n\nIn this talk\, we first examine the presenc
e and functional relevance of these connectivity patterns and how they nat
urally emerge from the physical constraints of neuronal morphology. We the
n distill the underlying mechanism into a point-neuron stochastic algorith
m that reproduces both the basic network statistics and the higher-order s
tructure observed in biology.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/120/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sofia Lambropoulou (National Technical University Athens)
DTSTART:20260313T160000Z
DTEND:20260313T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/121
DESCRIPTION:Title: The theory of doubly periodic tangles\nby Sofia Lambropoulou
(National Technical University Athens) as part of GEOTOP-A seminar\n\n\nA
bstract\nDoubly periodic tangles (DP tangles) are entanglements of curves
embedded in the thickened plane that are periodically repeated in two tran
sversal directions. They are useful in many scientific fields for the stud
y of physical systems. A better understanding of their topology\, often as
sociated to some physical properties\, could allow the prediction of funct
ions of the system. In the first part we will establish the topological ba
ckground of the theory of DP tangles. DP tangles arise as universal covers
of knots and links in the thickened torus. We study their DP isotopies vi
a an equivalence relation between their generating (flat) motifs. In the s
econd part we present some isotopy invariants of DP tangles\, used for dis
tinguishing their properties.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/121/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eleni Panagiotou (Arizona State University)
DTSTART:20260327T160000Z
DTEND:20260327T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/122
DESCRIPTION:Title: Novel metrics of entanglement of open curves in 3-space and thei
r applications to proteins\nby Eleni Panagiotou (Arizona State Univer
sity) as part of GEOTOP-A seminar\n\n\nAbstract\nFilamentous materials may
exhibit structure-dependent material properties and function that depend
on their entanglement. Even though intuitively entanglement is often under
stood in terms of knotting or linking\, many of the filamentous systems in
the natural world are not mathematical knots or links. In this talk\, we
will introduce a novel and general framework in knot theory that can chara
cterize the complexity of open curves in 3-space. This leads to new metric
s of entanglement of open curves in 3-space that generalize classical topo
logical invariants\, like for example\, the Jones polynomial and Vassiliev
invariants. For open curves\, these are continuous functions of the curve
coordinates and converge to topological invariants of classical knots and
links when the endpoints of the curves tend to coincide. These methods pr
ovide an innovative approach to advance important questions in knot theory
. As an example\, we will see how the theory of linkoids enables the first
\, to our knowledge\, parallel algorithm for computing the Jones polynomia
l.\nImportantly\, this approach opens exciting applications to systems tha
t can be modeled as open curves in 3-space\, such as polymers and proteins
\, for which new quantitative relationships between their structure and ma
terial properties become evident. As an example\, we apply our methods to
proteins to understand the interplay between their structures and function
s. We show that our proposed quantitative topological metrics based on sta
tic protein structures alone correlate with protein dynamics and protein f
unction. The methods and results represent a new framework for advancing k
not theory\, as well as its applications to filamentous materials\, which
can be validated by experimental data and integrated into machine-learning
algorithms.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/122/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolas Schonsheck (Rockefeller University)
DTSTART:20260410T160000Z
DTEND:20260410T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/123
DESCRIPTION:Title: Identifying\, tracking\, and learning the grid cell circular coo
rdinate systems\nby Nikolas Schonsheck (Rockefeller University) as par
t of GEOTOP-A seminar\n\nInteractive livestream: https://us02web.zoom.us/j
/82059652404?pwd=pP6yon4bHdJbbrHJtAW8Fbq7k3Ua6r.1\n\nAbstract\nBrains use
a variety of coordinate systems to encode information. Sometimes these coo
rdinate systems are linear and can be recovered from population activity u
sing standard techniques. Often\, however\, they are not: many coordinate
systems exhibit nonlinear global topology for which such tools can be less
effective. Notably\, grid cells in the entorhinal cortex comprise two lin
early independent circular coordinate systems that\, together\, exhibit to
roidal topology. Recent recordings using high-density probes confirm this
toroidal topology persists during spatial and non-spatial behavior\, and c
an be quantified and decoded with persistent (co)homology.\n\n \n\nWe ask
a next natural question: is the propagation of circular coordinate systems
through neural circuits a generic feature of biological neural networks\,
or must this be learned? If learning is necessary\, how does it occur? We
apply methods from topological data analysis developed to quantitatively
measure propagation of such nonlinear manifolds across populations to addr
ess these problems. We identify a collection of connectivity and parameter
regimes for feed-forward networks in which learning is required\, and dem
onstrate that simple Hebbian spike-timing dependent plasticity reorganizes
such networks to correctly propagate circular coordinate systems. We also
observe during this learning process the emergence of geometrically non-l
ocal experimentally observed receptive field types: bimodally-tuned head-d
irection cells and cells with spatially periodic\, band-like receptive fie
lds.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/123/
URL:https://us02web.zoom.us/j/82059652404?pwd=pP6yon4bHdJbbrHJtAW8Fbq7k3Ua
6r.1
END:VEVENT
BEGIN:VEVENT
SUMMARY:Henry Adams (University of Florida)
DTSTART:20260508T160000Z
DTEND:20260508T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/124
DESCRIPTION:by Henry Adams (University of Florida) as part of GEOTOP-A sem
inar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/124/
