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BEGIN:VEVENT
SUMMARY:Ran Levi (University of Aberdeen)
DTSTART:20200420T140000Z
DTEND:20200420T150000Z
DTSTAMP:20260404T110913Z
UID:OATS/1
DESCRIPTION:Title: Complexes of Tournaments in Directed Networks\nby Ran Levi (Univer
sity of Aberdeen) as part of Online algebraic topology seminar\n\n\nAbstra
ct\nClique graphs whose edges are oriented are referred to in the combinat
orics literature as tournaments. We consider a family of semi-simplicial s
ets\, that we refer to as “tournaplexes"\, whose simplices are tournamen
ts. In particular\, given a directed graph G\, we associate with it a “f
lag tournaplex" which is a tournaplex containing the directed flag complex
of G\, but also the geometric realisation of cliques that are not directe
d. We define several types of filtration on tournaplexes\, and exploiting
persistent homology\, we observe that filtered flag tournaplexes provide f
iner means of distinguishing graph dynamics than the directed flag complex
. We then demonstrate the power of those ideas by applying them to graph d
ata arising from the Blue Brain Project’s digital reconstruction of a ra
t’s neocortex.\n
LOCATION:https://stable.researchseminars.org/talk/OATS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andy Baker (University of Glasgow)
DTSTART:20200427T140000Z
DTEND:20200427T150000Z
DTSTAMP:20260404T110913Z
UID:OATS/2
DESCRIPTION:Title: Fun and games with the Steenrod algebra\nby Andy Baker (University
of Glasgow) as part of Online algebraic topology seminar\n\n\nAbstract\nT
he mod 2 Steenrod algebra is an important tool in unstable and stable homo
topy theory but it is also interesting as a purely algebraic gadget. I wil
l briefly review its algebraic structure and that of some important finit
e subHopf algebras. Then I will discuss some realisability questions for m
odules\, ranging from classical examples to modules over the E-infinity ri
ng spectra kO and tmf localised at 2. I hope this talk will be accessible
to beginners and also have some things to interest experts.\n
LOCATION:https://stable.researchseminars.org/talk/OATS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Constanze Roitzheim (University of Kent)
DTSTART:20200504T140000Z
DTEND:20200504T150000Z
DTSTAMP:20260404T110913Z
UID:OATS/3
DESCRIPTION:Title: Equivariant homotopy commutativity\, trees and chicken feet\nby Co
nstanze Roitzheim (University of Kent) as part of Online algebraic topolog
y seminar\n\n\nAbstract\nCommutativity up to homotopy can be daunting\, an
d it becomes even more difficult to track when equivariant structures get
introduced. In the case of a finite group\, however\, the options for equi
variant homotopy commutativity can be encoded using simple combinatorics\,
and we will show some examples.\n
LOCATION:https://stable.researchseminars.org/talk/OATS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emanuele Dotto (University of Warwick)
DTSTART:20200518T140000Z
DTEND:20200518T150000Z
DTSTAMP:20260404T110913Z
UID:OATS/4
DESCRIPTION:Title: Witt vectors with coefficients and characteristic polynomials over non
-commutative rings\nby Emanuele Dotto (University of Warwick) as part
of Online algebraic topology seminar\n\n\nAbstract\nThe characteristic pol
ynomial of a matrix with entries in a commutative ring $R$ naturally takes
value in the ring of Witt vectors of $R$. In joint work with Krause\, Nik
olaus and Patchkoria\, we extend the classical Witt vectors construction t
o allow as input pairs of a ring $R$ and a bimodule $M$. I will explain ho
w this construction relates to topological Hochschild homology\, the Hill-
Hopkins-Ravenel norm\, and the characteristic polynomial.\n
LOCATION:https://stable.researchseminars.org/talk/OATS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kathryn Hess (EPFL)
DTSTART:20200608T140000Z
DTEND:20200608T150000Z
DTSTAMP:20260404T110913Z
UID:OATS/5
DESCRIPTION:Title: Calculus from comonads\nby Kathryn Hess (EPFL) as part of Online a
lgebraic topology seminar\n\n\nAbstract\n(Joint work with Brenda Johnson.)
