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BEGIN:VEVENT
SUMMARY:Martin Mion-Mouton (Technion)
DTSTART:20220320T110000Z
DTEND:20220320T123000Z
DTSTAMP:20260404T131149Z
UID:mathematicsofmotion/1
DESCRIPTION:Title: Partially hyperbolic diffeomorphisms of contact type an
d path geometries\nby Martin Mion-Mouton (Technion) as part of The mat
hematics of motion\n\n\nAbstract\nAnosov-contact flows with smooth invaria
nt distributions have been classified by successive works of Ghys (in dime
nsion three) and Benoist-Foulon-Labourie (in any dimension) in the 90’s.
In this talk\, we will be interested with the analog question for discret
e-time dynamics\, that is for the partially hyperbolic diffeomorphisms –
that have a dynamical behaviour close to the time-one of an Anosov flow.
More precisely\, we will present the classification of three-dimensional p
artially hyperbolic diffeomorphisms (without wandering points) of contact
type having smooth invariant distributions. We will see that the absence o
f the flow heavily changes the situation\, and that the rigid geometric st
ructure defined by the stable and unstable distributions\, called a path g
eometry\, plays a central role in this study through the point of view of
Cartan geometries.\n
LOCATION:https://stable.researchseminars.org/talk/mathematicsofmotion/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anette Karrer (Technion)
DTSTART:20220410T100000Z
DTEND:20220410T113000Z
DTSTAMP:20260404T131149Z
UID:mathematicsofmotion/2
DESCRIPTION:Title: Dynamics on boundaries of CAT(0) groups\nby Anette
Karrer (Technion) as part of The mathematics of motion\n\n\nAbstract\nA CA
T(0) group is a finitely generated group that acts nicely on a CAT(0) spac
e\, i.e. a geodesic metric space of non-positive curvature. Associated to
such spaces are different kinds of topological spaces\, called boundaries
on which the group acts naturally. This enables us to study dynamics on th
ese boundaries.\n\nIn this talk I will explain what is meant by “classic
al North-south-dynamics” on these boundaries. Then I will describe a gen
eralization introduced by Guralnik and Swenson that leads to a certain hig
her-dimensional version of classical North-south-dynamics.\n
LOCATION:https://stable.researchseminars.org/talk/mathematicsofmotion/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tsviqa Lakrec (Universität Zürich)
DTSTART:20220424T100000Z
DTEND:20220424T113000Z
DTSTAMP:20260404T131149Z
UID:mathematicsofmotion/3
DESCRIPTION:by Tsviqa Lakrec (Universität Zürich) as part of The mathema
tics of motion\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/mathematicsofmotion/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Goldberg (Technion)
DTSTART:20220508T100000Z
DTEND:20220508T113000Z
DTSTAMP:20260404T131149Z
UID:mathematicsofmotion/4
DESCRIPTION:Title: Surface Diffusion\; Well Posedness and Stability\nb
y Daniel Goldberg (Technion) as part of The mathematics of motion\n\n\nAbs
tract\nIn the physical study of solid state materials multiple geometric e
volution equations arise. We examine one of them\, Surface Diffusion. It i
s a fourth order nonlinear parabolic Partial Differential Equation. We can
ask the following questions: For which initial conditions is there a uniq
ue solution? In which spaces does the solution live? What is its general b
ehaviour? In this talk we will delve into the Well-Posedness of Surface Di
ffusion by using the theory of Maximal Regularity and into the stability o
f its solutions near steady states by taking advantage of its Gradient Flo
w property.\n
LOCATION:https://stable.researchseminars.org/talk/mathematicsofmotion/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Tsodikovich (Tel Aviv University)
DTSTART:20220522T100000Z
DTEND:20220522T113000Z
DTSTAMP:20260404T131149Z
UID:mathematicsofmotion/5
DESCRIPTION:Title: A Billiard analogue of the Blaschke-Santalo inequality<
/a>\nby Daniel Tsodikovich (Tel Aviv University) as part of The mathematic
s of motion\n\n\nAbstract\nThe Blaschke-Santalo inequality is a classical
inequality in convex geometry. This inequality is about the product of the
volumes of a convex body and its dual. In this talk we investigate an ana
logue of this inequality\, where the volume is replaced with the length of
the shortest billiard trajectory. We focus on the two dimensional case. W
e will describe what the analogue of the “Santalo point” is in this se
tting\, show an analogue of the inequality itself\, and discuss maximizers
in classes of polygons.\n
LOCATION:https://stable.researchseminars.org/talk/mathematicsofmotion/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eran Igra (Technion)
DTSTART:20220619T100000Z
DTEND:20220619T113000Z
