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BEGIN:VEVENT
SUMMARY:Martin Mion-Mouton (Technion)
DTSTART:20220320T110000Z
DTEND:20220320T123000Z
DTSTAMP:20260422T225822Z
UID:mathematicsofmotion/1
DESCRIPTION:Title: Partially hyperbolic diffeomorphisms of contact type and path
geometries\nby Martin Mion-Mouton (Technion) as part of The mathematic
s of motion\n\n\nAbstract\nAnosov-contact flows with smooth invariant dist
ributions have been classified by successive works of Ghys (in dimension t
hree) and Benoist-Foulon-Labourie (in any dimension) in the 90’s. In thi
s talk\, we will be interested with the analog question for discrete-time
dynamics\, that is for the partially hyperbolic diffeomorphisms – that h
ave a dynamical behaviour close to the time-one of an Anosov flow. More pr
ecisely\, we will present the classification of three-dimensional partiall
y hyperbolic diffeomorphisms (without wandering points) of contact type ha
ving smooth invariant distributions. We will see that the absence of the f
low heavily changes the situation\, and that the rigid geometric structure
defined by the stable and unstable distributions\, called a path geometry
\, plays a central role in this study through the point of view of Cartan
geometries.\n
LOCATION:https://researchseminars.org/talk/mathematicsofmotion/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anette Karrer (Technion)
DTSTART:20220410T100000Z
DTEND:20220410T113000Z
DTSTAMP:20260422T225822Z
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 CAT(0) gr
oup is a finitely generated group that acts nicely on a CAT(0) space\, i.e
. a geodesic metric space of non-positive curvature. Associated to such sp
aces are different kinds of topological spaces\, called boundaries on whic
h the group acts naturally. This enables us to study dynamics on these bou
ndaries.\n\nIn this talk I will explain what is meant by “classical Nort
h-south-dynamics” on these boundaries. Then I will describe a generaliza
tion introduced by Guralnik and Swenson that leads to a certain higher-dim
ensional version of classical North-south-dynamics.\n
LOCATION:https://researchseminars.org/talk/mathematicsofmotion/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tsviqa Lakrec (Universität Zürich)
DTSTART:20220424T100000Z
DTEND:20220424T113000Z
DTSTAMP:20260422T225822Z
UID:mathematicsofmotion/3
DESCRIPTION:by Tsviqa Lakrec (Universität Zürich) as part of The mathema
tics of motion\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/mathematicsofmotion/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Goldberg (Technion)
DTSTART:20220508T100000Z
DTEND:20220508T113000Z
DTSTAMP:20260422T225822Z
UID:mathematicsofmotion/4
DESCRIPTION:Title: Surface Diffusion\; Well Posedness and Stability\nby Danie
l Goldberg (Technion) as part of The mathematics of motion\n\n\nAbstract\n
In the physical study of solid state materials multiple geometric evolutio
n equations arise. We examine one of them\, Surface Diffusion. It is a fou
rth order nonlinear parabolic Partial Differential Equation. We can ask th
e following questions: For which initial conditions is there a unique solu
tion? In which spaces does the solution live? What is its general behaviou
r? In this talk we will delve into the Well-Posedness of Surface Diffusion
by using the theory of Maximal Regularity and into the stability of its s
olutions near steady states by taking advantage of its Gradient Flow prope
rty.\n
LOCATION:https://researchseminars.org/talk/mathematicsofmotion/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Tsodikovich (Tel Aviv University)
DTSTART:20220522T100000Z
DTEND:20220522T113000Z
DTSTAMP:20260422T225822Z
UID:mathematicsofmotion/5
DESCRIPTION:Title: A Billiard analogue of the Blaschke-Santalo inequality\nby
Daniel Tsodikovich (Tel Aviv University) as part of The mathematics of mo
