BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Michael Entov (Technion)
DTSTART;VALUE=DATE-TIME:20200422T111000Z
DTEND;VALUE=DATE-TIME:20200422T123000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/1
DESCRIPTION:Title: Rigi
dity of Lagrangian tori in K3 surfaces\nby Michael Entov (Technion) as
part of Geometry and Dynamics seminar\n\n\nAbstract\nA Kahler-type form i
s a symplectic form compatible with an integrable \ncomplex structure. She
ridan and Smith previously proved\, using deep \nmethods of homological mi
rror symmetry\, that for any Maslov-zero \nLagrangian torus L in a K3 surf
ace M equipped with a Kahler-type \nform of a *particular kind*\, the inte
gral homology class of L has \nto be non-zero and primitive. I will discus
s how to extend this \nresult to *arbitrary* Kahler-type forms on M using
dynamical \nproperties of the action of the diffeomorphism group of M on t
he \nspace of such forms. These dynamical properties are obtained using \n
a version of Ratner's theorem. This is a joint work in progress \nwith M.V
erbitsky.\n
LOCATION:https://researchseminars.org/talk/GDS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boris Vertman (University of Oldenburg)
DTSTART;VALUE=DATE-TIME:20200506T111000Z
DTEND;VALUE=DATE-TIME:20200506T123000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/2
DESCRIPTION:Title: Mean
curvature flow in Lorentzian space times\nby Boris Vertman (Universit
y of Oldenburg) as part of Geometry and Dynamics seminar\n\n\nAbstract\nHy
persurfaces of zero or constant mean curvature play a central \nrole in th
e proof of the Positive Mass Theorem and also in the \nanalysis of the Cau
chy problem for asymptotically flat space-times. \nMean curvature flow can
be a tool to construct such hypersurfaces. \nWe discuss local existence o
f the flow for non-compact space-like \nhypersurfaces in Robertson-Walker
space-times. This is a joint project \nwith Giuseppe Gentile.\n
LOCATION:https://researchseminars.org/talk/GDS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Ioos (Tel Aviv University)
DTSTART;VALUE=DATE-TIME:20200513T111000Z
DTEND;VALUE=DATE-TIME:20200513T123000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/3
DESCRIPTION:Title: Almo
st-representations of the Lie algebra of SU(2) and quantization of the sph
ere\nby Louis Ioos (Tel Aviv University) as part of Geometry and Dynam
ics seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GDS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tsachik Gelander (Weizmann Institute of Science)
DTSTART;VALUE=DATE-TIME:20200520T111000Z
DTEND;VALUE=DATE-TIME:20200520T123000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/4
DESCRIPTION:Title: Conv
ergence of normalized Betti numbers in nonpositive curvature\nby Tsach
ik Gelander (Weizmann Institute of Science) as part of Geometry and Dynami
cs seminar\n\n\nAbstract\nI will show that if X is any symmetric space oth
er than 3-dimensional \nhyperbolic space and M is any finite volume manifo
ld that is a quotient \nof X\, then the normalized Betti numbers of M are
"testable"\, i.e. one \ncan guess their values by sampling the manifold at
random places. This \nis joint with Abert\, Biringer and Bergeron\, and e
xtends some of our \nolder work with Nikolov\, Raimbault and Samet. The co
ntent of the recent \npaper involves a random discretization process that
converts the "thick \npart" of M into a simplicial complex\, together with
analysis of the \n"thin parts" of M. As a corollary\, we obtain that when
ever X is a higher \nrank irreducible symmetric space and M_i is any seque
nce of distinct \nfinite volume quotients of X\, the normalized Betti numb
ers of the M_i \nconverge to the "L^2-Betti numbers" of X.\n
LOCATION:https://researchseminars.org/talk/GDS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Ivrii (University of Toronto)
DTSTART;VALUE=DATE-TIME:20200527T111000Z
DTEND;VALUE=DATE-TIME:20200527T123000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/5
DESCRIPTION:Title: Heav
y atoms and molecules: Thomas-Fermi and Scott approximations\nby Victo
r Ivrii (University of Toronto) as part of Geometry and Dynamics seminar\n
\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GDS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Mazzucchelli (ENS de Lyon)
DTSTART;VALUE=DATE-TIME:20200603T111000Z
DTEND;VALUE=DATE-TIME:20200603T123000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/6
DESCRIPTION:Title: Clos
ed geodesics on reversible Finsler 2-spheres\nby Marco Mazzucchelli (E
NS de Lyon) as part of Geometry and Dynamics seminar\n\n\nAbstract\nIn thi
s talk\, I will show that two celebrated theorems on closed \ngeodesics of
Riemannian 2-spheres still hold for the larger class \nof reversible Fins
ler 2-spheres: Lusternik-Schnirelmann's theorem \nasserting the existence
of three simple closed geodesics\, and \nBangert-Franks-Hingston's theorem
asserting the existence of \ninfinitely many closed geodesics. I will ske
tch the proofs of \nthese statements\, employing in particular the Finsler
generalization \nof Grayson's curve shortening flow developed by Angenent
-Oaks. \nThis is joint work with Guido De Philippis\, Michele Marini\, and
\nStefan Suhr.\n
LOCATION:https://researchseminars.org/talk/GDS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ran Tessler (Weizmann Institute of Science)
DTSTART;VALUE=DATE-TIME:20200617T111000Z
DTEND;VALUE=DATE-TIME:20200617T123000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/8
DESCRIPTION:Title: Open
r-spin intersection theory\nby Ran Tessler (Weizmann Institute of Sci
ence) as part of Geometry and Dynamics seminar\n\n\nAbstract\nIn 1992 Witt
en conjectured that the intersection theory on the moduli \nof r-spin curv
es gives rise to a Gelfand Dickey tau function\, and \nproved his conjectu
re in genus 0.\nRecently\, in a joint work with Buryak and Clader we made
a similar \nconjecture/construction in the open setting:\nWe conjectured t
hat intersection theory on the moduli of r-spin \nsurfaces with boundaries
should give rise to the Gelfand Dickey *wave* \nfunction and proved it in
genus 0. In my talk I will describe all this\, \nin particular\, I'll exp
lain what is an r-spin structure\, what is the \nGelfand-Dickey hierarchy
and what is the motivation. If time permits\, \na mirror theorem (based on
work with Gross and Kelly) will also be shown.\n
LOCATION:https://researchseminars.org/talk/GDS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emanuel Milman (Technion)
DTSTART;VALUE=DATE-TIME:20200622T111000Z
DTEND;VALUE=DATE-TIME:20200622T123000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/9
DESCRIPTION:Title: Func
tional Inequalities on sub-Riemannian manifolds via QCD\nby Emanuel Mi
lman (Technion) as part of Geometry and Dynamics seminar\n\n\nAbstract\nWe
are interested in obtaining Poincare and log-Sobolev inequalities \non do
mains in sub-Riemannian manifolds (equipped with their natural \nsub-Riema
nnian metric and volume measure).\n\nIt is well-known that strictly sub-Ri
emannian manifolds do not satisfy \nany type of Curvature-Dimension condit
ion CD(K\,N)\, introduced by \nLott-Sturm-Villani some 15 years ago\, so w
e must follow a different \npath. We show that while ideal (strictly) sub-
Riemannian manifolds do \nnot satisfy any type of CD condition\, they do s
atisfy a quasi-convex \nrelaxation thereof\, which we name QCD(Q\,K\,N). A
s a consequence\, these \nspaces satisfy numerous functional inequalities
with exactly the same \nquantitative dependence (up to a factor of Q) as t
heir CD counterparts. \nWe achieve this by extending the localization para
digm to completely \ngeneral interpolation inequalities\, and a one-dimens
ional comparison \nof QCD densities with their "CD upper envelope". We th
us obtain the \nbest known quantitative estimates for (say) the L^p-Poinca
re and \nlog-Sobolev inequalities on domains in the ideal sub-Riemannian s
etting\, \nwhich in particular are independent of the topological dimensio
n. For \ninstance\, the classical Li-Yau / Zhong-Yang spectral-gap estimat
e holds \non all Heisenberg groups of arbitrary dimension up to a factor o
f 4.\n\nNo prior knowledge will be assumed\, and we will (hopefully) expla
in \nall of the above notions during the talk.\n
LOCATION:https://researchseminars.org/talk/GDS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Uri Bader (Weizmann Institute of Science)
DTSTART;VALUE=DATE-TIME:20200624T111000Z
DTEND;VALUE=DATE-TIME:20200624T123000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/10
DESCRIPTION:Title: Tot
ally geodesic subspaces and arithemeticity phenomena in hyperbolic manifol
ds\nby Uri Bader (Weizmann Institute of Science) as part of Geometry a
nd Dynamics seminar\n\n\nAbstract\nIn this talk I will survey a well known
\, still wonderful\, connection \nbetween geometry and arithmetics and dis
cuss old and new results in \nthis topic. The starting point of the story
is Cartan's discovery \nof the correspondence between semisimple Lie group
s and symmetric \nspaces. Borel and Harish-Chandra\, following Siegel\, la
ter realized \na fantastic further relation between arithmetic subgroups o
f semisimple \nLie groups and locally symmetric space - every arithemtic g
roup gives \na locally symmetric space of finite volume. The best known ex
ample \nis the modular curve which is associated in this way with the grou
p \nSL_2(Z). This relation has a partial converse\, going under the name \
n"arithmeticity theorem"\, which was proven\, under a higher rank \nassump
tion\, by Margulis and in some rank one situations by Corlette \nand Gromo
v-Schoen. The rank one setting is related to hyperbolic \ngeometry - real\
, complex\, quaternionic or octanionic.\nThere are several open questions
regarding arithmeticity of locally \nhyperbolic manifolds of finite volume
over the real or complex fields \nand there are empirical evidences relat
ing these questions to the \ngeometry of totally geodesic submanifolds. \n
Recently\, some of these questions were solved by Margulis-Mohammadi \n(re
al hyp. 3-dim)\, Baldi-Ullmo (complex hyp.) and B-Fisher-Miller-Stover. \n
The techniques involve a mixture of ergodic theory\, algebraic groups \nth
eory and hodge theory. After surveying the above story\, explaining \nall
the terms and discussing some open questions\, I hope to have a \nlittle t
ime to say something about the proofs.\n
LOCATION:https://researchseminars.org/talk/GDS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yusuke Kawamoto (Ecole Normale Superieure)
DTSTART;VALUE=DATE-TIME:20200701T111000Z
DTEND;VALUE=DATE-TIME:20200701T123000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/11
DESCRIPTION:Title: Hom
ogeneous quasimorphism\, C^0-topology and Lagrangian intersection\nby
Yusuke Kawamoto (Ecole Normale Superieure) as part of Geometry and Dynamic
s seminar\n\n\nAbstract\nThe goal of the talk is to construct a non-trivia
l homogeneous \nquasimorphism on the group of Hamiltonian diffeomorphisms
of the \n2- and 4-dimensional quadric which is continuous with respect to
both \nC^0-topology and the Hofer metric. This answers a variant of a ques
tion \nof Entov-Polterovich-Py. A comparison of spectral invariants for \n
quantum cohomology rings with different coefficient fields plays a \ncruci
al role in the proof which might be of independent interest. \nIf time per
mits\, we will see how this comparison can be used to answer \na question
of Polterovich-Wu.\n
LOCATION:https://researchseminars.org/talk/GDS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Lobb (Durham University)
DTSTART;VALUE=DATE-TIME:20201028T121000Z
DTEND;VALUE=DATE-TIME:20201028T133000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/12
DESCRIPTION:Title: The
rectangular peg problem\nby Andrew Lobb (Durham University) as part o
f Geometry and Dynamics seminar\n\n\nAbstract\nFor any smooth Jordan curve
and rectangle in the plane\, we show that \nthere exist four points on th