DTSTAMP:20260404T131149Z
UID:mathematicsofmotion/6
DESCRIPTION:Title: Knots and Chaos in the Rössler System\nby Eran Igr
a (Technion) as part of The mathematics of motion\n\n\nAbstract\nThe Röss
ler system is the “minimal” model for chaos\, in the sense that it is
“almost” linear – at least with respect to other well-known chaotic
systems. Despite that\, it generates a flow which exhibits many interestin
g properties – from spiral-like homoclinic bifrucations to period-doubli
ng routes to chaos. However\, most results on the Rössler System are nume
ric in nature\, and little is known rigorously about it. In this talk we w
ill see how imposing mild assumptions on the dynamics can allow us to draw
far-reaching conclusions. In particular\, we will prove how under these a
ssumptions it is possible to rigorously verify some of the numerics observ
ed in the Rössler System.\n\nBased on joint work with Prof. Tali Pinsky.\
n
LOCATION:https://stable.researchseminars.org/talk/mathematicsofmotion/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noy Soffer-Aranov (Technion)
DTSTART:20220825T104000Z
DTEND:20220825T114000Z
DTSTAMP:20260404T131149Z
UID:mathematicsofmotion/7
DESCRIPTION:Title: Fields Prize Talks: The Duffin-Schaefer Conjecture - on
James Maynard's Results\nby Noy Soffer-Aranov (Technion) as part of T
he mathematics of motion\n\n\nAbstract\nJames Maynard received the 2022 fi
elds medal on several groundbreaking results in number theory\, including
the Duffin Schaefer conjecture\, which is the most famous open problem in
metric number theory. The Duffin Schaefer conjecture was open since 1941\,
until 2019\, when Maynard and Koukouloupolus proved this conjecture. In t
his talk\, I will provide a sketch of their proof and briefly discuss some
of Maynard's results regarding prime numbers\, time permitting.\n\nNote
– this talk is a part of the Fields Prize talks at the Technion\, aimed
for a general mathematical audience. For more details\, please contact the
organizers.\n
LOCATION:https://stable.researchseminars.org/talk/mathematicsofmotion/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noy Soffer Aranov (Technion)
DTSTART:20220822T093000Z
DTEND:20220822T103000Z
DTSTAMP:20260404T131149Z
UID:mathematicsofmotion/8
DESCRIPTION:Title: Fields Prize Talks: Sphere Packings - on Maryna Viazovs
ka's result\nby Noy Soffer Aranov (Technion) as part of The mathematic
s of motion\n\n\nAbstract\nA sphere packing is a way to arrange balls of t
he same radius so that no two balls overlap. They appear naturally in crys
tals\, embryonic development and even stacking oranges in the supermarket.
Furthermore\, higher dimensional sphere packings appear in cryptography.
An interesting question in geometry is what is the most efficient sphere p
acking in each dimension. Until recently\, the answer to this question was
known only for dimensions 1\, 2 and 3. In 2017\, Maryna Viazovaska solved
the sphere packing problem in dimensions 8 and 24. Due to these impressiv
e results\, in 2022\, she became the second woman to win the prestigious F
ields medal. In this talk\, I will explain the mathematics behind sphere p
ackings and briefly explain Viazovska’s results.\n\nNote – this talk i
s a part of the Fields Prize talks at the Technion\, aimed for a general m
athematical audience. For more details\, please contact the organizers.\n
LOCATION:https://stable.researchseminars.org/talk/mathematicsofmotion/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alan Sorani (Technion)
DTSTART:20220822T104000Z
DTEND:20220822T114000Z
DTSTAMP:20260404T131149Z
UID:mathematicsofmotion/9
DESCRIPTION:Title: Fields Prize Talks: Hodge Theory in Combinatorics – J
une Huh’s results\nby Alan Sorani (Technion) as part of The mathemat
ics of motion\n\n\nAbstract\nJune Huh received the 2022 Fields Medal for h
is groundbreaking introduction of ideas from Hodge theory into combinatori
cs and for his use of these ideas to prove multiple long-standing conjectu
res. Matroids are combinatorical objects used as models for independence i
n vector spaces and graphs. In his research\, June Huh constructed a “co
homology ring” of a Matroid and showed that properties appearing in Hodg
e theory hold in this setting: The Hard Lefschetz theorem and the Hodge-Ri
emann relations. Using these properties\, Huh proved combinatorical conjec
tures on matroids\, which generalize easily stated problems in Euclidean g
eometry. In this talk\, I will give some combinatorical background\, descr
ibe the methods introduced by Huh and discuss some of the conjectures now
solved through these methods.\n\nNote – this talk is a part of the Field
s Prize talks at the Technion\, aimed for a general mathematical audience.