tion\n\n\nAbstract\nThe Blaschke-Santalo inequality is a classical inequal
ity in convex geometry. This inequality is about the product of the volume
s of a convex body and its dual. In this talk we investigate an analogue o
f this inequality\, where the volume is replaced with the length of the sh
ortest billiard trajectory. We focus on the two dimensional case. We will
describe what the analogue of the “Santalo point” is in this setting\,
show an analogue of the inequality itself\, and discuss maximizers in cla
sses of polygons.\n
LOCATION:https://researchseminars.org/talk/mathematicsofmotion/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eran Igra (Technion)
DTSTART:20220619T100000Z
DTEND:20220619T113000Z
DTSTAMP:20260422T225822Z
UID:mathematicsofmotion/6
DESCRIPTION:Title: Knots and Chaos in the Rössler System\nby Eran Igra (Tech
nion) as part of The mathematics of motion\n\n\nAbstract\nThe Rössler sys
tem is the “minimal” model for chaos\, in the sense that it is “almo
st” linear – at least with respect to other well-known chaotic systems
. Despite that\, it generates a flow which exhibits many interesting prope
rties – from spiral-like homoclinic bifrucations to period-doubling rout
es to chaos. However\, most results on the Rössler System are numeric in
nature\, and little is known rigorously about it. In this talk we will see
how imposing mild assumptions on the dynamics can allow us to draw far-re
aching conclusions. In particular\, we will prove how under these assumpti
ons it is possible to rigorously verify some of the numerics observed in t
he Rössler System.\n\nBased on joint work with Prof. Tali Pinsky.\n
LOCATION:https://researchseminars.org/talk/mathematicsofmotion/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noy Soffer-Aranov (Technion)
DTSTART:20220825T104000Z
DTEND:20220825T114000Z
DTSTAMP:20260422T225822Z
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 The math
ematics of motion\n\n\nAbstract\nJames Maynard received the 2022 fields me
dal on several groundbreaking results in number theory\, including the Duf
fin 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 this tal
k\, I will provide a sketch of their proof and briefly discuss some of May
nard'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 ge
neral mathematical audience. For more details\, please contact the organiz
ers.\n
LOCATION:https://researchseminars.org/talk/mathematicsofmotion/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noy Soffer Aranov (Technion)
DTSTART:20220822T093000Z
DTEND:20220822T103000Z
DTSTAMP:20260422T225822Z
UID:mathematicsofmotion/8
DESCRIPTION:Title: Fields Prize Talks: Sphere Packings - on Maryna Viazovska's re
sult\nby Noy Soffer Aranov (Technion) as part of The mathematics of mo
tion\n\n\nAbstract\nA sphere packing is a way to arrange balls of the same
radius so that no two balls overlap. They appear naturally in crystals\,
embryonic development and even stacking oranges in the supermarket. Furthe
rmore\, higher dimensional sphere packings appear in cryptography. An inte
resting question in geometry is what is the most efficient sphere packing
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 sp
here packing problem in dimensions 8 and 24. Due to these impressive resul
ts\, in 2022\, she became the second woman to win the prestigious Fields m
edal. In this talk\, I will explain the mathematics behind sphere packings
and briefly explain Viazovska’s results.\n\nNote – this talk is a par
t of the Fields Prize talks at the Technion\, aimed for a general mathemat
ical audience. For more details\, please contact the organizers.\n
LOCATION:https://researchseminars.org/talk/mathematicsofmotion/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alan Sorani (Technion)
DTSTART:20220822T104000Z
DTEND:20220822T114000Z
DTSTAMP:20260422T225822Z
UID:mathematicsofmotion/9