e Jordan curve forming the vertices of a \nrectangle similar to the given
one. Joint work with Josh Greene.\n
LOCATION:https://researchseminars.org/talk/GDS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laszlo Lempert (Purdue University)
DTSTART;VALUE=DATE-TIME:20201104T151000Z
DTEND;VALUE=DATE-TIME:20201104T163000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/13
DESCRIPTION:Title: On
the adjoint action of symplectomorphism groups\nby Laszlo Lempert (Pur
due University) as part of Geometry and Dynamics seminar\n\n\nAbstract\nMo
tivated by constructions in Kähler geometry\, in this talk we consider \n
a compact symplectic manifold $(X\,\\omega)$ and the group $G$ of its \nsy
mplectomorphisms. We study the action of $G$ on the Fréchet space \n$C^\\
infty(X)$ of smooth functions\, by pullback\, and describe properties of \
nconvex functions $p:C^\\infty(X)\\to\\mathbb R$ that are invariant under
this \naction.\n
LOCATION:https://researchseminars.org/talk/GDS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bo Berndtsson (Chalmers University of Technology)
DTSTART;VALUE=DATE-TIME:20201111T121000Z
DTEND;VALUE=DATE-TIME:20201111T133000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/14
DESCRIPTION:Title: Com
plex integrals and Kuperberg's proof of the Bourgain-Milman theorem\nb
y Bo Berndtsson (Chalmers University of Technology) as part of Geometry an
d Dynamics seminar\n\n\nAbstract\nI will show a function version of the Bo
urgain-Milman theorem:\n$$ \\int e^{-\\phi}\\int e^{-\\phi^*}\\geq \\pi^n
$$\,\nif $\\phi$ is a symmetric convex function on $\\R^n$ and $\\phi^*$
is its \nLegendre transform. The proof is inspired by Kuperberg's proof of
the \nBourgain-Milman theorem but uses complex analytic techniques.\n
LOCATION:https://researchseminars.org/talk/GDS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Misha Bialy (Tel Aviv University)
DTSTART;VALUE=DATE-TIME:20201118T121000Z
DTEND;VALUE=DATE-TIME:20201118T133000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/15
DESCRIPTION:Title: The
Birkhoff-Poritsky conjecture for centrally-symmetric billiard tables\
nby Misha Bialy (Tel Aviv University) as part of Geometry and Dynamics sem
inar\n\n\nAbstract\nIn this talk (joint work with A.E. Mironov) I shall di
scuss a recent \nproof of the Birkhoff-Poritsky conjecture for centrally-s
ymmetric \nC^2-smooth convex planar billiards. We assume that the domain
between \nthe invariant curve of 4-periodic orbits and the boundary of the
phase \ncylinder is foliated by C^0-invariant curves. Under this assumpti
on we \nprove that the billiard curve is an ellipse. The main ingredients
of \nthe proof are : (1) the non-standard generating function for convex \
nbilliards\; (2) the remarkable structure of the invariant curve \nconsist
ing of 4-periodic orbits\; and (3) the integral-geometry \napproach initia
ted for rigidity results of circular billiards. \nSurprisingly\, our resul
t yields a Hopf-type rigidity for billiard \nin ellipse.\n
LOCATION:https://researchseminars.org/talk/GDS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vinicius G. B. Ramos (IMPA\, Brazil)
DTSTART;VALUE=DATE-TIME:20201202T151000Z
DTEND;VALUE=DATE-TIME:20201202T163000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/16
DESCRIPTION:Title: Exa
mples around the strong Viterbo conjecture\nby Vinicius G. B. Ramos (I
MPA\, Brazil) as part of Geometry and Dynamics seminar\n\n\nAbstract\nThe
Viterbo conjecture states that the ball maximizes any normalized \nsymplec
tic capacity within all convex sets in R^{2n} of a fixed volume \nand that
it is the unique maximizer. A stronger conjecture says that \nall normali
zed capacities coincide for convex sets. In joint work with \nGutt and Hut
chings\, we prove the stronger conjecture for a somewhat \ndifferent class
of 4-dimensional domains\, namely toric domains with a \ndynamically conv
ex toric boundary. In joint work with Ostrover and Sepe\, \nwe prove that
a 4-dimensional Lagrangian product which is a maximizer \nof the Hofer-Zeh
nder capacity is non-trivially symplectomorphic to a \nball giving further
evidence to the uniqueness claim of Viterbo's \nconjecture. In this talk\
, I will explain the proof of these two results.\n
LOCATION:https://researchseminars.org/talk/GDS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frol Zapolsky (University of Haifa)
DTSTART;VALUE=DATE-TIME:20201125T121000Z
DTEND;VALUE=DATE-TIME:20201125T133000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/17
DESCRIPTION:Title: Rel
ative symplectic cohomology and ideal-valued measures\nby Frol Zapolsk
y (University of Haifa) as part of Geometry and Dynamics seminar\n\n\nAbst
ract\nIn a joint work in progress together with A. Dickstein\, Y. Ganor\,
and \nL. Polterovich we prove new symplectic rigidity results. First\, we
\ncategorify the notion of a heavy subset of a symplectic manifold (due \n
to Entov-Polterovich)\, and in particular provide a simple algebraic \ncri
terion which guarantees that two heavy sets intersect. Next\, we \ntreat i
nvolutive maps defined on a symplectic manifold M\; a smooth \nmap M -> B
is involutive if pullbacks of smooth functions on B Poisson \ncommute. For
such maps we prove a refinement of Entov-Polterovich's \nnondisplaceable
fiber theorem\, as well as a symplectic Tverberg-type \ntheorem\, which ro
ughly says that each involutive map into a manifold \nof sufficiently low
dimension has a fiber which intersects a wide \nfamily of subsets of M.\n\
nAll of these results are proved using a generalized version of Gromov's \
nnotion of ideal-valued measures\, which furnish an easily digestible \nwa
y to package the relevant information. We construct such measures \nusing
relative symplectic cohomology\, an invariant recently introduced \nby U.
Varolgunes\, who also proved the Mayer-Vietoris property for it\, \non whi
ch our work relies in a crucial manner. Our main technical \ninnovation is
the relative symplectic cohomology of a pair\, whose \nconstruction is in
spired by homotopy theory.\n
LOCATION:https://researchseminars.org/talk/GDS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lev Birbrair (Universidade Federal do Ceará\, Brazil)
DTSTART;VALUE=DATE-TIME:20201209T121000Z
DTEND;VALUE=DATE-TIME:20201209T133000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/18
DESCRIPTION:Title: Lip
schitz geometry of surface germs in $\\R^4$: metric knots\nby Lev Birb
rair (Universidade Federal do Ceará\, Brazil) as part of Geometry and Dyn
amics seminar\n\n\nAbstract\nA link at the origin of an isolated singulari
ty of a two-dimensional \nsemialgebraic surface in $\\R^4$ is a topologica
l knot (or link) in $S^3$. \nWe study the connection between the ambient L
ipschitz geometry of \nsemialgebraic surface germs in $\\R^4$ and the knot
theory. Namely\, for \nany knot $K$\, we construct a surface $X_K$ in $\\
R^4$ such that: $X_K$ \nhas a trivial knot at the origin\; the germs $X_K$
are outer bi-Lipschitz \nequivalent for all $K$\; two germs $X_{K}$ and $
X_{K'}$ are ambient \nbi-Lipschitz equivalent only if the knots $K$ and $K
'$ are isotopic.\n
LOCATION:https://researchseminars.org/talk/GDS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Barak Weiss (Tel Aviv University)
DTSTART;VALUE=DATE-TIME:20201216T121000Z
DTEND;VALUE=DATE-TIME:20201216T133000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/19
DESCRIPTION:Title: Erg
odicity of rel foliations on the space of holomorphic one forms\nby Ba
rak Weiss (Tel Aviv University) as part of Geometry and Dynamics seminar\n
\n\nAbstract\nThe rel foliation is a foliation of the moduli space of abel
ian \ndifferentials obtained by "moving the zeroes of the one form while \
nkeeping all absolute periods fixed". It has been studied in complex \nana
lysis and dynamics under different names (isoperiodic foliation\, \nSchiff
er variation\, kernel foliation). Until recent years the question \nof its
ergodicity was wide open. Recently partial results were obtained \nby Cal
samiglia-Deroin-Francaviglia and by Hamenstadt. In our work we \ncompletel
y resolve the ergodicity question. Joint work in progress with \nJon Chaik
a and Alex Eskin\, based on a far-reaching extension of a \ncelebrated res
ult of Eskin and Mirzakhani. All relevant notions will \nbe explained in
the lecture and no prior familiarity with dynamics on \nspaces of one form
s will be assumed.\n
LOCATION:https://researchseminars.org/talk/GDS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ood Shabtai (Tel Aviv University)
DTSTART;VALUE=DATE-TIME:20201223T121000Z
DTEND;VALUE=DATE-TIME:20201223T133000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/20
DESCRIPTION:Title: On
polynomials in two spectral projections of spin operators\nby Ood Shab
tai (Tel Aviv University) as part of Geometry and Dynamics seminar\n\n\nAb
stract\nWe discuss the semiclassical behavior of an arbitrary bivariate \n
polynomial evaluated on a pair of spectral projections of spin \noperators
\, and compare it with its value on a pair of random \nprojections.\n
LOCATION:https://researchseminars.org/talk/GDS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shira Tanny (Tel Aviv University)
DTSTART;VALUE=DATE-TIME:20201230T121000Z
DTEND;VALUE=DATE-TIME:20201230T133000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/21
DESCRIPTION:Title: A m
ax-inequality for spectral invariants of disjointly supported Hamiltonians
\nby Shira Tanny (Tel Aviv University) as part of Geometry and Dynamic
s seminar\n\n\nAbstract\nThe relation between spectral invariants of disjo
intly supported \nHamiltonians and that of their sum was studied by Humili
ere\, Le Roux \nand Seyfaddini on aspherical manifolds. We study this rela
tion in a \nwider setting and derive applications to Polterovich's Poisson
bracket \ninvariant. This is a work in progress.\n
LOCATION:https://researchseminars.org/talk/GDS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vincent Humilière (Sorbonne University)
DTSTART;VALUE=DATE-TIME:20210106T121000Z
DTEND;VALUE=DATE-TIME:20210106T133000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/22
DESCRIPTION:Title: Is
the group of compactly supported area preserving homeomorphisms of the 2-d
isk simple?\nby Vincent Humilière (Sorbonne University) as part of Ge
ometry and Dynamics seminar\n\n\nAbstract\nThis long standing open problem
has been recently solved in joint work \nwith Dan Cristofaro-Gardiner and
Sobhan Seyfaddini. I will present some \nbackground and the main ideas th
at lead to the proof. It is based on \ntools from symplectic topology and
more precisely on a theory due to \nHutchings\, called Periodic Floer Homo
logy.\n
LOCATION:https://researchseminars.org/talk/GDS/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Mangoubi (The Hebrew University of Jerusalem)
DTSTART;VALUE=DATE-TIME:20210113T121000Z
DTEND;VALUE=DATE-TIME:20210113T133000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/23
DESCRIPTION:Title: A L
ocal version of Courant's Nodal domain Theorem\nby Dan Mangoubi (The H
ebrew University of Jerusalem) as part of Geometry and Dynamics seminar\n\
n\nAbstract\nLet u_k be an eigenfunction of a vibrating string (with fixed
ends) \ncorresponding to the k-th eigenvalue. It is not difficult to show
that \nthe number of zeros of u_k is exactly k+1. Equivalently\, the numb
er of \nconnected components of the complement of $u_k=0$ is $k$.\n\nIn 19
23 Courant found that in higher dimensions (considering eigenfunctions \no
f the Laplacian on a closed Riemannian manifold M) the number of connected
\ncomponents of the open set $M\\setminus {u_k=0}$ is at most $k$.\n\nIn
1988 Donnelly and Fefferman gave a bound on the number of connected \ncomp
onents of $B\\setminus {u_k=0}$\, where $B$ is a ball in $M$. However\, \n
their estimate was not sharp (even for spherical harmonics).\n\nWe describ
e the ideas which give the sharp bound on the number of connected \ncompon
ents in a ball. The talk is based on a joint work with S. Chanillo\, \nA.