The many theories of "calculus" introduced in algebraic topology over th
e past couple of decades--e.g.\, Goodwillie's calculus of homotopy functor
s\, the Goodwillie-Weiss manifold calculus\, the orthogonal calculus\, and
the Johnson-McCarthy cotriple calculus--all have a similar flavor\, thoug
h the objects studied and exact methods applied are not the same. We hav
e constructed a relatively simple category-theoretic machine for producing
towers of functors from a small category into a simplicial model category
\, determined conditions under which such tower-building machines constitu
te a calculus\, and showed that this framework encompasses certain well kn
own calculi\, as well as providing new classes of examples. The cogs and
gears of our machine are cubical diagrams of reflective subcategories and
the comonads they naturally give rise to.\n\nIn this talk\, I will assume
no familiarity with comonads and only basic knowledge of simplicial model
categories.\n
LOCATION:https://stable.researchseminars.org/talk/OATS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Henry Adams (Colorado State University)
DTSTART:20200525T140000Z
DTEND:20200525T150000Z
DTSTAMP:20260404T110913Z
UID:OATS/6
DESCRIPTION:Title: Vietoris-Rips complexes and Borsuk-Ulam theorems\nby Henry Adams (
Colorado State University) as part of Online algebraic topology seminar\n\
n\nAbstract\nGiven a metric space X and a scale parameter r\, the Vietoris
-Rips simplicial complex VR(X\;r) has X as its vertex set\, and contains a
finite subset as a simplex if its diameter is at most r. Vietoris-Rips co
mplexes were invented by Vietoris in order to define a (co)homology theory
for metric spaces\, and by Rips for use in geometric group theory. More r
ecently\, they have found applications in computational topology for appro
ximating of the shape of a dataset. I will explain how the Vietoris-Rips c
omplexes of the circle\, as the scale parameter r increases\, obtain the h
omotopy types of the circle\, the 3-sphere\, the 5-sphere\, the 7-sphere\,
...\, until they are finally contractible. Only very little is understood
about the homotopy types of the Vietoris-Rips complexes of the n-sphere.
Knowing the homotopy connectivities of Vietoris-Rips complexes of spheres
allows one to prove generalizations of the Borsuk-Ulam theorem for maps fr
om the n-sphere into k-dimensional Euclidean space with k > n. Joint work
with John Bush and Florian Frick.\n
LOCATION:https://stable.researchseminars.org/talk/OATS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kirsten Wickelgren (Duke University)
DTSTART:20200601T140000Z
DTEND:20200601T150000Z
DTSTAMP:20260404T110913Z
UID:OATS/7
DESCRIPTION:Title: There are 160\,839<1> + 160\,650<-1> 3-planes in a 7-dimensional cubic
hypersurface\nby Kirsten Wickelgren (Duke University) as part of Onli
ne algebraic topology seminar\n\n\nAbstract\nThe expression in the title i
s a bilinear form and it comes from an Euler number in A1-algebraic topolo
gy. Such Euler numbers can be constructed with Hochschild homology\, self-
duality of Koszul complexes\, pushforwards in SL_c oriented cohomology the
ories\, and sums of local degrees. We show an integrality result for A1-Eu
ler numbers and apply this to the enumeration of d-planes in complete inte
rsections. Classically such counts are valid over C and sometimes extended
to the real numbers\, but A1-homotopy theory allows one to perform counts
over a large class of fields\, and records information about the solution
s in bilinear form. The example in the title then follows from work of Fin
ashin--Kharlamov. This is joint work with Tom Bachmann.\n
LOCATION:https://stable.researchseminars.org/talk/OATS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Markus Szymik (NTNU)
DTSTART:20200615T140000Z
DTEND:20200615T150000Z
DTSTAMP:20260404T110913Z
UID:OATS/8
DESCRIPTION:Title: Trigraded spectral sequences for principal fibrations\nby Markus S
zymik (NTNU) as part of Online algebraic topology seminar\n\n\nAbstract\nT
he Leray--Serre and the Eilenberg--Moore spectral sequence are fundamental
tools for computing the cohomology of a group or\, more generally\, of a
space. In joint work with Frank Neumann (Leicester)\, we describe the rel
ationship between these two spectral sequences in the situation when both
of them share the same abutment. This talk is an introduction to the topi
c with many examples. It should be suitable for an audience from graduate
students in algebraic topology onward\, and I will only assume some casua
l acquaintance with spectral sequences.\n
LOCATION:https://stable.researchseminars.org/talk/OATS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ulrich Pennig (Cardiff University)
DTSTART:20200511T140000Z
DTEND:20200511T150000Z
DTSTAMP:20260404T110913Z
UID:OATS/9
DESCRIPTION:Title: Loops\, groups\, and twists - the role of K-theory in mathematical phy
sics\nby Ulrich Pennig (Cardiff University) as part of Online algebrai
c topology seminar\n\n\nAbstract\nWhile K-theory has its origins in Grothe
ndieck's formulation and proof of his version of the Riemann-Roch theorem\
, it now plays a significant role in many diverse branches of mathematics:
It provides a fundamental example of a cohomology theory\, and it is one
of the most important invariants of C*-algebras. In the first half of the
talk\, I will define the K-groups and discuss some of their applications.