DESCRIPTION:Title: Fields Prize Talks: Hodge Theory in Combinatorics – June Huh
’s results\nby Alan Sorani (Technion) as part of The mathematics of
motion\n\n\nAbstract\nJune Huh received the 2022 Fields Medal for his grou
ndbreaking introduction of ideas from Hodge theory into combinatorics and
for his use of these ideas to prove multiple long-standing conjectures. Ma
troids are combinatorical objects used as models for independence in vecto
r spaces and graphs. In his research\, June Huh constructed a “cohomolog
y ring” of a Matroid and showed that properties appearing in Hodge theor
y hold in this setting: The Hard Lefschetz theorem and the Hodge-Riemann r
elations. Using these properties\, Huh proved combinatorical conjectures o
n matroids\, which generalize easily stated problems in Euclidean geometry
. In this talk\, I will give some combinatorical background\, describe 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 Fields Prize
talks at the Technion\, aimed for a general mathematical audience. For mo
re details\, please contact the organizers.\n
LOCATION:https://researchseminars.org/talk/mathematicsofmotion/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ron Rosenthal (Technion)
DTSTART:20220825T093000Z
DTEND:20220825T103000Z
DTSTAMP:20260422T225822Z
UID:mathematicsofmotion/10
DESCRIPTION:Title: Fields Prize Talks: Phase transitions in statistical physics
– Hugo Duminil-Copin’s results\nby Ron Rosenthal (Technion) as par
t of The mathematics of motion\n\n\nAbstract\nThe past decades have seen t
remendous progress in our understanding of the behavior of many probabilis
tic models related to statistical mechanics and in particular their behavi
or near their “critical point”. In this talk we will provide introduct
ion to such models and discuss the contribution of Hugo Duminil-Copin and
his collaborators to these developments.\n\nNote – this talk is a part o
f the Fields Prize talks at the Technion\, aimed for a general mathematica
l audience. For more details\, please contact the organizers.\n
LOCATION:https://researchseminars.org/talk/mathematicsofmotion/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Teddy Lazebnik (University College London)
DTSTART:20221114T120000Z
DTEND:20221114T133000Z
DTSTAMP:20260422T225822Z
UID:mathematicsofmotion/11
DESCRIPTION:Title: SciMED: A Computational Framework For Physics-Informed Symbol
ic Regression with Scientist-In-The-Loop\nby Teddy Lazebnik (Universit
y College London) as part of The mathematics of motion\n\n\nAbstract\nDisc
overing a meaningful\, dimensionally homogeneous\, symbolic expression tha
t explains experimental data is a fundamental challenge in many scientific
fields. We present a novel\, open-source computational framework called S
cientist-Machine Equation Detector (SciMED)\, which integrates scientific
discipline wisdom in a scientist-in-the-loop approach with state-of-the-ar
t symbolic regression (SR) methods.\n\nSciMED combines a genetic algorithm
-based wrapper selection method with automatic machine learning and two le
vels of SR methods. We test SciMED on four configurations of the settling
of a sphere with and without a non-linear aerodynamic drag force. We show
that SciMED is sufficiently robust to discover the correct physically mean
ingful symbolic expressions from noisy data. Our results indicate better p
erformance on these tasks than the state-of-the-art SR software package.\n
LOCATION:https://researchseminars.org/talk/mathematicsofmotion/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Taehyeong Kim (Technion)
DTSTART:20221121T103000Z
DTEND:20221121T120000Z
DTSTAMP:20260422T225822Z
UID:mathematicsofmotion/12
DESCRIPTION:Title: Entropy rigidity and its application to Diophantine approxima
tion\nby Taehyeong Kim (Technion) as part of The mathematics of motion
\n\n\nAbstract\nIn 1985\, Dani studied the connection between homogeneous