Logunov and E. Malinnikova\, with a contribution due to F. Nazarov.\n
LOCATION:https://researchseminars.org/talk/GDS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boaz Klartag (Weizmann Institute of Science)
DTSTART;VALUE=DATE-TIME:20210303T121000Z
DTEND;VALUE=DATE-TIME:20210303T133000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/24
DESCRIPTION:Title: Rig
idity of Riemannian embeddings of discrete metric spaces\nby Boaz Klar
tag (Weizmann Institute of Science) as part of Geometry and Dynamics semin
ar\n\n\nAbstract\nLet M be a complete\, connected Riemannian surface and\n
suppose that S is a discrete subset of M. What can we learn about M\nfrom
the knowledge of all distances in the surface between pairs of\npoints of
S? We prove that if the distances in S correspond to the\ndistances in a 2
-dimensional lattice\, or more generally in an\narbitrary net in R^2\, the
n M is isometric to the Euclidean plane. We\nthus find that Riemannian emb
eddings of certain discrete metric spaces\nare rather rigid. A corollary i
s that a subset of Z^3 that strictly\ncontains a two-dimensional lattice c
annot be isometrically embedded in\nany complete Riemannian surface. This
is a joint work with M. Eilat.\n
LOCATION:https://researchseminars.org/talk/GDS/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Cristofaro-Gardiner (IAS Princeton\; University of Californ
ia\, Santa Cruz)
DTSTART;VALUE=DATE-TIME:20210310T121000Z
DTEND;VALUE=DATE-TIME:20210310T133000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/25
DESCRIPTION:Title: The
subleading asymptotics of the ECH spectrum\nby Daniel Cristofaro-Gard
iner (IAS Princeton\; University of California\, Santa Cruz) as part of Ge
ometry and Dynamics seminar\n\n\nAbstract\nEmbedded contact homology can b
e used to associate a sequence of spectral \ninvariants\, called ECH spect
ral invariants\, to any closed three-manifold \nwith a contact form. In p
revious joint work\, we proved a “Volume Property” \nthat recovers the
volume of any such manifold from the asymptotics of its \nECH spectral in
variants. I will discuss recent work aimed at better \nunderstanding the
subleading asymptotics of this sequence. The main \nsubject of my talk wi
ll be a joint work with Nikhil Savale in which we \nprove a new bound on t
he growth rate of the subleading asymptotics. \nI will also briefly menti
on a conjecture\, due to Hutchings\, concerning \nrecovering the “contac
t Ruelle invariant” from the subleading asymptotics.\n
LOCATION:https://researchseminars.org/talk/GDS/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Faifman (Tel Aviv University)
DTSTART;VALUE=DATE-TIME:20210317T121000Z
DTEND;VALUE=DATE-TIME:20210317T133000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/26
DESCRIPTION:Title: Aro
und the Funk metric and its billiards\nby Dmitry Faifman (Tel Aviv Uni
versity) as part of Geometry and Dynamics seminar\n\n\nAbstract\nThe Funk
metric in the interior of a convex body is a lesser known \nrelative of th
e projectively-invariant Hilbert metric\, yet in some \nways simpler and m
ore natural. Starting with a few simple observations\, \nwe will explore s
ome Funk-inspired generalizations of well-known \nresults in the geometry
of normed spaces and Minkowski billiards\, \nsuch as Sch\\"affer's dual gi
rth conjecture and the Gutkin-Tabachnikov \nduality. I will also offer a F
unk approach to the integrability of the \nhyperbolic billiard in a conic.
Time permitting\, I will discuss the \nvolume of metric balls in Funk geo
metry\, leading to a generalization \nof the Blaschke-Santalo inequality.\
n
LOCATION:https://researchseminars.org/talk/GDS/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Peralta-Salas (ICMAT Madrid)
DTSTART;VALUE=DATE-TIME:20210324T121000Z
DTEND;VALUE=DATE-TIME:20210324T133000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/27
DESCRIPTION:Title: Tur
ing completeness and universality of steady Euler flows\nby Daniel Per
alta-Salas (ICMAT Madrid) as part of Geometry and Dynamics seminar\n\n\nAb
stract\nI will review recents results on the Turing completeness and unive
rsality \nof steady solutions to the Euler equations. In particular\, I wi
ll show \nthe existence of three-dimensional fluid flows exhibiting undeci
dable \ntrajectories and discuss other universality features such as embed
dability \nof diffeomorphisms into steady Euler states. These results are
motivated by \nTao's programme to address the blow-up problem for the Navi
er-Stokes \nequations based on the Turing completeness of the fluid flows.
This is \nbased on joint works with Robert Cardona\, Eva Miranda and Fran
cisco Presas.\n
LOCATION:https://researchseminars.org/talk/GDS/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Rosen (Ruhr-Universität Bochum)
DTSTART;VALUE=DATE-TIME:20210407T111000Z
DTEND;VALUE=DATE-TIME:20210407T123000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/28
DESCRIPTION:Title: Ran
dom inscribed polytopes in Non-Euclidean Geometries\nby Daniel Rosen (
Ruhr-Universität Bochum) as part of Geometry and Dynamics seminar\n\n\nAb
stract\nRandom polytopes have a long history\, going back to Sylvester's f
amous \nfour-point problem. Since then their study has become a mainstream
topic \nin convex and stochastic geometry\, with close connection to poly
topal \napproximation problems\, among other things. In this talk we will
consider \nrandom polytopes in constant curvature geometries\, and show th
at their \nvolume satisfies a central limit theorem. The proof uses Stein'
s method \nfor normal approximation\, and extends to general projective Fi
nsler metrics.\n
LOCATION:https://researchseminars.org/talk/GDS/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Melistas (University of Georgia)
DTSTART;VALUE=DATE-TIME:20210421T111000Z
DTEND;VALUE=DATE-TIME:20210421T123000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/29
DESCRIPTION:Title: The
Large-Scale Geometry of Overtwisted Contact Forms\nby Thomas Melistas
(University of Georgia) as part of Geometry and Dynamics seminar\n\n\nAbs
tract\nInspired by the symplectic Banach-Mazur distance\, proposed by Ostr
over\n and Polterovich in the setting of non-degenerate starshaped domains
of \nLiouville manifolds\, we define a distance on the space of contact f
orms \nsupporting a given contact structure on a closed contact manifold.