For more details\, please contact the organizers.\n
LOCATION:https://stable.researchseminars.org/talk/mathematicsofmotion/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ron Rosenthal (Technion)
DTSTART:20220825T093000Z
DTEND:20220825T103000Z
DTSTAMP:20260404T131149Z
UID:mathematicsofmotion/10
DESCRIPTION:Title: Fields Prize Talks: Phase transitions in statistical p
hysics – Hugo Duminil-Copin’s results\nby Ron Rosenthal (Technion)
as part of The mathematics of motion\n\n\nAbstract\nThe past decades have
seen tremendous progress in our understanding of the behavior of many pro
babilistic models related to statistical mechanics and in particular their
behavior near their “critical point”. In this talk we will provide in
troduction to such models and discuss the contribution of Hugo Duminil-Cop
in and his collaborators to these developments.\n\nNote – this talk is a
part of the Fields Prize talks at the Technion\, aimed for a general math
ematical audience. For more details\, please contact the organizers.\n
LOCATION:https://stable.researchseminars.org/talk/mathematicsofmotion/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Teddy Lazebnik (University College London)
DTSTART:20221114T120000Z
DTEND:20221114T133000Z
DTSTAMP:20260404T131149Z
UID:mathematicsofmotion/11
DESCRIPTION:Title: SciMED: A Computational Framework For Physics-Informed
Symbolic Regression with Scientist-In-The-Loop\nby Teddy Lazebnik (Un
iversity College London) as part of The mathematics of motion\n\n\nAbstrac
t\nDiscovering a meaningful\, dimensionally homogeneous\, symbolic express
ion that explains experimental data is a fundamental challenge in many sci
entific fields. We present a novel\, open-source computational framework c
alled Scientist-Machine Equation Detector (SciMED)\, which integrates scie
ntific discipline wisdom in a scientist-in-the-loop approach with state-of
-the-art symbolic regression (SR) methods.\n\nSciMED combines a genetic al
gorithm-based wrapper selection method with automatic machine learning and
two levels of SR methods. We test SciMED on four configurations of the se
ttling of a sphere with and without a non-linear aerodynamic drag force. W
e show that SciMED is sufficiently robust to discover the correct physical
ly meaningful symbolic expressions from noisy data. Our results indicate b
etter performance on these tasks than the state-of-the-art SR software pac
kage.\n
LOCATION:https://stable.researchseminars.org/talk/mathematicsofmotion/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Taehyeong Kim (Technion)
DTSTART:20221121T103000Z
DTEND:20221121T120000Z
DTSTAMP:20260404T131149Z
UID:mathematicsofmotion/12
DESCRIPTION:Title: Entropy rigidity and its application to Diophantine ap
proximation\nby Taehyeong Kim (Technion) as part of The mathematics of
motion\n\n\nAbstract\nIn 1985\, Dani studied the connection between homog
eneous dynamics and Diophantine approximation\, which is called Dani’s c
orrespondence. Since then\, various dynamical methods have been widely use
d in the study of metric Diophantine approximation.\n\nIn this talk\, we m
ainly focus on dynamical entropy on homogeneous spaces. We first review th
e entropy rigidity on homogeneous dynamics and study its application to Di
ophantine approximation following Lim-de Saxcé-Shapira (2018). Finally\,
we introduce an effective version of entropy rigidity and extend the previ
ous result by Lim-de Saxcé-Shapira. This is joint work with Wooyeon Kim a
nd Seonhee Lim.\n\nNote – this is a joint talk with the GDRT seminar in
the Technion.\n
LOCATION:https://stable.researchseminars.org/talk/mathematicsofmotion/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anurag Rao (Technion)
DTSTART:20221121T120000Z
DTEND:20221121T133000Z
DTSTAMP:20260404T131149Z
UID:mathematicsofmotion/13
DESCRIPTION:Title: Dynamical questions arising from Dirichlet’s theorem
on Diophantine approximation\nby Anurag Rao (Technion) as part of The
mathematics of motion\n\n\nAbstract\nWe study the notion of Dirichlet imp
rovability in a variety of settings and make a comparison study between Di
richlet-improvable numbers and badly-approximable numbers as initiated by