In the second half\, I will concentrate on equivariant twisted K-theory\,
which is related to the representation theory of loop groups and the geome
try of two-dimensional quantum field theories by a theorem of Freed\, Hopk
ins\, and Teleman. I will finish with an outline of joint work with D. Eva
ns\, in which we study generalizations of this work to higher twists.\n
LOCATION:https://stable.researchseminars.org/talk/OATS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeremy Hahn (MIT)
DTSTART:20200921T130000Z
DTEND:20200921T140000Z
DTSTAMP:20260404T110913Z
UID:OATS/10
DESCRIPTION:Title: Nishida Nilpotence\nby Jeremy Hahn (MIT) as part of Online algebr
aic topology seminar\n\n\nAbstract\nIn 1973\, Nishida proved that every po
sitive degree class in the stable homotopy groups of spheres is nilpotent.
We will discuss some modern perspectives on Nishida's original proof. W
hile this will be a mostly expository talk aimed at graduate students\, if
time permits we will end with a discussion of some open nilpotence questi
ons in motivic stable homotopy theory.\n
LOCATION:https://stable.researchseminars.org/talk/OATS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lennart Meier (Utrecht)
DTSTART:20200928T140000Z
DTEND:20200928T150000Z
DTSTAMP:20260404T110913Z
UID:OATS/11
DESCRIPTION:Title: Elliptic cohomology of level n\nby Lennart Meier (Utrecht) as par
t of Online algebraic topology seminar\n\n\nAbstract\nElliptic genera have
played an important role in algebraic topology and algebraic geometry sin
ce the 1980s. To every almost-complex manifold they associate a modular fo
rm for the congruence subgroups $\\Gamma_1(n)$. More recently\, elliptic c
ohomology theories have been built that are natural targets of elliptic ge
nera for families. I will give an overview of these theories and report in
particular on certain $C_2$-equivariant refinements.\n
LOCATION:https://stable.researchseminars.org/talk/OATS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Viktoriya Ozornova (Ruhr-Universität Bochum)
DTSTART:20201005T140000Z
DTEND:20201005T150000Z
DTSTAMP:20260404T110913Z
UID:OATS/12
DESCRIPTION:Title: Models of (infty\,2)-categories\nby Viktoriya Ozornova (Ruhr-Univ
ersität Bochum) as part of Online algebraic topology seminar\n\n\nAbstrac
t\nAn $(\\infty\,2)$-category should be a weak version of a strict $2$-cat
egory\, in which compositions are well-defined\, associative and unital up
to some higher coherence. There are various models making this precise. I
n this talk\, I will describe a direct comparison between two particular m
odels (which will be introduced)\, namely $\\Theta_2$-spaces and saturated
$2$-complicial sets. This is joint work in progress with Julie Bergner an
d Martina Rovelli.\n
LOCATION:https://stable.researchseminars.org/talk/OATS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Birgit Richter (Universität Hamburg)
DTSTART:20201019T140000Z
DTEND:20201019T150000Z
DTSTAMP:20260404T110913Z
UID:OATS/13
DESCRIPTION:Title: Detecting and describing ramification for structured ring spectra
\nby Birgit Richter (Universität Hamburg) as part of Online algebraic top
ology seminar\n\n\nAbstract\nThis is a report on joint work in progress wi
th Eva Höning. \n\nRamification for commutative ring spectra can be detec
ted by relative topological Hochschild homology and by the spectrum of Kä
hler differentials. For rings of integers in an extension of number fields
\, it is important to distinguish between tame and wild ramification. Noet
her's theorem characterizes tame ramification in terms of a normal basis a
nd tame ramification can also be detected via the surjectivity of the norm
map. We take the latter fact and use the Tate cohomology spectrum to dete
ct wild ramification in the context of commutative ring spectra. In the ta
lk\, I will discuss several examples in the context of topological K-theor
y and modular forms.\n
LOCATION:https://stable.researchseminars.org/talk/OATS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Drew Heard (NTNU)
DTSTART:20201102T150000Z
DTEND:20201102T160000Z
DTSTAMP:20260404T110913Z