dynamics and Diophantine approximation\, which is called Dani’s correspo
ndence. Since then\, various dynamical methods have been widely used in th
e study of metric Diophantine approximation.\n\nIn this talk\, we mainly f
ocus on dynamical entropy on homogeneous spaces. We first review the entro
py rigidity on homogeneous dynamics and study its application to Diophanti
ne approximation following Lim-de Saxcé-Shapira (2018). Finally\, we intr
oduce an effective version of entropy rigidity and extend the previous res
ult by Lim-de Saxcé-Shapira. This is joint work with Wooyeon Kim and Seon
hee Lim.\n\nNote – this is a joint talk with the GDRT seminar in the Tec
hnion.\n
LOCATION:https://researchseminars.org/talk/mathematicsofmotion/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anurag Rao (Technion)
DTSTART:20221121T120000Z
DTEND:20221121T133000Z
DTSTAMP:20260422T225822Z
UID:mathematicsofmotion/13
DESCRIPTION:Title: Dynamical questions arising from Dirichlet’s theorem on Dio
phantine approximation\nby Anurag Rao (Technion) as part of The mathem
atics of motion\n\n\nAbstract\nWe study the notion of Dirichlet improvabil
ity in a variety of settings and make a comparison study between Dirichlet
-improvable numbers and badly-approximable numbers as initiated by Davenpo
rt-Schmidt. The question we try to answer\, in each of the settings\, is
– whether the set of badly-approximable numbers is contained in the set
of Dirichlet-improvable numbers. We show how this translates into a questi
on about the possible limit points of bounded orbits in the space of two-d
imensional lattices under the diagonal flow. Our main result gives a const
ruction of a full Hausdorff dimension set of lattices with bounded orbit a
nd with a prescribed limit point.\n\nNote – this is a joint talk with th
e GDRT seminar in the Technion.\n
LOCATION:https://researchseminars.org/talk/mathematicsofmotion/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Agamemnon Zafeiropoulos (Technion)
DTSTART:20221128T120000Z
DTEND:20221128T133000Z
DTSTAMP:20260422T225822Z
UID:mathematicsofmotion/14
DESCRIPTION:Title: Poissonian correlations: higher orders and weaker variants\nby Agamemnon Zafeiropoulos (Technion) as part of The mathematics of mot
ion\n\n\nAbstract\nLet $\\xn \\subseteq [0\,1]$ be sequence of points in t
he unit interval. We say that $\\xn$ has Poissonian pair correlations (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 uniformly dist
ributed. We show that the same conclusion is true for sequences with Poiss
onian correlations of any order $k\\gs 3.$ Moreover we define weaker varia
nts of the notion of PPC and examine their relations with equidistribution
. (Joint work with M. Hauke.)\n\nNote – this is a joint talk with the GD
RT seminar in the Technion.\n
LOCATION:https://researchseminars.org/talk/mathematicsofmotion/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eran Igra (Technion)
DTSTART:20221219T103000Z
DTEND:20221219T120000Z
DTSTAMP:20260422T225822Z
UID:mathematicsofmotion/15
DESCRIPTION:Title: Polynomial dynamics in three dimensional flows\nby Eran I
gra (Technion) as part of The mathematics of motion\n\n\nAbstract\nConside
r a smooth flow with a chaotic attractor in $\\mathbb{R}^3$. Provided the
dynamics are sufficiently contracting\, we would expect the first-return m
ap of the attractor to behave like a one-dimensional map. In particular\,
let us consider the Rössler model\, whose first return map were long know
n in simulations to behave like n-modal mappings. Can we prove anything ab
out this peculiar connection analytically?\n\nIn this talk\, we will see h
ow imposing some mild assumptions on the Rössler model (all of which can
be justified numerically) implies how around some heteroclinic parameters\
, the Rössler flow can be described as a suspended quadratic polynomial.