Davenport-Schmidt. The question we try to answer\, in each of the settings
\, is – whether the set of badly-approximable numbers is contained in th
e set of Dirichlet-improvable numbers. We show how this translates into a
question about the possible limit points of bounded orbits in the space of
two-dimensional lattices under the diagonal flow. Our main result gives a
construction of a full Hausdorff dimension set of lattices with bounded o
rbit and with a prescribed limit point.\n\nNote – this is a joint talk w
ith the GDRT seminar in the Technion.\n
LOCATION:https://stable.researchseminars.org/talk/mathematicsofmotion/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Agamemnon Zafeiropoulos (Technion)
DTSTART:20221128T120000Z
DTEND:20221128T133000Z
DTSTAMP:20260404T131149Z
UID:mathematicsofmotion/14
DESCRIPTION:Title: Poissonian correlations: higher orders and weaker vari
ants\nby Agamemnon Zafeiropoulos (Technion) as part of The mathematics
of motion\n\n\nAbstract\nLet $\\xn \\subseteq [0\,1]$ be sequence of poin
ts in the unit interval. We say that $\\xn$ has Poissonian pair correlatio
ns (PPC) if \\[ \\lim_{N\\to \\infty} \\frac{1}{N}\\#\\Big\\{ m\,n\\ls N\,
m\\neq n : \\|x_m-x_n\\| \\ls \\frac{s}{N} \\Big\\} = 2s \\qquad \\text{
for all } s>0. \\]\n\nIt is known that sequences with PPC are also uniform
ly distributed. We show that the same conclusion is true for sequences wit
h Poissonian correlations of any order $k\\gs 3.$ Moreover we define weake
r variants of the notion of PPC and examine their relations with equidistr
ibution. (Joint work with M. Hauke.)\n\nNote – this is a joint talk with
the GDRT seminar in the Technion.\n
LOCATION:https://stable.researchseminars.org/talk/mathematicsofmotion/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eran Igra (Technion)
DTSTART:20221219T103000Z
DTEND:20221219T120000Z
DTSTAMP:20260404T131149Z
UID:mathematicsofmotion/15
DESCRIPTION:Title: Polynomial dynamics in three dimensional flows\nby
Eran Igra (Technion) as part of The mathematics of motion\n\n\nAbstract\n
Consider a smooth flow with a chaotic attractor in $\\mathbb{R}^3$. Provid
ed the dynamics are sufficiently contracting\, we would expect the first-r
eturn map of the attractor to behave like a one-dimensional map. In partic
ular\, let us consider the Rössler model\, whose first return map were lo
ng known in simulations to behave like n-modal mappings. Can we prove anyt
hing about this peculiar connection analytically?\n\nIn this talk\, we wil
l see how imposing some mild assumptions on the Rössler model (all of whi
ch can be justified numerically) implies how around some heteroclinic para
meters\, the Rössler flow can be described as a suspended quadratic polyn
omial. In particular\, this allows us to describe the parameter space arou
nd the said heteroclinic parameters as a blown-up and suspended period-dou
bling curve.\n\nBased on work in progress.\n
LOCATION:https://stable.researchseminars.org/talk/mathematicsofmotion/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Or Landesberg (Yale University)
DTSTART:20230102T150000Z
DTEND:20230102T163000Z
DTSTAMP:20260404T131149Z
UID:mathematicsofmotion/16
DESCRIPTION:Title: Horospherical group actions and rigidity of infinite m
easures in higher rank\nby Or Landesberg (Yale University) as part of
The mathematics of motion\n\n\nAbstract\nHorospherical group actions on ho
mogeneous spaces exhibit remarkable rigidity\, as first demonstrated by Fu
rstenberg’s proof of unique ergodicity of the horocycle flow on compact
hyperbolic surfaces. Subsequent work by Dani\, Veech\, Margulis and Ratner
led to a complete classification of all finite ergodic measures with resp
ect to such actions. In contrast\, much less is known regarding infinite e
rgodic Radon measures — a natural object to consider in the context of i
nfinite volume homogeneous spaces. In this talk we will describe an infini
te measure rigidity result for horospherical group actions on a certain fa
mily of homogeneous spaces of higher rank. As a consequence we derive a un
ique ergodicity type statement for quotients by Zariski dense Anosov subgr
oups. Based on joint work with Minju Lee\, Elon Lindenstrauss and Hee Oh.\
n