We \ncompare it to a recently defined contact Banach-Mazur distance by Ros
en \nand Zhang and we use it in order to bi-Lipschitz embed part of the \n
2-dimensional Euclidean space into the space of overtwisted contact \nform
s supporting a given contact structure on a smooth closed manifold.\n
LOCATION:https://researchseminars.org/talk/GDS/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zvi Shem-Tov (The Hebrew University of Jerusalem)
DTSTART;VALUE=DATE-TIME:20210428T111000Z
DTEND;VALUE=DATE-TIME:20210428T123000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/30
DESCRIPTION:Title: Con
jugation-invariant norms on arithmetic groups\nby Zvi Shem-Tov (The He
brew University of Jerusalem) as part of Geometry and Dynamics seminar\n\n
\nAbstract\nA classical theorem of Ostrowski says that every absolute valu
e on the \nfield of rational numbers\, or equivalently on the ring of inte
gers\, is \nequivalent to either the standard (real) absolute value\, or a
$p$-adic \nabsolute value\, for which the closure of the integers is comp
act. In \nthis talk we will see a non-abelian analogue of this result for
\n$SL(n\\ge3\,\\Z)$\, and related groups of arithmetic type. We will see \
na relation to the celebrated Margulis' normal subgroup theorem\, and \nde
rive rigidity results for homomorphisms into certain non-locally \ncompact
groups -- those endowed with a bi-invariant metric. We will \nalso discus
s a relation to the deep work of Nikolov-Segal on profinite \ngroups. This
is a joint work with Leonid Polterovich and Yehuda Shalom.\n
LOCATION:https://researchseminars.org/talk/GDS/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Otto van Koert (Seoul National University)
DTSTART;VALUE=DATE-TIME:20210505T111000Z
DTEND;VALUE=DATE-TIME:20210505T123000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/31
DESCRIPTION:Title: A g
eneralization of the Poincare-Birkhoff fixed point theorem and the restric
ted three-body problem\nby Otto van Koert (Seoul National University)
as part of Geometry and Dynamics seminar\n\n\nAbstract\nIn joint work with
Agustin Moreno\, we propose a generalization of the \nPoincare-Birkhoff f
ixed point theorem. We start with a construction of \nglobal hypersurfaces
of section in the spatial three-body problem\, describe \nsome return map
s and suggest some generalizations of the Poincare-Birkhoff \nfixed point
theorem. We use symplectic homology in the proof of our theorem.\n
LOCATION:https://researchseminars.org/talk/GDS/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Georgios Dimitroglou Rizell (Uppsala University)
DTSTART;VALUE=DATE-TIME:20210512T111000Z
DTEND;VALUE=DATE-TIME:20210512T123000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/32
DESCRIPTION:Title: Non
-degeneracy of Legendrians from bifurcation of contact homology\nby Ge
orgios Dimitroglou Rizell (Uppsala University) as part of Geometry and Dyn
amics seminar\n\n\nAbstract\nWe show that the invariance of Legendrian con
tact homology can be \nformulated in terms of a bifurcation analysis whose
action properties \nare continuous with respect to the oscillatory norm o
f the contact \nHamiltonian. (I.e. the barcode varies continuously with re
spect to \nthe same.) Combined with work of Rosen-Zhang this implies non-d
egeneracy \nof the Shelukhin-Chekanov-Hofer metric on the space of Legendr
ian \nembeddings. We also explain how convex surface techniques in dimensi
on \nthree can be used to prove a statement related to the converse: a \nn
on-Legendrian knot cannot be approximated by the image of a Legendrian \nk
not under a sequence of C0-converging contactomorphisms. This is joint \nw
ork with M. Sullivan.\n
LOCATION:https://researchseminars.org/talk/GDS/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luis Diogo (Fluminense Federal University)
DTSTART;VALUE=DATE-TIME:20210519T111000Z
DTEND;VALUE=DATE-TIME:20210519T123000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/33
DESCRIPTION:Title: Mon
otone Lagrangians in cotangent bundles of spheres\nby Luis Diogo (Flum
inense Federal University) as part of Geometry and Dynamics seminar\n\n\nA
bstract\nAmong all Lagrangian submanifolds of a symplectic manifold\, the
class of \nmonotone Lagrangians is often very rich and nicely suited to be
ing studied \nusing pseudoholomophic curves. We find a family of monotone
Lagrangians \nin cotangent bundles of spheres with the following property:
every compact \nmonotone Lagrangian with non-trivial Floer cohomology can
not be displaced \nby a Hamiltonian diffeomorphism from at least one eleme
nt in the family. \nThis follows from the fact that the Lagrangians in the
family split-generate \nthe compact monotone Fukaya category. This is joi
nt work with Mohammed Abouzaid.\n
LOCATION:https://researchseminars.org/talk/GDS/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan David Evans (Lancaster University)
DTSTART;VALUE=DATE-TIME:20210526T111000Z
DTEND;VALUE=DATE-TIME:20210526T123000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/34
DESCRIPTION:Title: A L
agrangian Klein bottle you can't squeeze\nby Jonathan David Evans (Lan
caster University) as part of Geometry and Dynamics seminar\n\n\nAbstract\
nGiven a nonorientable Lagrangian surface L in a symplectic 4-manifold\, \
nhow far can you deform the symplectic form before there is no Lagrangian
\nsurface isotopic to L? I will discuss this problem in general and explai
n \nthe solution in a particular case.\n
LOCATION:https://researchseminars.org/talk/GDS/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeff Hicks (University of Cambridge)
DTSTART;VALUE=DATE-TIME:20210602T111000Z
DTEND;VALUE=DATE-TIME:20210602T123000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/35
DESCRIPTION:Title: Dec
ompositions of Lagrangian Cobordisms\nby Jeff Hicks (University of Cam
bridge) as part of Geometry and Dynamics seminar\n\n\nAbstract\nConsider a
symplectic manifold X\, and its product with the complex plane X x C. \nA
Lagrangian cobordism is a Lagrangian submanifold in X x C whose noncompac
t \nends suitably limit to Lagrangian submanifolds of X. In this talk\, we
'll discuss \nhow every Lagrangian submanifold can be decomposed into some
simple pieces - \nsurgery traces and suspensions of exact homotopy. Furth
ermore\, we'll speculate \nabout the connection between these decompositio
ns and the work of Biran and Cornea \nrelating Lagrangian cobordisms to eq
uivalences of Lagrangian Floer cohomology.\n
LOCATION:https://researchseminars.org/talk/GDS/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Itamar Rosenfeld Rauch (Technion\, Haifa)
DTSTART;VALUE=DATE-TIME:20210609T111000Z
DTEND;VALUE=DATE-TIME:20210609T123000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/36
DESCRIPTION:Title: On
the Hofer Girth of the Sphere of Great Circles\nby Itamar Rosenfeld Ra
uch (Technion\, Haifa) as part of Geometry and Dynamics seminar\n\n\nAbstr
act\nAn equator of $S^2$ is an embedded circle that divides the sphere int
o two \nequal area discs. Chekanov introduced a distance function on the s
pace of \nequators\, induced by the Hofer norm. We define the Hofer girth
of this \nspace\, roughly speaking\, as the smallest diameter of a non-con
tractible \nsphere in this space\, as inspired by the classic metric invar
iant of systoles. \nA somewhat natural embedding of $S^2$ in the space of
equators sends each \npoint to the great circle perpendicular to it\; this
embedding is called the \nsphere of great circles.\nIn this talk we will
discuss a few properties of Hofer girth\, and show that \nthe diameter of
the sphere of great circles is not optimal\, by constructing \na strictly
better candidate.\n
LOCATION:https://researchseminars.org/talk/GDS/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcelo R.R. Alves (University of Antwerp)
DTSTART;VALUE=DATE-TIME:20210616T111000Z
DTEND;VALUE=DATE-TIME:20210616T123000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/37
DESCRIPTION:Title: Ent
ropy collapse versus entropy rigidity for Reeb and Finsler flows\nby M
arcelo R.R. Alves (University of Antwerp) as part of Geometry and Dynamics
seminar\n\n\nAbstract\nThe topological entropy of a flow on a compact man
ifold is a measure \nof complexity related to many other notions of growth
. By celebrated \nworks of Katok and Besson-Courtois-Gallot\, the topologi
cal entropy \nof geodesic flows of Riemannian metrics with a fixed volume
on a \nmanifold M that carries a metric of negative curvature is uniformly
\nbounded from below by a positive constant depending only on M. We show
\nthat this result persists for all (possibly irreversible) Finsler \nflow
s\, but that on every closed contact manifold there exists a Reeb \nflow o
f fixed volume and arbitrarily small entropy. This is joint work \nwith Al
berto Abbondandolo\, Murat Saglam and Felix Schlenk.\n
LOCATION:https://researchseminars.org/talk/GDS/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Tsodikovich (Tel Aviv University)
DTSTART;VALUE=DATE-TIME:20211027T111000Z
DTEND;VALUE=DATE-TIME:20211027T123000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/38
DESCRIPTION:Title: Bil
liard Tables with rotational symmetry\nby Daniel Tsodikovich (Tel Aviv
University) as part of Geometry and Dynamics seminar\n\n\nAbstract\nConsi
der the following simple geometric fact: the only centrally symmetric \nco
nvex curve of constant width is a circle. The condition of having constant
\nwidth is equivalent for the (Birkhoff) billiard map to have a 1-paramet
er \nfamily of two periodic orbits. We generalize this statement to curves
that \nare invariant under a rotation by angle $\\frac{2\\pi}{k}$\, for
which the \nbilliard map has a 1-parameter family of k-periodic orbits. We
will also \nconsider a similar setting for other billiard systems: outer
billiards\, \nsymplectic billiards\, and (a special case of) Minkowski bil
liards. \nJoint work with Misha Bialy.\n
LOCATION:https://researchseminars.org/talk/GDS/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Egor Shelukhin (University of Montreal)
DTSTART;VALUE=DATE-TIME:20211103T141000Z
DTEND;VALUE=DATE-TIME:20211103T153000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/39
DESCRIPTION:Title: Ham
iltonian no-torsion\nby Egor Shelukhin (University of Montreal) as par
t of Geometry and Dynamics seminar\n\n\nAbstract\nWe generalize in several
ways Polterovich's well-known theorem that the \nHamiltonian group of a c
losed symplectically aspherical manifold admits \nno non-trivial elements
of finite order. We prove an analogous statement \nfor Calabi-Yau and nega
tively monotone manifolds. For positively monotone \nmanifolds we prove th
at non-trivial torsion implies geometric uniruledness \nof the manifold\,
answering a question of McDuff-Salamon. Moreover\, in this \ncase the foll
owing symplectic Newman theorem holds: a small Hofer-ball \naround the ide
ntity contains no finite subgroup. This is joint work with \nMarcelo Atall
ah.\n
LOCATION:https://researchseminars.org/talk/GDS/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Umut Varolgunes (Stanford University\, University of Edinburgh)
DTSTART;VALUE=DATE-TIME:20211110T121000Z
DTEND;VALUE=DATE-TIME:20211110T133000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/40
DESCRIPTION:Title: Try
ing to quantify Gromov's non-squeezing theorem\nby Umut Varolgunes (St
anford University\, University of Edinburgh) as part of Geometry and Dynam
ics seminar\n\n\nAbstract\nGromov's celebrated result says (colloquially)
that one cannot symplectically \nembed a ball of radius 1.1 into a cylinde
r of radius 1. I will show that in \n4d if one removes from this ball a La
grangian plane passing through the \norigin\, then such an embedding becom
es possible. I will also show that this \ngives the smallest Minkowski dim
ension of a closed subset with this property. \nI will end with many quest
ions. This is based on joint work with K. Sackel\, \nA. Song and J. Zhu.\n
LOCATION:https://researchseminars.org/talk/GDS/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pazit Haim Kislev (Tel Aviv University)
DTSTART;VALUE=DATE-TIME:20211117T121000Z
DTEND;VALUE=DATE-TIME:20211117T133000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/41
DESCRIPTION:Title: Sym
plectic capacities of p-products\nby Pazit Haim Kislev (Tel Aviv Unive
rsity) as part of Geometry and Dynamics seminar\n\n\nAbstract\nIn this tal
k we discuss symplectic capacities of convex domains and their \nbehavior
with respect to symplectic p-products. One application\, by using \na "ten
sor power trick"\, is to show that it is enough to prove Viterbo's \nvolum
e-capacity conjecture in the asymptotic regime when the dimension is \nsen
t to infinity. In addition\, we introduce a conjecture about higher order
\ncapacities of p-products and show that if it holds then there are no \nn
on-trivial p-decompositions of the symplectic ball.\n