In particular\, this allows us to describe the parameter space around the
said heteroclinic parameters as a blown-up and suspended period-doubling c
urve.\n\nBased on work in progress.\n
LOCATION:https://researchseminars.org/talk/mathematicsofmotion/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Or Landesberg (Yale University)
DTSTART:20230102T150000Z
DTEND:20230102T163000Z
DTSTAMP:20260422T225822Z
UID:mathematicsofmotion/16
DESCRIPTION:Title: Horospherical group actions and rigidity of infinite measures
in higher rank\nby Or Landesberg (Yale University) as part of The mat
hematics of motion\n\n\nAbstract\nHorospherical group actions on homogeneo
us spaces exhibit remarkable rigidity\, as first demonstrated by Furstenbe
rg’s proof of unique ergodicity of the horocycle flow on compact hyperbo
lic surfaces. Subsequent work by Dani\, Veech\, Margulis and Ratner led to
a complete classification of all finite ergodic measures with respect to
such actions. In contrast\, much less is known regarding infinite ergodic
Radon measures — a natural object to consider in the context of infinite
volume homogeneous spaces. In this talk we will describe an infinite meas
ure rigidity result for horospherical group actions on a certain family of
homogeneous spaces of higher rank. As a consequence we derive a unique er
godicity type statement for quotients by Zariski dense Anosov subgroups. B
ased on joint work with Minju Lee\, Elon Lindenstrauss and Hee Oh.\n
LOCATION:https://researchseminars.org/talk/mathematicsofmotion/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ariel Alexi (Bar Ilan University)
DTSTART:20230109T120000Z
DTEND:20230109T133000Z
DTSTAMP:20260422T225822Z
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 pa
rt of The mathematics of motion\n\n\nAbstract\nPandemics are becoming more
common as the world becomes more urbanized. To minimize their impact and
keep life as normal as possible\, governments need to have good pandemic i
ntervention policies (IPs) in place that consider the behaviors of people
in different types of buildings\, rooms and social contexts. In this study
\, we used a model of a diverse heterogeneous population and in silico sim
ulations to see how effective pandemic IPs are in different types of enclo
sed 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 w
earing masks\, have a similar effect on pandemic spread across all four bu
ilding types\, but space-based IPs\, like social distancing\, vary signifi
cantly.\n
LOCATION:https://researchseminars.org/talk/mathematicsofmotion/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tali Monderer (Technion)
DTSTART:20230116T120000Z
DTEND:20230116T133000Z
DTSTAMP:20260422T225822Z
UID:mathematicsofmotion/18
DESCRIPTION:by Tali Monderer (Technion) as part of The mathematics of moti
on\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/mathematicsofmotion/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ori Katz (Weizmann Institute of Science)
DTSTART:20230123T120000Z
DTEND:20230123T133000Z
DTSTAMP:20260422T225822Z
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 mathematics
of motion\n\n\nAbstract\nDifferential buoyancy sources at an ocean surfac
e may induce a density-driven flow that joins faster flow components to cr
eate a multi-scale\, 3D flow. Potential temperature and salinity are activ
e tracers that determine the ocean’s potential density: their distributi
on strongly affects the density-driven component\, while the overall flow
affects their distribution. We present a robust framework that allows one
to study the effects of a general prescribed 3D flow on a density-driven v
elocity component through temperature and salinity transport\, by construc
ting a modular 3D model of intermediate complexity. The model contains an
incompressible velocity that couples two advection–diffusion equations f
or the two tracers. Instead of solving the Navier–Stokes equations for t
he velocity\, we consider a prescribed flow composed of several spatially
predetermined modes. One of these modes models the density-driven flow: it
s spatial form describes a density-driven flow structure and its strength
is determined dynamically by averaged density differences. The other modes
are completely predetermined\, consisting of any incompressible\, possibl
y unsteady\, 3D flow\, e.g.\, as determined by kinematic models\, observat
ions\, or simulations. The result is a hybrid kinematic–dynamic model\,
formulated as a nonlinear\, weakly coupled system of two non-local PDEs. W
e prove its well-posedness in the sense of Hadamard and obtain a priori ri
gorous bounds regarding analytical solutions. When the relevant Rayleigh n