UID:OATS/14
DESCRIPTION:Title: Support theory for triangulated categories in algebra and topology\nby Drew Heard (NTNU) as part of Online algebraic topology seminar\n\n\n
Abstract\nWe will survey the support theory of triangulated categories thr
ough the machinery of tensor-triangulated geometry. We will discuss the st
ratification theory of Benson—Iyengar—Krause for triangulated categori
es\, the construction by Balmer of the spectrum of a tensor-triangulated c
ategory\, and the relation between the two. Time permitting\, we will disc
uss a recent application to the category of derived Mackey functors\, join
t with Beren Sanders.\n
LOCATION:https://stable.researchseminars.org/talk/OATS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julie Bergner (University of Virginia)
DTSTART:20201130T150000Z
DTEND:20201130T160000Z
DTSTAMP:20260404T110913Z
UID:OATS/15
DESCRIPTION:Title: Variants of the Waldhausen S-construction\nby Julie Bergner (Univ
ersity of Virginia) as part of Online algebraic topology seminar\n\n\nAbst
ract\nThe S-construction\, first defined in the setting of cofibration cat
egories by Waldhausen\, gives a way to define the algebraic K-theory assoc
iated to certain kinds of categorical input. It was proved by Galvez-Carr
illo\, Kock\, and Tonks that the result of applying this construction to a
n exact category is a decomposition space\, also called a 2-Segal space\,
and Dyckerhoff and Kapranov independently proved the same result for the s
lightly more general input of proto-exact categories. In joint work with
Osorno\, Ozornova\, Rovelli\, and Scheimbauer\, we proved that these resul
ts can be maximally generalized to the input of augmented stable double Se
gal spaces\, so that the S-construction defines an equivalence of homotopy
theories. In this talk\, we'll review the S-construction and the reasoni
ng behind these stages of generalization. Time permitting\, we'll discuss
attempts to characterize those augmented stable double Segal spaces that
correspond to cyclic spaces\, which is work in progress with Walker Stern.
\n
LOCATION:https://stable.researchseminars.org/talk/OATS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Marie Bohmann (Vanderbilt)
DTSTART:20201110T150000Z
DTEND:20201110T160000Z
DTSTAMP:20260404T110913Z
UID:OATS/16
DESCRIPTION:Title: Algebraic K-theory for Lawvere theories: assembly and Morita invarian
ce\nby Anna Marie Bohmann (Vanderbilt) as part of Online algebraic to
pology seminar\n\n\nAbstract\nMuch like operads and monads\, Lawvere theor
ies are a way of encoding algebraic structures\, such as those of modules
over a ring or sets with a group action. In this talk\, we discuss the al
gebraic K-theory of Lawvere theories\, which contains information about au
tomorphism groups of these structures. We'll discuss both particular exam
ples and general constructions in the K-theory of Lawvere theories\, inclu
ding examples showing the limits of Morita invariance and the construction
of assembly-style maps. This is joint work with Markus Szymik.\n
LOCATION:https://stable.researchseminars.org/talk/OATS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Angélica Osorno (Reed)
DTSTART:20201012T150000Z
DTEND:20201012T160000Z
DTSTAMP:20260404T110913Z
UID:OATS/17
DESCRIPTION:Title: Transfer systems and weak factorization systems\nby Angélica Oso
rno (Reed) as part of Online algebraic topology seminar\n\n\nAbstract\n$N_
\\infty$ operads over a group G encode homotopy commutative operations tog
ether with a class of equivariant transfer (or norm) maps. Their homotopy
theory is given by transfer systems\, which are certain discrete objects t
hat have a rich combinatorial structure defined in terms of the subgroup l
attice of G. In this talk\, we will show that when G is finite Abelian\, t
ransfer systems are in bijection with weak factorization systems on the po
set category of subgroups of G. This leads to an involution on the lattice
of transfer systems\, generalizing the work of Balchin–Bearup–Pech–
Roitzheim for cyclic groups of squarefree order. We will conclude with an