LOCATION:https://stable.researchseminars.org/talk/mathematicsofmotion/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ariel Alexi (Bar Ilan University)
DTSTART:20230109T120000Z
DTEND:20230109T133000Z
DTSTAMP:20260404T131149Z
UID:mathematicsofmotion/17
DESCRIPTION:Title: From the room to the street\, how to control pandemics
from a computational perspective\nby Ariel Alexi (Bar Ilan University
) as part of The mathematics of motion\n\n\nAbstract\nPandemics are becomi
ng more common as the world becomes more urbanized. To minimize their impa
ct and keep life as normal as possible\, governments need to have good pan
demic intervention policies (IPs) in place that consider the behaviors of
people in different types of buildings\, rooms and social contexts. In thi
s study\, we used a model of a diverse heterogeneous population and in sil
ico simulations to see how effective pandemic IPs are in different types o
f enclosed and open spaces\, such as rooms\, buildings\, and streets. Our
results revealed that each building type has a unique pattern of pandemic
spread\, so a customized IP is needed. We also found that time-based IPs\,
like wearing masks\, have a similar effect on pandemic spread across all
four building types\, but space-based IPs\, like social distancing\, vary
significantly.\n
LOCATION:https://stable.researchseminars.org/talk/mathematicsofmotion/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tali Monderer (Technion)
DTSTART:20230116T120000Z
DTEND:20230116T133000Z
DTSTAMP:20260404T131149Z
UID:mathematicsofmotion/18
DESCRIPTION:by Tali Monderer (Technion) as part of The mathematics of moti
on\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/mathematicsofmotion/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ori Katz (Weizmann Institute of Science)
DTSTART:20230123T120000Z
DTEND:20230123T133000Z
DTSTAMP:20260404T131149Z
UID:mathematicsofmotion/19
DESCRIPTION:Title: A Kinematic-Dynamic 3D Model For Density Driven Ocean
Flows\nby Ori Katz (Weizmann Institute of Science) as part of The math
ematics of motion\n\n\nAbstract\nDifferential buoyancy sources at an ocean
surface may induce a density-driven flow that joins faster flow component
s to create a multi-scale\, 3D flow. Potential temperature and salinity ar
e active tracers that determine the ocean’s potential density: their dis
tribution strongly affects the density-driven component\, while the overal
l flow affects their distribution. We present a robust framework that allo
ws one to study the effects of a general prescribed 3D flow on a density-d
riven velocity component through temperature and salinity transport\, by c
onstructing a modular 3D model of intermediate complexity. The model conta
ins an incompressible velocity that couples two advection–diffusion equa
tions for the two tracers. Instead of solving the Navier–Stokes equation
s for the velocity\, we consider a prescribed flow composed of several spa
tially predetermined modes. One of these modes models the density-driven f
low: its spatial form describes a density-driven flow structure and its st
rength is determined dynamically by averaged density differences. The othe
r modes are completely predetermined\, consisting of any incompressible\,
possibly unsteady\, 3D flow\, e.g.\, as determined by kinematic models\, o
bservations\, or simulations. The result is a hybrid kinematic–dynamic m
odel\, formulated as a nonlinear\, weakly coupled system of two non-local
PDEs. We prove its well-posedness in the sense of Hadamard and obtain a pr
iori rigorous bounds regarding analytical solutions. When the relevant Ray
leigh number is small enough\, we show\, both rigorously and numerically\,
that for all initial conditions\, the corresponding solutions converge to
a unique steady state. Motivated by the Atlantic Meridional Overturning C
irculation\, the model’s relevance to oceanic systems is demonstrated by
tuning the parameters to mimic the North Atlantic ocean. We show that in
one limit the model may recover a simplified oceanic box model\, including
a bi-stable regime\, and in another limit a kinematic model of oceanic ch
aotic advection\, suggesting it can be utilized to study spatially depende
nt feedback processes in the ocean.\n