umber is small enough\, we show\, both rigorously and numerically\, that f
or all initial conditions\, the corresponding solutions converge to a uniq
ue steady state. Motivated by the Atlantic Meridional Overturning Circulat
ion\, the model’s relevance to oceanic systems is demonstrated by tuning
the parameters to mimic the North Atlantic ocean. We show that in one lim
it the model may recover a simplified oceanic box model\, including a bi-s
table regime\, and in another limit a kinematic model of oceanic chaotic a
dvection\, suggesting it can be utilized to study spatially dependent feed
back processes in the ocean.\n
LOCATION:https://researchseminars.org/talk/mathematicsofmotion/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Ingebretson (University of Illinois Chicago)
DTSTART:20230404T070000Z
DTEND:20230404T083000Z
DTSTAMP:20260422T225822Z
UID:mathematicsofmotion/20
DESCRIPTION:Title: On the symbolic dynamics and fractal geometry of the Kuperber
g minimal set\nby Daniel Ingebretson (University of Illinois Chicago)
as part of The mathematics of motion\n\n\nAbstract\nIn 1994\, Krystyna Kup
erberg disproved the smooth Seifert conjecture by exhibiting a smooth flow
on the 3-sphere with no periodic orbits. This example was later found to
have a unique minimal set with a complicated geometry. In this talk\, we w
ill summarize Kuperberg's construction and explore some dynamical and geom
etric properties of the minimal set.\n
LOCATION:https://researchseminars.org/talk/mathematicsofmotion/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Łukasz Cholewa (AGH University of Science and Technology)
DTSTART:20230418T123000Z
DTEND:20230418T140000Z
DTSTAMP:20260422T225822Z
UID:mathematicsofmotion/21
DESCRIPTION:Title: On dynamics of expanding Lorenz maps\nby Łukasz Cholewa
(AGH University of Science and Technology) as part of The mathematics of m
otion\n\n\nAbstract\nLorenz maps are piecewise monotone interval maps with
a single discontinuity. Such maps appear as Poincaré maps in geometric m
odels of well known Lorenz attractor\, but they also have important connec
tions with number theory and fractal geometry. In this talk I will discuss
two approaches to analyzing the dynamics of Lorenz maps. The rst one is p
resenting expanding Lorenz map as a continuous map acting on the Cantor sp
ace by using a procedure called Standard doubling points construction. The
second approach is based on the kneading theory. It allows us to describe
the trajectory of any point under a given expanding Lorenz map by a certa
in binary sequence and use the symbolic dynamics to study this map.\n\nI w
ill also present some applications of introduced tools. In particular\, I
will show that $α$-limit sets in Lorenz maps do not have to be completely
invariant by constructing an appropriate example.\nThis result and its co
nsequences indicate the existence of incorrect statements in the literatur
e (cf. Yiming Ding\, Renormalization and $α$-limit set for expanding Lore
nz maps\, 2011). I will also\ndiscuss some recent progress in improving th
ese statements. This talk will be based on a joint work with Piotr Oprocha
.\n
LOCATION:https://researchseminars.org/talk/mathematicsofmotion/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Snir Hordan (Technion)
DTSTART:20230613T113000Z
DTEND:20230613T130000Z
DTSTAMP:20260422T225822Z
UID:mathematicsofmotion/22
DESCRIPTION:Title: Complete Neural Networks for Complete Euclidean Graphs\nb
y Snir Hordan (Technion) as part of The mathematics of motion\n\n\nAbstrac
t\nA point cloud is a collection of n points in d-dimensional space\, wher
e typically n applications $d = 3$. Machine learning on point clouds has g
arnered much interest in the ML community\, with applications in chemistry
\, physical systems\, and even image processing. Many successful architect
ures for point clouds are invariant by construction to the natural symmetr
ies of point clouds: permutations and rigid motions. Yet\, to date\, no ar
chitecture with polynomial complexity is known to be complete\, that 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 Weisfeiler-Leman
test. The Weisfeiler-Leman Graph Isomorphism test has long been a corners
tone test in the combinatorial graph setting. It characterizes each subgra
ph by its adjacency structure and then uses a notion of a subgraph’s nei
ghborhood to iteratively refine this characterization. This process is rem
iniscent of message-passing schemes in GNNs and has thus garnered keen int
erest in the machine learning community. It has inspired neural network ar
chitectures and is a benchmark for determining the\nexpressivity of GNNs.