enumeration of saturated transfer systems and comments on the Rubin and Bl
umberg–Hill saturation conjecture.\n\nThis is joint work with Evan Franc
here\, Usman Hafeez\, Peter Marcus\, Kyle Ormsby\, Weihang Qin\, and Riley
Waugh.\n
LOCATION:https://stable.researchseminars.org/talk/OATS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manuel Rivera (Purdue)
DTSTART:20201123T150000Z
DTEND:20201123T160000Z
DTSTAMP:20260404T110913Z
UID:OATS/18
DESCRIPTION:Title: The coalgebra of chains and the fundamental group\nby Manuel Rive
ra (Purdue) as part of Online algebraic topology seminar\n\n\nAbstract\nRa
tional homotopy theory tells us that simply connected spaces\, up to ratio
nal homotopy equivalence\, may be classified algebraically by means of rat
ional cocommutative coalgebras (Quillen) or in the finite type case by rat
ional dg commutative algebras (Sullivan). Goerss and Mandell proved versio
ns of these results for fields of arbitrary characteristic by means of sim
plicial cocommutative coalgebras and E-infinity algebras\, respectively. T
he algebraic structures in these settings are considered up to quasi-isomo
rphism.\nIn this talk\, I will describe how to extend these results to spa
ces with arbitrary fundamental group.The key new observation is that the h
omotopy cocommutative coalgebraic structure of the chains on a space deter
mines the fundamental group in complete generality. The corresponding alge
braic notion of weak equivalence between coalgebras is drawn from Koszul d
uality. The end goal of this program is to completely understand homotopy
types in terms of algebraic “chain level” structure. This is joint wor
k with M. Zeinalian and F. Wierstra.\n
LOCATION:https://stable.researchseminars.org/talk/OATS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarah Whitehouse (Sheffield)
DTSTART:20201116T150000Z
DTEND:20201116T160000Z
DTSTAMP:20260404T110913Z
UID:OATS/19
DESCRIPTION:Title: Model category structures and spectral sequences\nby Sarah Whiteh
ouse (Sheffield) as part of Online algebraic topology seminar\n\n\nAbstrac
t\nI'll discuss a family of model category structures such that weak equiv
alences are morphisms inducing an isomorphism at a fixed stage of a spectr
al sequence. The talk will focus on joint work with Xin Fu\, Ai Guan and M
uriel Livernet\, giving such model structures for multicomplexes. A multic
omplex (also known as a twisted chain complex) is an algebraic structure g
eneralizing the notion of a chain complex and that of a bicomplex. These s
tructures have arisen in many different places and play an important role
in homological and homotopical algebra.\n
LOCATION:https://stable.researchseminars.org/talk/OATS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Grigory Garkusha (Swansea)
DTSTART:20201026T160000Z
DTEND:20201026T170000Z
DTSTAMP:20260404T110913Z
UID:OATS/20
DESCRIPTION:Title: Motivic Gamma-spaces\nby Grigory Garkusha (Swansea) as part of On
line algebraic topology seminar\n\n\nAbstract\nThis is a joint work with I
van Panin and Paul Arne Østvær. We combine several mini miracles to achi
eve an elementary understanding of infinite loop spaces and very effective
spectra in the algebro-geometric setting of motivic homotopy theory. Our
approach combines Gamma-spaces and framed correspondences into the concept
of motivic Gamma-spaces\; these are continuous or enriched functors of tw
o variables that take values in motivic spaces and are equipped with a fra
ming. We craft proofs of our main results by imposing further axioms on mo
tivic Gamma-spaces such as a Segal condition for simplicial Nisnevich shea
ves\, cancellation\, A1- and sigma-invariance\, Nisnevich excision\, Susli
n contractibility\, and grouplikeness. This adds to the discussion in the
literature on coexisting points of view on the A1-homotopy theory of algeb
raic varieties. As prime examples we discuss the motivic sphere spectrum\,
algebraic cobordism\, motivic cohomology\, and Milnor-Witt motivic cohomo
logy.\n
LOCATION:https://stable.researchseminars.org/talk/OATS/20/
END:VEVENT
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