LOCATION:https://researchseminars.org/talk/GDS/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gerhard Knieper (Ruhr University Bochum)
DTSTART;VALUE=DATE-TIME:20211124T121000Z
DTEND;VALUE=DATE-TIME:20211124T133000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/42
DESCRIPTION:Title: Gro
wth rate of closed geodesics on surfaces without conjugate points\nby
Gerhard Knieper (Ruhr University Bochum) as part of Geometry and Dynamics
seminar\n\n\nAbstract\nLet (M\,g) be a closed Riemannian surface of of gen
us at least 2 and no \nconjugate points. By the uniformization theorem suc
h a surface admits\na metric of negative curvature and therefore the topol
ogical entropy h \nof the geodesic flow is positive. Denote by P(t) the n
umber of free \nhomotopy classes containing a closed geodesic of period $
\\le t $. We \nwill show: P(t) is asymptotically equivalent to e^(ht)/(ht)
=F(t)\, i.e. \nthe ratio of P and F converges to 1 as t tends to infinit
y. \nAn important ingredient in the proof is a mixing flow invariant measu
re \ngiven by the unique measure of maximal entropy. Under suitable hyperb
olicity \nassumptions this result carries over to closed Riemannian manifo
lds without \nconjugate and higher dimension.\n\nFor closed manifolds of n
egative curvature the above estimate is well known \nand has been original
ly obtained by Margulis. In a recent preprint\nthe estimate has been also
obtained by Ricks for certain closed manifolds \n(rank 1 mflds) of non-po
sitive curvature. This is a joint work with Vaughn \nClimenhaga and Khadim
War.\n
LOCATION:https://researchseminars.org/talk/GDS/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sara Tukachinsky (Tel Aviv University)
DTSTART;VALUE=DATE-TIME:20211129T131000Z
DTEND;VALUE=DATE-TIME:20211129T143000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/43
DESCRIPTION:Title: Bou
nding chains as a tool in open Gromov-Witten theory\nby Sara Tukachins
ky (Tel Aviv University) as part of Geometry and Dynamics seminar\n\n\nAbs
tract\nModuli spaces of J-holomorphic disks have boundary. This interferes
with \ndesirable structures\, such as Lagrangian Floer theory or open Gro
mov-Witten \ninvariants. One tool for balancing out boundary contributions
is a bounding \nchain. In this talk I will give some background on the pr
oblem\, then discuss \nin detail what bounding chains are\, how they can b
e constructed\, and how \nthey are used to define invariants. \nThe work o
f several people will be mentioned\, among them a joint work \nwith J. Sol
omon.\n
LOCATION:https://researchseminars.org/talk/GDS/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Ioos (Max Planck Institute)
DTSTART;VALUE=DATE-TIME:20211208T121000Z
DTEND;VALUE=DATE-TIME:20211208T133000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/44
DESCRIPTION:Title: Qua
ntization in stages and canonical metrics\nby Louis Ioos (Max Planck I
nstitute) as part of Geometry and Dynamics seminar\n\n\nAbstract\nIn this
talk\, I will introduce the notion of quantization in stages\, which \nlie
s at the basis of fundamental physical set-ups such as the Stern-Gerlach \
nexperiment\, and explain how it can be realized over compact symplectic p
hase \nspaces via the use of Berezin-Toeplitz quantization of vector bundl
es. In \nparticular\, I will introduce and show how to compute the associa
ted quantum \nnoise. I will then describe an application to Hermite-Einste
in metrics on \nstable vector bundles over a projective manifold\, and if
time permits\, I will \nshow how a refinement of these results in the case
of the trivial line bundle \ncan be applied to Kähler metrics of constan
t scalar curvature.\n
LOCATION:https://researchseminars.org/talk/GDS/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Philippe Charron (Technion)
DTSTART;VALUE=DATE-TIME:20211215T121000Z
DTEND;VALUE=DATE-TIME:20211215T133000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/45
DESCRIPTION:Title: Ple
ijel's theorem for Schrödinger operators\nby Philippe Charron (Techni
on) as part of Geometry and Dynamics seminar\n\n\nAbstract\nWe will discus
s some recent results regarding the number of nodal domains \nof Laplace a
nd Schrödinger operators. Improving on Courant's seminal work\, \nPleijel
's original proof in 1956 was only for domains in R^2 with Dirichlet \nbou
ndary conditions\, but it was later generalized to manifolds (Peetre and \
nBérard-Meyer) with Dirichlet boundary conditions\, then to planar domain
s with \nNeumann Boundary conditions (Polterovich\, Léna)\, but also to t
he quantum \nharmonic oscillator (C.) and to Schrödinger operators with r
adial potentials \n(C. - Helffer - Hoffmann-Ostenhof). In this recent work
with Corentin Léna\, \nwe proved Pleijel's asymptotic upper bound for a
much larger class of \nSchrödinger operators which are not necessarily ra
dial. In this talk\, I will \nexplain the problems that arise from studyin
g Schrödinger operators as well \nas the successive improvements in the m
ethods that led to the current results.\n
LOCATION:https://researchseminars.org/talk/GDS/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simion Filip (University of Chicago)
DTSTART;VALUE=DATE-TIME:20211222T121000Z
DTEND;VALUE=DATE-TIME:20211222T133000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/46
DESCRIPTION:Title: Ano
sov representations\, Hodge theory\, and Lyapunov exponents\nby Simion
Filip (University of Chicago) as part of Geometry and Dynamics seminar\n\
n\nAbstract\nDiscrete subgroups of semisimple Lie groups arise in a variet
y of contexts\, \nsometimes "in nature" as monodromy groups of families of
algebraic manifolds\, \nand other times in relation to geometric structur
es and associated dynamical \nsystems. I will discuss a class of such disc
rete subgroups that arise from \ncertain variations of Hodge structure and
lead to Anosov representations\, thus \nrelating algebraic and dynamical
situations. Among many consequences of these \nrelations\, I will explain
Torelli theorems for certain families of Calabi-Yau \nmanifolds (including
the mirror quintic)\, uniformization results for domains \nof discontinui
ty of the associated discrete groups\, and also a proof of a \nconjecture
of Eskin\, Kontsevich\, Moller\, and Zorich on Lyapunov exponents. \nThe d
iscrete groups of interest live inside the real linear symplectic group\,
\nand the domains of discontinuity are inside Lagrangian Grassmanians and
other \nassociated flag manifolds. The necessary context and background wi
ll be explained.\n
LOCATION:https://researchseminars.org/talk/GDS/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Uljarević (University of Belgrade)
DTSTART;VALUE=DATE-TIME:20220105T121000Z
DTEND;VALUE=DATE-TIME:20220105T133000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/47
DESCRIPTION:Title: Con
tact non-squeezing via selective symplectic homology\nby Igor Uljarevi
ć (University of Belgrade) as part of Geometry and Dynamics seminar\n\n\n
Abstract\nIn this talk\, I will introduce a new version of symplectic homo
logy\, \ncalled "selective symplectic homology"\, that is associated to a\
nLiouville domain and an open subset of its boundary. The selective\nsympl
ectic homology is obtained as the direct limit of Floer homology\ngroups f
or Hamiltonians whose slopes tend to infinity on the open subset\nbut rema
in close to 0 and positive on the rest of the boundary.\n\nI will show how
selective symplectic homology can be used to prove\ncontact non-squeezing
phenomena. One such phenomenon concerns homotopy\nspheres that can be fil
led by a Weinstein domain with infinite\ndimensional symplectic homology:
there exists a (smoothly) embedded closed\nball in such a sphere that cann
ot be contactly squeezed into every\nnon-empty open subset. As a consequen
ce\, there exists a contact structure\non the standard smooth sphere (in c
ertain dimensions) that is homotopic to\nthe standard contact structure bu
t which exhibits\nnon-trivial contact non-squeezing.\n
LOCATION:https://researchseminars.org/talk/GDS/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joé Brendel (University of Neuchâtel)
DTSTART;VALUE=DATE-TIME:20220302T121000Z
DTEND;VALUE=DATE-TIME:20220302T133000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/48
DESCRIPTION:Title: Squ
eezing the symplectic ball (up to a subset)\nby Joé Brendel (Universi
ty of Neuchâtel) as part of Geometry and Dynamics seminar\n\n\nAbstract\n
In a recent preprint\, Sackel-Song-Varolgunes-Zhu investigate quantitative
\nquestions surrounding Gromov's non-squeezing theorem. In particular\, t
hey \nshow that if one can embed the four-ball into a cylinder of smaller
capacity \nafter the removal of a subset\, then this subset has Minkowski
dimension at \nleast two. Furthermore\, they give an explicit example of s
uch a "squeezing \nup to a subset" where the subset they remove has dimens
ion two and allows \nsqueezing by a factor of two (in terms of capacities)
. In this talk\, we will \ndiscuss certain squeezings by a factor of up to
three. The construction is \ninspired by degenerations of the complex pro
jective plane and almost toric \nfibrations. If time permits\, we will giv
e a construction by hand and discuss \nhow this leads to a different viewp
oint on almost toric fibrations and \npotential squeezings in higher dimen
sions. This is partially based on work \nthat will appear as an appendix o
f the SSVZ paper.\n
LOCATION:https://researchseminars.org/talk/GDS/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jake Solomon (Hebrew University of Jerusalem)
DTSTART;VALUE=DATE-TIME:20220309T121000Z
DTEND;VALUE=DATE-TIME:20220309T133000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/49
DESCRIPTION:Title: The
cylindrical transform\nby Jake Solomon (Hebrew University of Jerusale
m) as part of Geometry and Dynamics seminar\n\n\nAbstract\nA Lagrangian su
bmanifold of a Calabi-Yau manifold is called positive if the \nrestriction
to it of the real part of the holomorphic volume form is positive. \nThe
space of positive Lagrangians admits a Riemannian metric of non-positive \
ncurvature. Understanding the geodesics of the space of positive Lagrangia
n \nsubmanifolds would shed light on questions ranging from the uniqueness
and \nexistence of volume minimizing Lagrangian submanifolds to Arnold's
nearby \nLagrangian conjecture. The geodesic equation is a non-linear dege
nerate elliptic \nPDE. I will describe work with A. Yuval on the cylindric
al transform\, which \nconverts the geodesic equation to a family of non-d
egenerate elliptic boundary \nvalue problems. As a result\, we obtain exam
ples of geodesics in arbitrary \ndimension that are not invariant under an
y isometries. The talk will be aimed \nat a broad audience.\n
LOCATION:https://researchseminars.org/talk/GDS/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dustin Connery-Grigg (University of Montreal)
DTSTART;VALUE=DATE-TIME:20220316T141000Z
DTEND;VALUE=DATE-TIME:20220316T153000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/50
DESCRIPTION:by Dustin Connery-Grigg (University of Montreal) as part of Ge
ometry and Dynamics seminar\n\n\nAbstract\nIn general\, it is difficult to
relate the structure of the Hamiltonian Floer \ncomplex of a generic pair
(H\,J) to the dynamical behaviour of the Hamiltonian \nsystem generated b
y H. However\, it turns out that in dimension 2\, topological \nobstructio
ns coming from the braid-theoretic structure of the periodic orbits \nallo
w us to make significant inroads into understanding the geometric and dyna
mical \ncontent of Hamiltonian Floer theory. Some highlights include a top
ological \ncharacterization of those Floer chains which represent the fund
amental class \n(and which moreover lie in the image of some chain-level P
SS map)\, as well as \nan interpretation of the structure of Floer chain c
omplexes in homologically \nnon-trivial degrees in terms of particularly w
ell-behaved singular foliations \nwhich may be thought of as generalizatio
ns of Poincare sections. In this talk\, \nI will present the main ideas an
d techniques which go into establishing such \nresults and attempt to sket
ch some of the main lines of argument involved in \ntheir proof.\n
LOCATION:https://researchseminars.org/talk/GDS/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pranav Chakravarthy (Hebrew University of Jerusalem)
DTSTART;VALUE=DATE-TIME:20220323T121000Z
DTEND;VALUE=DATE-TIME:20220323T133000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/51
DESCRIPTION:Title: Hom
otopy type of equivariant symplectomorphisms of rational ruled surfaces\nby Pranav Chakravarthy (Hebrew University of Jerusalem) as part of Geom
etry and Dynamics seminar\n\n\nAbstract\nIn this talk\, we present results
on the homotopy type of the group of \nequivariant symplectomorphisms of
$S^2 \\times S^2$ and $\\mathbb{C}P^2$ blown \nup once\, under the presen
ce of Hamiltonian group actions of either $S^1$ or \nfinite cyclic groups.