LOCATION:https://stable.researchseminars.org/talk/mathematicsofmotion/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Ingebretson (University of Illinois Chicago)
DTSTART:20230404T070000Z
DTEND:20230404T083000Z
DTSTAMP:20260404T131149Z
UID:mathematicsofmotion/20
DESCRIPTION:Title: On the symbolic dynamics and fractal geometry of the K
uperberg minimal set\nby Daniel Ingebretson (University of Illinois Ch
icago) as part of The mathematics of motion\n\n\nAbstract\nIn 1994\, Kryst
yna Kuperberg disproved the smooth Seifert conjecture by exhibiting a smoo
th flow on the 3-sphere with no periodic orbits. This example was later fo
und to have a unique minimal set with a complicated geometry. In this talk
\, we will summarize Kuperberg's construction and explore some dynamical a
nd geometric properties of the minimal set.\n
LOCATION:https://stable.researchseminars.org/talk/mathematicsofmotion/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Łukasz Cholewa (AGH University of Science and Technology)
DTSTART:20230418T123000Z
DTEND:20230418T140000Z
DTSTAMP:20260404T131149Z
UID:mathematicsofmotion/21
DESCRIPTION:Title: On dynamics of expanding Lorenz maps\nby Łukasz C
holewa (AGH University of Science and Technology) as part of The mathemati
cs of motion\n\n\nAbstract\nLorenz maps are piecewise monotone interval ma
ps with a single discontinuity. Such maps appear as Poincaré maps in geom
etric models of well known Lorenz attractor\, but they also have important
connections with number theory and fractal geometry. In this talk I will
discuss two approaches to analyzing the dynamics of Lorenz maps. The rst o
ne is presenting expanding Lorenz map as a continuous map acting on the Ca
ntor space by using a procedure called Standard doubling points constructi
on. The second approach is based on the kneading theory. It allows us to d
escribe the trajectory of any point under a given expanding Lorenz map by
a certain binary sequence and use the symbolic dynamics to study this map.
\n\nI will also present some applications of introduced tools. In particul
ar\, I will show that $α$-limit sets in Lorenz maps do not have to be com
pletely invariant by constructing an appropriate example.\nThis result and
its consequences indicate the existence of incorrect statements in the li
terature (cf. Yiming Ding\, Renormalization and $α$-limit set for expandi
ng Lorenz maps\, 2011). I will also\ndiscuss some recent progress in impro
ving these statements. This talk will be based on a joint work with Piotr
Oprocha.\n
LOCATION:https://stable.researchseminars.org/talk/mathematicsofmotion/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Snir Hordan (Technion)
DTSTART:20230613T113000Z
DTEND:20230613T130000Z
DTSTAMP:20260404T131149Z
UID:mathematicsofmotion/22
DESCRIPTION:Title: Complete Neural Networks for Complete Euclidean Graphs
\nby Snir Hordan (Technion) as part of The mathematics of motion\n\n\n
Abstract\nA point cloud is a collection of n points in d-dimensional space
\, where typically n applications $d = 3$. Machine learning on point cloud
s has garnered much interest in the ML community\, with applications in ch
emistry\, physical systems\, and even image processing. Many successful ar
chitectures for point clouds are invariant by construction to the natural
symmetries of point clouds: permutations and rigid motions. Yet\, to date\
, no architecture with polynomial complexity is known to be complete\, tha
t is\, able to distinguish between any pair of non-isomorphic point clouds
.\n\nWe will show how we can remedy this theoretical gap via the Weisfeile
r-Leman test. The Weisfeiler-Leman Graph Isomorphism test has long been a
cornerstone test in the combinatorial graph setting. It characterizes each
subgraph by its adjacency structure and then uses a notion of a subgraph
’s neighborhood to iteratively refine this characterization. This proces
s is reminiscent of message-passing schemes in GNNs and has thus garnered
keen interest in the machine learning community. It has inspired neural ne
twork architectures and is a benchmark for determining the\nexpressivity o
f GNNs. While WL has been applied in the Euclidean setting\, it was done m