While WL has been applied in the Euclidean setting\, it was done mostly ex
perimentally and with vague theoretical foundations.\n\nIn this talk\, we
show that point clouds can be completely determined\, up to permutation an
d rigid motion\, by applying the 3-WL graph isomorphism test to the point
cloud’s centralized Gram matrix. Moreover\, we formulate a Euclidean var
iant of the 2-WL test and show that it is also sufficient to achieve compl
eteness. We then show how our complete Euclidean WL tests can be simulated
by a Euclidean graph neural network of moderate size and demonstrate thei
r separation capability on highly-symmetrical point clouds. This talk aims
to engage a broad audience\, assuming no prior knowledge of the field.\n\
nBased on joint work with Nadav Dym and Tal Amir.\n
LOCATION:https://researchseminars.org/talk/mathematicsofmotion/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Natalia Wodka-Cholewa (AGH University of Science and Technology)
DTSTART:20230516T080000Z
DTEND:20230516T093000Z
DTSTAMP:20260422T225822Z
UID:mathematicsofmotion/23
DESCRIPTION:Title: Computer assisted proof of diffusion - application to PER3BP<
/a>\nby Natalia Wodka-Cholewa (AGH University of Science and Technology) a
s part of The mathematics of motion\n\n\nAbstract\nIn this talk we will co
nsider 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 treated a
s a perturbation of the circular\nproblem (PCR3BP) and the perturbation pa
rameter ε is the eccentricity of the primaries.\nIn [1] we present a comp
uter assisted proof of diffusion of the considered problem\, in a\nJupiter
-Sun system. You can find an analytic proof of diffusion in the PER3BP\, b
ut it required\nthat the mass of one of the primaries is sufficiently smal
l\, and that the angular momentum of\nthe massless particle is sufficientl
y large.\nThe system we study has a normally hyperbolic invariant manifold
(NHIM) before the\nperturbation. It has stable and unstable manifolds\, w
hich intersect transversally. Diffusion\nmechanism that we used is based o
n existence of trajectories that shadow this transversal\nintersections an
d change energy under the influence of the perturbation. We show that for\
nsufficiently small perturbations we have orbits with explicit energy chan
ges. 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 O
rbits Along\nNormally Hyperbolic Manifolds II: Application to the Restrict
ed Three Body Problem\,\nCommunications in Nonlinear Science and Numerical
Simulation 111 (2022) 106424. doi:\nhttps://doi.org/10.1016/j.cnsns.2022.
106424.\n
LOCATION:https://researchseminars.org/talk/mathematicsofmotion/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Itamar Vigodorovich (Weizmann Institute)
DTSTART:20230510T123000Z
DTEND:20230510T140000Z
DTSTAMP:20260422T225822Z
UID:mathematicsofmotion/24
DESCRIPTION:Title: Stability of groups and dynamical systems\nby Itamar Vigo
dorovich (Weizmann Institute) as part of The mathematics of motion\n\n\nAb
stract\nFor an homeomorphism T on a compact metric space X\, we may ask th
e following stability question: is every almost orbit close to an actual o
rbit? This property holds in many hyperbolic systems\, and it implies dens
ity of periodic measures in the space of all invariant probability measure
s. \n\nAfter discussing this property\, I will relate it to group stabili
ty: is every almost homomorphism close to an acutal homorphism? For exampl
e\, when the group under consideration is Z^2\, this is related to the cla
ssical question in linear algebra of whether two matrices that almost comm
ute must be nearby matrices that actually do commute. \n\nThe relation be
tween these two topic goes through harmonic analysis\, and more specifical
ly character theory. \n\nThe talk is based on a joint work with Arie Levi
t.\n
LOCATION:https://researchseminars.org/talk/mathematicsofmotion/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Goldberg (Technion)
DTSTART:20230517T093000Z
DTEND:20230517T103000Z
DTSTAMP:20260422T225822Z