For Hamiltonian circle actions\, we prove that the \ncentralizers are ho
motopy equivalent to either a torus or to the homotopy \npushout of two to
ri depending on whether the circle action extends to a single \ntoric acti
on or to exactly two non-equivalent toric actions. We can show that \nthe
same holds for the centralizers of most finite cyclic groups in the \nHami
ltonian group. Our results rely on J-holomorphic techniques\, on Delzant's
\nclassification of toric actions\, on Karshon's classification of Hamilt
onian \ncircle actions on 4-manifolds\, and on the Chen-Wilczy\\'nski smoo
th \nclassification of $\\mathbb{Z}_n$-actions on Hirzebruch surfaces.\n
LOCATION:https://researchseminars.org/talk/GDS/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maksim Stokic (Tel Aviv University)
DTSTART;VALUE=DATE-TIME:20220330T111000Z
DTEND;VALUE=DATE-TIME:20220330T123000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/52
DESCRIPTION:Title: $C^
0$ contact geometry of isotropic submanifolds\nby Maksim Stokic (Tel A
viv University) as part of Geometry and Dynamics seminar\n\n\nAbstract\nTh
e celebrated Eliashberg-Gromov rigidity theorem states that a diffeomorphi
sm \nwhich is a $C^0$-limit of symplectomorphisms is itself symplectic. Co
ntact \nversion of this rigidity theorem holds true as well. Motivated by
this\, contact \nhomeomorphisms are defined as $C^0$-limits of contactomor
phisms. Isotropic \nsubmanifolds are a particularly interesting class of s
ubmanifolds\, and in this \ntalk we will try to answer whether or not isot
ropic property is preserved by \ncontact homeomorphisms. Legendrian subman
ifolds are isotropic submanifolds of \nmaximal dimension and we expect tha
t the rigidity holds in this case. We give \na new proof of the rigidity i
n dimension 3\, and provide some type of rigidity \nin higher dimensions.
On the other hand\, we show that the subcritical isotropic \ncurves are fl
exible\, and we prove quantitative $h$-principle for subcritical \nisotrop
ic embeddings which is our main tool for proving the flexibility result.\n
LOCATION:https://researchseminars.org/talk/GDS/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sheng-Fu Chiu (Institute of Mathematics\, Academia Sinica\, Taiwan
)
DTSTART;VALUE=DATE-TIME:20220406T111000Z
DTEND;VALUE=DATE-TIME:20220406T123000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/53
DESCRIPTION:Title: Fro
m Energy-Time Uncertainty to Symplectic Displacement Energy\nby Sheng-
Fu Chiu (Institute of Mathematics\, Academia Sinica\, Taiwan) as part of G
eometry and Dynamics seminar\n\n\nAbstract\nHeisenberg's Uncertainty Princ
iple is one of the most celebrated features of \nquantum mechanics\, which
states that one cannot simultaneously obtain the \nprecise measurements o
f two conjugated physical quantities such as the pair \nof position and mo
mentum or the pair of electric potential and charge density. \nAmong the d
ifferent formulations of this fundamental quantum property\, the \nuncerta
inty between energy and time has a special place. This is because the \nti
me is rather a variable parametrizing the system evolution than a physical
\nquantity waiting for determination. Physicists working on the foundatio
n of \nquantum theory have understood this energy-time relation by a unive
rsal bound \nof how fast any quantum system with given energy can evolve f
rom one state to \nanother in a distinguishable (orthogonal) way. Recently
\, there have been many \narguing that this bound is not a pure quantum ph
enomenon but a general \ndynamical property of Hilbert space. In this talk
\, in contrast to the usual \nHilbert space formalism\, we will provide a
homological viewpoint of this \nevolutional speed limit based on a persist
ence-like distance of the derived \ncategory of sheaves : during a time pe
riod what is the minimal energy needed \nfor a system to evolve from one s
heaf to a status that is distinguishable from \na given subcategory? As an
application\, we will also discuss its geometric \nincarnation in the dyn
amics of classical mechanics\, namely the notion of \nsymplectic displacem
ent. We will see how this categorical energy manages to \ncharacterize the
symplectic energy for disjointing a Lagrangian from an open set.\n
LOCATION:https://researchseminars.org/talk/GDS/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Brandenbursky (Ben-Gurion University)
DTSTART;VALUE=DATE-TIME:20220427T111000Z
DTEND;VALUE=DATE-TIME:20220427T120000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/54
DESCRIPTION:Title: C^0
-gap between entropy-zero Hamiltonians and autonomous diffeomorphisms of s
urfaces\nby Michael Brandenbursky (Ben-Gurion University) as part of G
eometry and Dynamics seminar\n\n\nAbstract\nLet Σ be a surface equipped w
ith an area form. There is a long standing open \nquestion by Katok\, whic
h\, in particular\, asks whether every entropy-zero \nHamiltonian diffeomo
rphism of a surface lies in the C^0-closure of the set \nof integrable dif
feomorphisms. A slightly weaker version of this question \nasks: ``Does ev
ery entropy-zero Hamiltonian diffeomorphism of a surface lie \nin the C^0-
closure of the set of autonomous diffeomorphisms?'' In this talk \nI will
answer in negative the later question. In particular\, I will show that \n
on a surface Σ the set of autonomous Hamiltonian diffeomorphisms is not \
nC^0-dense in the set of entropy-zero Hamiltonians. Explicitly constructed
\nexamples of such Hamiltonians cannot be approximated by autonomous \ndi
ffeomorphisms. (Joint with M. Khanevsky).\n
LOCATION:https://researchseminars.org/talk/GDS/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Umut Varolgunes (Bogazici University)
DTSTART;VALUE=DATE-TIME:20220427T121000Z
DTEND;VALUE=DATE-TIME:20220427T130000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/55
DESCRIPTION:Title: Com
putations in relative symplectic cohomology using local to global methods<
/a>\nby Umut Varolgunes (Bogazici University) as part of Geometry and Dyna
mics seminar\n\n\nAbstract\nConsider a complete Lagrangian torus fibration
p(n) from a symplectic manifold \nto the plane with at most one singular
fiber which is a two torus pinched at \nn-meridians. Relative symplectic c
ohomology in degree 0 defines a sheaf of \nalgebras in the base with respe
ct to an appropriate G-topology and grading \ndatum. I will explain how on
e can compute this sheaf for all p(n) using \ngeneral properties and expli
cit computations for p(0). This is a joint work \nwith Yoel Groman.\n
LOCATION:https://researchseminars.org/talk/GDS/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Egor Shelukhin (University of Montreal)
DTSTART;VALUE=DATE-TIME:20220501T110000Z
DTEND;VALUE=DATE-TIME:20220501T115000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/56
DESCRIPTION:Title: The
transcendental Bézout problem revisited\nby Egor Shelukhin (Universi
ty of Montreal) as part of Geometry and Dynamics seminar\n\n\nAbstract\nB
ézout's classical theorem states that n complex polynomials of degree k o
n C^n \nhave at most k^n isolated common zeros. The logarithm of the maxim
al function \nof an entire function on C\, instead of the degree\, control
s the number of zeros \nin a ball of radius r. The transcendental Bézout
problem seeks to extend this \nestimate to entire self-mappings f of C^n v
ia the n-th power of the logarithm \nof the maximal function. A celebrated
counterexample of Cornalba-Shiffman shows \nthat this is dramatically fal
se for n>1. However\, it is true on average\, under \nlower bounds on the
Jacobian\, or in a weaker form for small constant perturbations \nof f. We
explain how topological considerations of persistent homology and \nMorse
theory shed new light on this question proving the expected bound for a \
nrobust count of zeros. This is part of a larger joint project with Buhovs
ky\, \nPayette\, Polterovich\, Polterovich\, and Stojisavljevic.\n
LOCATION:https://researchseminars.org/talk/GDS/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hyunmoon Kim (Seoul National University)
DTSTART;VALUE=DATE-TIME:20220511T111000Z
DTEND;VALUE=DATE-TIME:20220511T123000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/57
DESCRIPTION:Title: Com
plex Lagrangian subspaces and representations of the canonical commutation
relations\nby Hyunmoon Kim (Seoul National University) as part of Geo
metry and Dynamics seminar\n\n\nAbstract\nComplex Lagrangian subspaces wer
e introduced as polarizations on symplectic \nmanifolds in geometric quant
ization. We will look at their role in the linear \ngeometry more carefull
y. A transverse pair of complex Lagrangian subspaces \nparametrizes repres
entations of the canonical commutation relations and this \nbrings togethe
r some different perspectives from which the representations \nwere studie
d. I will suggest how this result can be interpreted using concepts \nfrom
geometry and very little concepts from physics.\n
LOCATION:https://researchseminars.org/talk/GDS/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ofir Karin (Tel Aviv University)
DTSTART;VALUE=DATE-TIME:20220518T111000Z
DTEND;VALUE=DATE-TIME:20220518T120000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/58
DESCRIPTION:Title: App
roximation of Generating Function Barcode for Hamiltonian Diffeomorphisms<
/a>\nby Ofir Karin (Tel Aviv University) as part of Geometry and Dynamics
seminar\n\n\nAbstract\nPersistence modules and barcodes are used in symple
ctic topology to define \nnew invariants of Hamiltonian diffeomorphisms\,
however methods that explicitly \ncalculate these barcodes are often uncle
ar. In this talk I will explain the \nnecessary background and define one
such invariant called the GF-barcode of \ncompactly supported Hamiltonian
diffeomorphisms of $ \\mathbb{R}^{2n} $ by \napplying Morse theory to gene
rating functions quadratic at infinity associated \nto such Hamiltonian di
ffeomorphisms and provide an algorithm (i.e a finite \nsequence of explici
t calculation steps) that approximates it along with a \nfew computation e
xamples. Joint work with Pazit Haim-Kislev.\n