ostly experimentally and with vague theoretical foundations.\n\nIn this ta
lk\, we show that point clouds can be completely determined\, up to permut
ation and rigid motion\, by applying the 3-WL graph isomorphism test to th
e point cloud’s centralized Gram matrix. Moreover\, we formulate a Eucli
dean variant of the 2-WL test and show that it is also sufficient to achie
ve completeness. We then show how our complete Euclidean WL tests can be s
imulated by a Euclidean graph neural network of moderate size and demonstr
ate their separation capability on highly-symmetrical point clouds. This t
alk aims to engage a broad audience\, assuming no prior knowledge of the f
ield.\n\nBased on joint work with Nadav Dym and Tal Amir.\n
LOCATION:https://stable.researchseminars.org/talk/mathematicsofmotion/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Natalia Wodka-Cholewa (AGH University of Science and Technology)
DTSTART:20230516T080000Z
DTEND:20230516T093000Z
DTSTAMP:20260404T131149Z
UID:mathematicsofmotion/23
DESCRIPTION:Title: Computer assisted proof of diffusion - application to
PER3BP\nby Natalia Wodka-Cholewa (AGH University of Science and Techno
logy) as part of The mathematics of motion\n\n\nAbstract\nIn this talk we
will consider the Planar Elliptic Restricted Three Body Problem (PER3BP)\,
\nwhich describes the motion of a massless body in gravitational influence
of two large bodies\n- we call them primaries. The elliptic problem is tr
eated as a perturbation of the circular\nproblem (PCR3BP) and the perturba
tion parameter ε is the eccentricity of the primaries.\nIn [1] we present
a computer assisted proof of diffusion of the considered problem\, in a\n
Jupiter-Sun system. You can find an analytic proof of diffusion in the PER
3BP\, but it required\nthat the mass of one of the primaries is sufficient
ly small\, and that the angular momentum of\nthe massless particle is suff
iciently large.\nThe system we study has a normally hyperbolic invariant m
anifold (NHIM) before the\nperturbation. It has stable and unstable manifo
lds\, which intersect transversally. Diffusion\nmechanism that we used is
based on existence of trajectories that shadow this transversal\nintersect
ions and change energy under the influence of the perturbation. We show th
at for\nsufficiently small perturbations we have orbits with explicit ener
gy changes. The change does\nnot depend on the size of the perturbation.\n
\nThis talk is based on joint work with Maciej Capinski.\n\nReferences\n[1
] Capi ́nski Maciej\, Wodka-Cholewa Natalia\, Computer Assisted Proof of
Drift Orbits Along\nNormally Hyperbolic Manifolds II: Application to the R
estricted Three Body Problem\,\nCommunications in Nonlinear Science and Nu
merical Simulation 111 (2022) 106424. doi:\nhttps://doi.org/10.1016/j.cnsn
s.2022.106424.\n
LOCATION:https://stable.researchseminars.org/talk/mathematicsofmotion/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Itamar Vigodorovich (Weizmann Institute)
DTSTART:20230510T123000Z
DTEND:20230510T140000Z
DTSTAMP:20260404T131149Z
UID:mathematicsofmotion/24
DESCRIPTION:Title: Stability of groups and dynamical systems\nby Itam
ar Vigodorovich (Weizmann Institute) as part of The mathematics of motion\
n\n\nAbstract\nFor an homeomorphism T on a compact metric space X\, we may
ask the following stability question: is every almost orbit close to an a
ctual orbit? This property holds in many hyperbolic systems\, and it impli
es density of periodic measures in the space of all invariant probability
measures. \n\nAfter discussing this property\, I will relate it to group
stability: is every almost homomorphism close to an acutal homorphism? For
example\, when the group under consideration is Z^2\, this is related to
the classical question in linear algebra of whether two matrices that almo
st commute must be nearby matrices that actually do commute. \n\nThe rela
tion between these two topic goes through harmonic analysis\, and more spe
cifically character theory. \n\nThe talk is based on a joint work with Ar
ie Levit.\n
LOCATION:https://stable.researchseminars.org/talk/mathematicsofmotion/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Goldberg (Technion)
DTSTART:20230517T093000Z