UID:mathematicsofmotion/25
DESCRIPTION:Title: Abel Prize Talk - Luis Caffarelli\, the Messi of Math\nby
Daniel Goldberg (Technion) as part of The mathematics of motion\n\n\nAbst
ract\nHow does the temperature around a cube of ice evolve as it melts? (P
roperties of the Stefan problem)\n\nCan a continuous flow of water suddenl
y spin out of control? (Blow-up of the Navier-Stokes equation)\n\nHow does
a membrane look when it is placed around an object? (The Obstacle problem
)\n\nThese seemingly simple physical questions have deep mathematical solu
tions (or partial solutions). Luis Caffarelli\, an argentine mathematician
dubbed the "Messi of Mathematics" studies these problems and provides ins
ightful answers. So much so that he is given the 2023 Abel Prize for his c
ontribution to Partial Differential Equations. He worked on free boundary
problems such as the ones described above as well as on the Monge-Ampère
equation.\n\nIn this talk we shall give a brief overview of the Navier-Sto
kes equation\, the Stefan and Obstacle problems as well as some of Luis Ca
ffarelli's corresponding results.\n\nFor more details and registration\, p
lease enter the following link - \n\nhttps://mathematicsofmotion.wordpress
.com/2023/05/07/luis-caffarelli-the-messi-of-math/\n
LOCATION:https://researchseminars.org/talk/mathematicsofmotion/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lior Alon (MIT)
DTSTART:20230523T143000Z
DTEND:20230523T160000Z
DTSTAMP:20260422T225822Z
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 concept of "q
uasi-periodic" sets\, functions\, and measures is prevalent in diverse mat
hematical fields such as Mathematical Physics\, Fourier Analysis\, and Num
ber Theory. In natural science\, Shechtman was awarded the 2011 Nobel Priz
e for the discovery of materials with\nquasi-periodic atomic structures\,
which are now known as Quasicrystals. \n\nThis talk will focus on one-dim
ensional Fourier quasicrystals (FQ). The Poisson summation formula shows t
hat counting measure of any discrete periodic set has the surprising prope
rty\, its Fourier transform is also discrete. The counting measure of a di
screte set rarely possesses a discrete Fourier transform. Consequently\, a
non-periodic set exhibiting this unique trait\, along with additional tec
hnical conditions\, is referred to as a Fourier quasicrystal (FQ). For a c
onsiderable period\, the existence of a non-periodic counting measure FQ w
ith bounded gaps\, as pondered by Meyer\, remained uncertain. However\, in
2020\, Kurasov and Sarnak provided a groundbreaking example\, illustratin
g such a measure and presenting a general construction method for FQs. The
ir approach involves constraining the zero sets of multivariate Lee-Yang p
olynomials to irrational lines within the torus.\n\nIn general\, it is unl
ikely that the counting measure of a discrete set would have a discrete Fo
urier transform. A non-periodic set with this property\, and some addition
al technical conditions\, is called a Fourier quasicrystal (FQ). A long-s
tanding question of Meyer was whether there exists a non-periodic countin
g measure FQ with bounded gaps. In 2020\, Kurasov and Sarnak provided a
n example of such\, and gave a general construction of FQs\, by restricti
ng the zero sets of multivariate Lee-Yang polynomials to irrational lines
in the torus. \n\nDuring this talk I will present a recent work\, showin
g that this construction generates all sets whose counting measure is an F
Q\, and that generically these sets are non-periodic with bounded gaps. Fu
rthermore\, leveraging the ergodicity of irrational linear flows on the t
orus\, we show that the gaps in such a set have a well-defined distributi
on with properties that can be deduced from the polynomial's structure. \
n\nThis talk aims to engage a broad audience\, assuming no prior knowledge
in the field.\n\nBased on joint works with Alex Cohen and Cynthia Vinzant
.\n
LOCATION:https://researchseminars.org/talk/mathematicsofmotion/26/
END:VEVENT
END:VCALENDAR