LOCATION:https://researchseminars.org/talk/GDS/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey Balitskiy (IAS Princeton\, and Institute for Information Tr
ansmission Problems RAS)
DTSTART;VALUE=DATE-TIME:20220518T121000Z
DTEND;VALUE=DATE-TIME:20220518T130000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/59
DESCRIPTION:Title: Sys
tolic freedom and rigidity modulo 2\nby Alexey Balitskiy (IAS Princeto
n\, and Institute for Information Transmission Problems RAS) as part of Ge
ometry and Dynamics seminar\n\n\nAbstract\nThe $k$-dimensional systole of
a closed Riemannian $n$-dimensional manifold $M$ \nis the infimal $k$-volu
me of a non-trivial $k$-cycle (with some coefficients). \nIn '90s\, Gromov
asked if the product of the $k$-systole and the $(n-k)$-systole \nis boun
ded from above by the volume of $M$ (up to a dimensional factor)\; this \n
would manifest the \\emph{systolic rigidity}. Freedman exhibited the first
\nexamples with $k=1$ and mod 2 coefficients where this fails\; this mani
fests \nthe \\emph{systolic freedom}. In a joint work in progress with Han
nah Alpert \nand Larry Guth\, we show that Freedman's examples are almost
as "free" as \npossible\, and the systolic rigidity almost holds\, with $k
=1$ and mod 2 \ncoefficients. Namely\, on a manifold of bounded local geom
etry\, \n$\\mbox{systole}_1(M) \\cdot \\mbox{systole}_{n-1}(M) \\le c_\\ep
silon \\mbox{volume}(M)^{1+\\epsilon}$\, \nas long as the left-hand side i
s finite ($H_1(M\; \\mathbb{Z}/2)$ is non-trivial). \nThe proof\, which I
will explain\, is based on the Schoen--Yau--Guth--Papasoglu \nminimal surf
ace method.\n
LOCATION:https://researchseminars.org/talk/GDS/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander A. Trost (Ruhr University Bochum)
DTSTART;VALUE=DATE-TIME:20220525T111000Z
DTEND;VALUE=DATE-TIME:20220525T123000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/60
DESCRIPTION:Title: Ele
mentary bounded generation for global function fields and some application
s\nby Alexander A. Trost (Ruhr University Bochum) as part of Geometry
and Dynamics seminar\n\n\nAbstract\nBounded generation (and elementary bou
nded generation) are essentially the \nability to write each element of a
given group as products with factors from \na finite collection of ”simp
le” subgroups of the group in question and with \na uniform bound on the
number of factors needed. These somewhat technical \nproperties were init
ially introduced in the study of the congruence subgroup \nproperty of ari
thmetic groups\, but they traditionally also found applications \nin the r
epresentation theory of these groups\, their subgroup growth and \nKazdhan
’s Property (T). Recently however\, there has been renewed interest in \
nthese properties from the area of geometric group theory as bounded eleme
ntary \ngeneration appears naturally as a technical assumption in various
results \nstudying arithmetic groups ranging from the study of conjugation
-invariant \nnorms on\, say\, SLn as well as in the study of the first-ord
er theories of \narithmetic groups. Classical results in this area were us
ually concerned with \ngroups arising from number fields though and somewh
at surprisingly there are \nfew such results for groups arising from globa
l function fields. In this talk\, \nI will give a short introduction about
the history of bounded generation in \ngeneral and then present a general
bounded generation for split Chevalley \ngroups arising from global funct
ion fields together with some applications \nif time allows.\n
LOCATION:https://researchseminars.org/talk/GDS/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthias Meiwes (RWTH Aachen University)
DTSTART;VALUE=DATE-TIME:20220601T111000Z
DTEND;VALUE=DATE-TIME:20220601T123000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/61
DESCRIPTION:Title: Ent
ropy\, braids\, and Hofer's metric\nby Matthias Meiwes (RWTH Aachen Un
iversity) as part of Geometry and Dynamics seminar\n\n\nAbstract\nTopologi
cal entropy captures the orbit complexity of a dynamical system with \nthe
help of a single non-negative number. Detecting robustness of this number
\nunder perturbation is a way to understand stability features of a chaot
ic system.\nIn my talk\, I will address the problem of robustness of entro
py for Hamiltonian \ndiffeomorphisms in terms of Hofer's metric. Our main
focus lies on dimension 2\, \nwhere there is a strong connection between t
opological entropy and the existence \nof specific braid types of periodic
orbits. I explain that the construction of \neggbeater maps of Polterovic
h-Shelukhin and their generalizations by Chor provide \nrobustness even un
der large perturbation: the entropy will not drop much when \nperturbing t
he specific diffeomorphism in some ball of large Hofer-radius. \nI further
more discuss a result that any braid of non-degenerate one-periodic \norbi
ts with pairwise homotopic strands persists under generic Hofer-small \npe
rturbations\, which yields a local entropy robustness result for surfaces.
\nThis talk is based on joint works with Arnon Chor\, and Marcelo Alves.\n
LOCATION:https://researchseminars.org/talk/GDS/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Miyamoto (University of Toronto)
DTSTART;VALUE=DATE-TIME:20220608T111000Z
DTEND;VALUE=DATE-TIME:20220608T123000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/62
DESCRIPTION:Title: Qua
sifold groupoids and diffeological quasifolds\nby David Miyamoto (Univ
ersity of Toronto) as part of Geometry and Dynamics seminar\n\n\nAbstract\
nA quasifold is a space that is locally modeled by quotients of R^n \nby c
ountable group actions. These arise in Elisa Prato's generalization of \nt
he Delzant theorem to irrational polytopes\, and include orbifolds and \nm
anifolds. We approach quasifolds in two ways: by viewing them as diffeolog
ical \nspaces\, we form the category of diffeological quasifolds\, and by
viewing them \nas Lie groupoids (with bibundles as morphisms)\, we form th
e category of \nquasifold groupoids. We show that\, restricting to effecti
ve groupoids\, and \nlocally invertible morphisms\, these two categories a
re equivalent. In \nparticular\, an effective quasifold groupoid is determ
ined by its diffeological \norbit space. This is join work with Yael Karsh
on.\n
LOCATION:https://researchseminars.org/talk/GDS/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cheuk Yu Mak (University of Edinburgh)
DTSTART;VALUE=DATE-TIME:20221026T111000Z
DTEND;VALUE=DATE-TIME:20221026T123000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/63
DESCRIPTION:Title: Som
e cute applications of Lagrangian cobordisms\nby Cheuk Yu Mak (Univers
ity of Edinburgh) as part of Geometry and Dynamics seminar\n\n\nAbstract\n
In this talk\, we will discuss\, from a quantitative aspect\, the followin
g \nsymplectic questions: packing Lagrangian submanifolds\, displacing Lag
rangian \nsubmanifolds\, and constructing Lagrangian surfaces with a presc
ribed genus. \nWe will illustrate some interesting features of these quest
ions using simple \nexamples. The focus will be put on explaining some new
ideas from the point \nof view of Lagrangian cobordisms. This is a joint
work with Jeff Hicks.\n
LOCATION:https://researchseminars.org/talk/GDS/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre-Alexandre Mailhot (University of Montreal)
DTSTART;VALUE=DATE-TIME:20221102T151000Z
DTEND;VALUE=DATE-TIME:20221102T163000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/64
DESCRIPTION:Title: Spe
ctral diameter\, Liouville domains and symplectic cohomology\nby Pierr
e-Alexandre Mailhot (University of Montreal) as part of Geometry and Dynam
ics seminar\n\n\nAbstract\nThe spectral norm provides a lower bound to the
Hofer norm. It is thus \nnatural to ask whether the diameter of the spect
ral norm is finite or not. \nIn the case of closed symplectic manifolds\,
there is no unified answer. \nFor instance\, for a certain class of symple
cticaly aspherical manifolds\, \nwhich contains surfaces\, the spectral di
ameter is infinite. However\, for \nCP^n\, the spectral diameter is known
to be finite. During this talk\, I will \nprove that\, in the case of Liou
ville domains\, the spectral diameter is \nfinite if and only if the sympl
ectic cohomology of the underlying manifold \nvanishes. With that relation
ship in hand\, we will explore applications to \nsymplecticaly aspherical
symplectic manifolds and give a new proof that the \nspectral diameter is
infinite on cotangent disk bundles.\n
LOCATION:https://researchseminars.org/talk/GDS/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Grigory Mikhalkin (University of Geneva)
DTSTART;VALUE=DATE-TIME:20221109T121000Z
DTEND;VALUE=DATE-TIME:20221109T133000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/65
DESCRIPTION:Title: Tor
ic geometry and tropical trigonometry\nby Grigory Mikhalkin (Universit
y of Geneva) as part of Geometry and Dynamics seminar\n\n\nAbstract\nToric
varieties were constructed as algebraic varieties about 50 years ago\, \n
and also as symplectic varieties about 40 years ago. The two constructions
\nare dual to each other\, but are based on the same geometry in R^n. Sym
metries \nin this geometry are linear transformations given by invertible
n-by-n \nmatrices with integer coefficients\, as well as all translations.
This makes \nthe notion of a tangent integer vector as well as a notion o
f tropical curve \nwell-defined. The talk will review basic constructions
with a focus on \ntropical triangles that underlie some recent progress in
symplectic embedding \nproblems.\n
LOCATION:https://researchseminars.org/talk/GDS/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jinxin Xue (Tsinghua University)
DTSTART;VALUE=DATE-TIME:20221116T121000Z
DTEND;VALUE=DATE-TIME:20221116T133000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/66
DESCRIPTION:Title: Dyn
amics of composite symplectic Dehn twists\nby Jinxin Xue (Tsinghua Uni
versity) as part of Geometry and Dynamics seminar\n\n\nAbstract\nIt is cla
ssically known in Nielson-Thurston theory that the mapping class \ngroup o
f a hyperbolic surface is generated by Dehn twists and most elements \nare
pseudo Anosov. Pseudo Anosov elements are interesting dynamical objects.