DTEND:20230517T103000Z
DTSTAMP:20260404T131149Z
UID:mathematicsofmotion/25
DESCRIPTION:Title: Abel Prize Talk - Luis Caffarelli\, the Messi of Math<
/a>\nby Daniel Goldberg (Technion) as part of The mathematics of motion\n\
n\nAbstract\nHow does the temperature around a cube of ice evolve as it me
lts? (Properties of the Stefan problem)\n\nCan a continuous flow of water
suddenly spin out of control? (Blow-up of the Navier-Stokes equation)\n\nH
ow does a membrane look when it is placed around an object? (The Obstacle
problem)\n\nThese seemingly simple physical questions have deep mathematic
al solutions (or partial solutions). Luis Caffarelli\, an argentine mathem
atician dubbed the "Messi of Mathematics" studies these problems and provi
des insightful answers. So much so that he is given the 2023 Abel Prize fo
r his contribution to Partial Differential Equations. He worked on free bo
undary problems such as the ones described above as well as on the Monge-A
mpère equation.\n\nIn this talk we shall give a brief overview of the Nav
ier-Stokes equation\, the Stefan and Obstacle problems as well as some of
Luis Caffarelli's corresponding results.\n\nFor more details and registrat
ion\, please enter the following link - \n\nhttps://mathematicsofmotion.wo
rdpress.com/2023/05/07/luis-caffarelli-the-messi-of-math/\n
LOCATION:https://stable.researchseminars.org/talk/mathematicsofmotion/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lior Alon (MIT)
DTSTART:20230523T143000Z
DTEND:20230523T160000Z
DTSTAMP:20260404T131149Z
UID:mathematicsofmotion/26
DESCRIPTION:Title: Gap Distribution of Fourier Quasicrystals\nby Lior
Alon (MIT) as part of The mathematics of motion\n\n\nAbstract\nThe concep
t of "quasi-periodic" sets\, functions\, and measures is prevalent in dive
rse mathematical fields such as Mathematical Physics\, Fourier Analysis\,
and Number Theory. In natural science\, Shechtman was awarded the 2011 Nob
el Prize for the discovery of materials with\nquasi-periodic atomic struct
ures\, which are now known as Quasicrystals. \n\nThis talk will focus on
one-dimensional Fourier quasicrystals (FQ). The Poisson summation formula
shows that counting measure of any discrete periodic set has the surprisin
g property\, its Fourier transform is also discrete. The counting measure
of a discrete set rarely possesses a discrete Fourier transform. Consequen
tly\, a non-periodic set exhibiting this unique trait\, along with additio
nal technical conditions\, is referred to as a Fourier quasicrystal (FQ).
For a considerable period\, the existence of a non-periodic counting measu
re FQ with bounded gaps\, as pondered by Meyer\, remained uncertain. Howev
er\, in 2020\, Kurasov and Sarnak provided a groundbreaking example\, illu
strating such a measure and presenting a general construction method for F
Qs. Their approach involves constraining the zero sets of multivariate Lee
-Yang polynomials to irrational lines within the torus.\n\nIn general\, it
is unlikely that the counting measure of a discrete set would have a disc
rete Fourier transform. A non-periodic set with this property\, and some a
dditional technical conditions\, is called a Fourier quasicrystal (FQ). A
long-standing question of Meyer was whether there exists a non-periodic
counting measure FQ with bounded gaps. In 2020\, Kurasov and Sarnak pro
vided an example of such\, and gave a general construction of FQs\, by re
stricting the zero sets of multivariate Lee-Yang polynomials to irrationa
l lines in the torus. \n\nDuring this talk I will present a recent work\,
showing that this construction generates all sets whose counting measure
is an FQ\, and that generically these sets are non-periodic with bounded g
aps. Furthermore\, leveraging the ergodicity of irrational linear flows o
n the torus\, we show that the gaps in such a set have a well-defined dis
tribution with properties that can be deduced from the polynomial's struct
ure. \n\nThis talk aims to engage a broad audience\, assuming no prior kn
owledge in the field.\n\nBased on joint works with Alex Cohen and Cynthia
Vinzant.\n
LOCATION:https://stable.researchseminars.org/talk/mathematicsofmotion/26/
END:VEVENT
END:VCALENDAR