END:VEVENT
BEGIN:VEVENT
SUMMARY:José Angel Frías García (Universidad Autónoma de Morelos)
DTSTART:20260522T160000Z
DTEND:20260522T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/125
DESCRIPTION:by José Angel Frías García (Universidad Autónoma de Morelo
s) as part of GEOTOP-A seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/125/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ljubica S. Velimirović (University of Niš)
DTSTART:20260605T160000Z
DTEND:20260605T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/126
DESCRIPTION:by Ljubica S. Velimirović (University of Niš) as part of GEO
TOP-A seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/126/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rade Živaljević (Mathematical Institute SANU)
DTSTART:20260227T160000Z
DTEND:20260227T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/127
DESCRIPTION:Title: Combinatorics\, geometry\, and topology of Bier spheres\nby
Rade Živaljević (Mathematical Institute SANU) as part of GEOTOP-A semina
r\n\n\nAbstract\nEach simplicial complex K (alias a simple game P([n])\\K)
) with n vertices is associated an (n-2)-dimensional\, combinatorial spher
e on (at most) 2n-vertices. This is the so called Bier sphere Bier(K) (nam
ed after Thomas Bier)\, formally defined as the deleted join of K with i
ts\n(combinatorial) Alexander dual. Bier spheres have been studied from th
e viewpoint of combinatorics (simplicial complexes)\, topology (polyhedral
products\, toric manifolds)\, convex polytopes (generalized permutohedra\
, algorithmic Steinitz problem)\, game theory (cooperative games)\,\nexper
imental mathematics (nonpolytopal spheres)\, combinatorial optimization (s
ubmodular functions)\, algebraic statistics (convex rank tests)\, etc.\nWe
present an overview of this area\, emphasizing the interplay of ideas fro
m different mathematical fields.\n\nFor illustration we show how:
\n
(i) Canonical cubulations of Bier spheres appear in toric topology as boun
daries of intersections of associated polyhedral products\;
\n(ii) C
haracterize “weighted majority games” as the games whose associated Bi
er spheres are canonically polytopal\;
\n(iii) Show\, by extensive c
omputer search\, that all Bier spheres with at most 11 vertices are (non-c
anonically) polytopal\;
\n(iv) Relate the homology of the associated
real and complex toric manifolds\, with the combinatorics of Bier(K)\;
\n(v) Discuss open problems\, including the problem of finding a non-p
olytopal simple game with the smallest number of players.
\n\nThe ta
lk is based on joint papers with Marinko Timotijević\, Filip Jevtić\, an
d Ivan Limonchenko.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/127/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ahtziri González-Lemus (Universidad Michoacana de San Nicolás de
Hidalgo)
DTSTART:20260417T160000Z
DTEND:20260417T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/128
DESCRIPTION:Title: Detecting the order of chaotic Lagrangian orbits in convective f
lows through their topological properties\nby Ahtziri González-Lemus
(Universidad Michoacana de San Nicolás de Hidalgo) as part of GEOTOP-A se
minar\n\n\nAbstract\nNatural convection is a fundamental mechanism of heat
and mass transport that plays a crucial role in both natural phenomena an
d technological applications. It governs large-scale processes such as atm
ospheric circulation and ocean currents\, and is also essential in enginee
ring contexts\, including crystal growth\, energy systems\, and thermal ma
nagement.\n\nIn this talk\, we numerically investigate the Lagrangian orbi
ts generated by a three-dimensional convective flow in a cubic domain\, re
stricted to regimes in which the flow remains in a steady state. These orb
its are modeled as finite point clouds in R^3\, enabling the characterizat
ion of their geometric structure via persistent homology. We use the Rayle
igh number as a control parameter of the flow. For low Rayleigh numbers\,
the orbits are organized into families of nested tori. As the Rayleigh num
ber increases\, a second family of nested tori emerges\, and the two famil
ies are separated by a chaotic region. We show that a topology-based metri
c allows one to detect an intrinsic ordering of the orbits within this cha
otic region according to their shape\, revealing a\nsmooth evolution despi
te the underlying dynamical complexity. In particular\, within the chaotic
region\, we identify an orbit whose topological properties are analogous
to those of a trivalent 2-stratifold\, highlighting the richness of the tr
ansition between ordered and chaotic dynamics.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/128/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dejan Govc (University of Ljubljana)
DTSTART:20260424T160000Z
DTEND:20260424T170000Z
DTSTAMP:20260404T111324Z
UID:GEOTOP-A/129
DESCRIPTION:Title: Surfaces in the d-Cube\nby Dejan Govc (University of Ljublja
na) as part of GEOTOP-A seminar\n\n\nAbstract\nTriangulating a surface mea
ns finding a subcomplex of a simplex that is homeomorphic to the surface.
Vertex-minimal triangulations of closed surfaces have been characterized i
n classical work of Jungerman and Ringel.\n\nThe corresponding problem for
cubes has been much less studied. Notably\, Coxeter found surfaces in the
$d$-cube of maximal possible genus and Schulz gave bounds on the dimensio
n of the cube required to realize a particular surface as a subcomplex. Th
ese latter bounds are tight for orientable surfaces and nonorientable surf
aces of even demigenus $k \\geq 12$\, while for surfaces of odd demigenus
they may be off by one.\n\nIn the cubical case\, minimizing the embedding
dimension is not equivalent to minimizing the number of vertices\, and fin
ding vertex-minimal cubical realizations of surfaces remains poorly unders
tood. We provide new theoretical bounds for this problem and\, using compu
tational methods\, give a complete enumeration of connected closed surface
s in the 5-cube. We find that there are 2690 isomorphism classes of such s
urfaces. As a consequence\, we obtain the minimal f-vectors of these surfa
ces in the 5-cube and complete Schulz's characterization for the even demi
genus case\, while discovering some new examples in the process. This is j
oint work with Andrea Aveni and Érika Roldán.\n
LOCATION:https://stable.researchseminars.org/talk/GEOTOP-A/129/
END:VEVENT
END:VCALENDAR