\nThey are featured by positive topological entropy and two invariant sing
ular \nfoliations expanded or contracted by the dynamics. We explore a gen
eralization \nof these ideas to symplectic mapping class groups. With the
symplectic Dehn \ntwists along Lagrangian spheres introduced by Arnold and
Seidel\, we show in \nvarious settings that the compositions of such twi
sts has features of pseudo \nAnosov elements\, such as positive topologica
l entropy\, invariant stable and \nunstable laminitions\, exponential grow
th of Floer homology group\, etc. This \nis a joint work with Wenmin Gong
and Zhijing Wang.\n
LOCATION:https://researchseminars.org/talk/GDS/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcelo S. Atallah (University of Montreal)
DTSTART;VALUE=DATE-TIME:20221123T151000Z
DTEND;VALUE=DATE-TIME:20221123T163000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/67
DESCRIPTION:Title: Fix
ed points of small Hamiltonian diffeomorphisms and the Flux conjectures\nby Marcelo S. Atallah (University of Montreal) as part of Geometry and
Dynamics seminar\n\n\nAbstract\nInspired by the work of Lalonde-McDuff-Pol
terovich\, we describe how the C^0 \nand C^1 flux conjectures relate to ne
w instances of the strong Arnol’d \nconjecture and make new progress on
the C^0 flux conjecture. This is joint \nwork in progress with Egor Sheluk
hin.\n
LOCATION:https://researchseminars.org/talk/GDS/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joé Brendel (Tel Aviv University)
DTSTART;VALUE=DATE-TIME:20221130T121000Z
DTEND;VALUE=DATE-TIME:20221130T133000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/68
DESCRIPTION:Title: Pin
wheels as Lagrangian barriers\nby Joé Brendel (Tel Aviv University) a
s part of Geometry and Dynamics seminar\n\n\nAbstract\nPinwheels are certa
in singular Lagrangians in four-dimensional \nsymplectic manifolds. In thi
s talk we focus on the case of the complex \nprojective plane\, where pinw
heels arise naturally as visible Lagrangians \nin its almost toric fibrati
ons or\, alternatively\, as vanishing cycles of \nits degenerations. Pinwh
eels have been shown to have interesting \nrigidity properties by Evans--S
mith. The goal of this talk is to show \nthat Lagrangian pinwheels are Lag
rangian barriers in the sense of Biran\, \nmeaning that their complement h
as strictly smaller Gromov width than the \nambient space. Furthermore\, w
e will discuss a connection to the Lagrange \nspectrum. This is joint work
with Felix Schlenk.\n
LOCATION:https://researchseminars.org/talk/GDS/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yoel Groman (Hebrew University of Jerusalem)
DTSTART;VALUE=DATE-TIME:20221207T121000Z
DTEND;VALUE=DATE-TIME:20221207T133000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/69
DESCRIPTION:Title: Clo
sed string mirrors of symplectic cluster manifolds\nby Yoel Groman (He
brew University of Jerusalem) as part of Geometry and Dynamics seminar\n\n
\nAbstract\nConsider a symplectic Calabi Yau manifold equipped with a Masl
ow 0 Lagrangian \ntorus fibration with singularities. According to modern
interpretations of \nthe SYZ conjecture\, there should be an associated a
nalytic mirror variety \nwith a non Archimedean torus fibration over the s
ame base. I will suggest a \ngeneral construction called the closed string
mirror which is based on \nrelative symplectic cohomologies of the fibers
. A priori the closed string \nmirror is only a set with a map to the base
\, but conjecturally under some \ngeneral hypotheses it is in fact an anal
ytic variety with its non Archimedean \ntorus fibration. I will discuss jo
int work with Umut Varolgunes where we prove \nthis in the case of four di
mensional symplectic cluster manifolds.\n
LOCATION:https://researchseminars.org/talk/GDS/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mira Shamis (Queen Mary University of London)
DTSTART;VALUE=DATE-TIME:20221214T121000Z
DTEND;VALUE=DATE-TIME:20221214T133000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/70
DESCRIPTION:Title: On
the abominable properties of the Almost Mathieu operator with Liouville fr
equencies\nby Mira Shamis (Queen Mary University of London) as part of
Geometry and Dynamics seminar\n\n\nAbstract\nWe show that\, for sufficien
tly well approximable frequencies\, several\nspectral characteristics of t
he Almost Mathieu operator can be as poor\nas at all possible in the class
of all discrete Schroedinger\noperators. For example\, the modulus of con
tinuity of the integrated\ndensity of states may be no better than logarit
hmic. Other\ncharacteristics to be discussed are homogeneity\, the Parreau
-Widom\nproperty\, and (for the critical AMO) the Hausdorff content of the
\nspectrum. Based on joint work with A. Avila\, Y. Last\, and Q. Zhou.\n
LOCATION:https://researchseminars.org/talk/GDS/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maksim Stokic (Tel Aviv University)
DTSTART;VALUE=DATE-TIME:20221221T121000Z
DTEND;VALUE=DATE-TIME:20221221T133000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/71
DESCRIPTION:Title: Fle
xibility of the adjoint action of the group of Hamiltonian diffeomorphisms
\nby Maksim Stokic (Tel Aviv University) as part of Geometry and Dynam
ics seminar\n\n\nAbstract\nThe space of Hamiltonian diffeomorphisms has a
structure of an infinite \ndimensional Frechet Lie group\, with Lie algebr
a isomorphic to the space \nof normalized functions and adjoint action giv
en by pull-backs. We show \nthat this action is flexible: for a non-zero n
ormalized function $f$\, \nany other normalized function can be written as
a sum of differences of \nelements in the orbit of $f$ generated by the a
djoint action. Additionally\, \nthe number of elements in this sum is domi
nated from above by the \n$L_{\\infty}$-norm of $f$. This result can be in
terpreted as an (bounded) \ninfinitesimal version of the Banyaga's result
on simplicity of $Ham(M\,\\omega)$. \nMoreover\, it can be used to remove
the $C^{\\infty}$-continuity condition \nin the Buhovsky-Ostrover theorem
on the uniqueness of Hofer's metric. \nThis is joint work with Lev Buhovsk
y.\n
LOCATION:https://researchseminars.org/talk/GDS/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Albert Fathi (Georgia Tech)
DTSTART;VALUE=DATE-TIME:20221228T121000Z
DTEND;VALUE=DATE-TIME:20221228T133000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/72
DESCRIPTION:Title: Smo
oth Lyapunov functions on closed subsets and isolating neighbourhoods\
nby Albert Fathi (Georgia Tech) as part of Geometry and Dynamics seminar\n
\n\nAbstract\nWe will discuss unified and simplified proofs of some previo
usly known \ntheorems relating dynamics and Lyapunov functions. In particu
lar\, we \nwill give a proof of the existence of isolating blocks for isol
ated \ninvariant sets.\n
LOCATION:https://researchseminars.org/talk/GDS/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shira Tanny (IAS Princeton)
DTSTART;VALUE=DATE-TIME:20230104T132000Z
DTEND;VALUE=DATE-TIME:20230104T143000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/73
DESCRIPTION:Title: Clo
sing lemmas in contact dynamics and holomorphic curves\nby Shira Tanny
(IAS Princeton) as part of Geometry and Dynamics seminar\n\n\nAbstract\nG
iven a flow on a manifold\, how to perturb it in order to create a periodi
c \norbit passing through a given region? While the first results in this
\ndirection were obtained in the 1960-ies\, various facets of this questio
n \nremain largely open. I will review recent advances on this problem in
the \ncontext of contact flows\, which are closely related to Hamiltonian
flows \nfrom classical mechanics. In particular\, I'll discuss a proof of
a \nconjecture of Irie stating that rotations of odd-dimensional ellipsoid
s \nadmit a surprisingly large class of perturbations creating periodic or
bits. \nThe proof involves methods of modern symplectic topology including
\npseudo-holomorphic curves and contact homology. The talk is based on a
\njoint work with Julian Chaidez\, Ipsita Datta and Rohil Prasad\, as well
\nas a work in progress joint with Julian Chaidez.\n
LOCATION:https://researchseminars.org/talk/GDS/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iosif Polterovich (University of Montreal)
DTSTART;VALUE=DATE-TIME:20230104T120000Z
DTEND;VALUE=DATE-TIME:20230104T131000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/74
DESCRIPTION:Title: Pó
lya's eigenvalue conjecture: some recent advances\nby Iosif Polterovic
h (University of Montreal) as part of Geometry and Dynamics seminar\n\n\nA
bstract\nThe celebrated Pólya’s conjecture (1954) in spectral geometry
states that \nthe eigenvalue counting functions of the Dirichlet and Neuma
nn Laplacian \non a bounded Euclidean domain can be estimated from above a
nd below\, \nrespectively\, by the leading term of Weyl’s asymptotics. T
he conjecture \nis known to be true for domains which tile the Euclidean s
pace\, however \nit remains largely open in full generality. In the talk w
e will explain \nthe motivation behind this conjecture and discuss some re
cent advances\, \nnotably\, the proof of Pólya’s conjecture for the dis
k. The talk is based \non a joint work with Nikolay Filonov\, Michael Levi
tin and David Sher.\n
LOCATION:https://researchseminars.org/talk/GDS/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuhan Sun (Rutgers University)
DTSTART;VALUE=DATE-TIME:20230111T151000Z
DTEND;VALUE=DATE-TIME:20230111T163000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/75
DESCRIPTION:Title: Hea
vy sets and relative symplectic cohomology\nby Yuhan Sun (Rutgers Univ
ersity) as part of Geometry and Dynamics seminar\n\n\nAbstract\nHeavy sets
were introduced by Entov-Polterovich around 2009. They reveal \nsuprising
rigidity of certain compact subsets of a closed symplectic manifold\, \nf
rom a functional persepective. When a compact subset is a smooth Lagrangia
n \nsubmanifold\, there is a well-established relation between its heavine
ss and \nthe non-vanishing of its Lagrangian Floer cohomology. In this tal
k we \ndescribe an equivalence between the heaviness of general compact su
bsets \nand the non-vanishing of another Floer-type invariant\, called the
relative \nsymplectic cohomology. If time permits\, we will discuss appli
cations and \nquestions we learned from this equivalence. Based on joint w
ork with C.Mak \nand U.Varolgunes.\n
LOCATION:https://researchseminars.org/talk/GDS/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Entov (Technion)
DTSTART;VALUE=DATE-TIME:20230118T121000Z
DTEND;VALUE=DATE-TIME:20230118T133000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/76
DESCRIPTION:Title: Kah
ler-type embeddings of balls into symplectic manifolds\nby Michael Ent
ov (Technion) as part of Geometry and Dynamics seminar\n\n\nAbstract\nA sy
mplectic embedding of a disjoint union of balls into a symplectic \nmanifo
ld M is called Kahler-type if it is holomorphic with respect \nto some (no
t a priori fixed) complex structure on M compatible with \nthe symplectic
form. Assume that M either of the following: CP^n (with \nthe standard sym
plectic form)\, an even-dimensional torus or a K3 surface \nequipped with
an irrational Kahler-type symplectic form. Then: \n\n1. Any two Kahler-typ
e embeddings of a disjoint union of balls into M \ncan be mapped into each
other by a symplectomorphism acting trivially on \nthe homology. If the e
mbeddings are holomorphic with respect to complex \nstructures compatible
with the symplectic form and lying in the same \nconnected component of th
e space of Kahler-type complex structures on M\, \nthen the symplectomorph
ism can be chosen to be smoothly isotopic to the \nidentity. \n\n2. Symple
ctic volume is the only obstruction for the existence of \nKahler-type emb
eddings of k^n equal balls (for any k) into CP^n and of \nany number of po
ssibly different balls into a torus or a K3 surface.\n \nThis is a joint w
ork with M.Verbitsky.\n
LOCATION:https://researchseminars.org/talk/GDS/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ely Kerman (University of Illinois Urbana-Champaign)
DTSTART;VALUE=DATE-TIME:20230315T121000Z
DTEND;VALUE=DATE-TIME:20230315T133000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/77
DESCRIPTION:Title: Mea
n width\, symplectic capacities and volume\nby Ely Kerman (University
of Illinois Urbana-Champaign) as part of Geometry and Dynamics seminar\n\n
\nAbstract\nIn this talk\, I will discuss an inequality between a symplect
ic version \nof the mean width of a convex body and its symplectic capacit
y. This is \nmotivated by and generalizes an equality established by Artst
ein-Avidan \nand Ostrover. The proof utilizes their symplectic Brunn-Minko
wski \ninequality together with a local version of Viterbo's conjecture \n
established by Abbondandolo and Benedetti. I will also describe several \n
examples and secondary results that suggest that the difference between \n
the symplectic mean width and the mean width is deeply related to toric \n
symmetry. This is joint work in progress with Jonghyeon Ahn.\n
LOCATION:https://researchseminars.org/talk/GDS/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pazit Haim-Kislev (Tel Aviv University)
DTSTART;VALUE=DATE-TIME:20230329T111000Z
DTEND;VALUE=DATE-TIME:20230329T123000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/78
DESCRIPTION:Title: Sym
plectic Barriers\nby Pazit Haim-Kislev (Tel Aviv University) as part o
f Geometry and Dynamics seminar\n\n\nAbstract\nIn his seminal 2001 paper\,
Biran introduced the concept of Lagrangian \nBarriers\, a symplectic rigi
dity phenomenon coming from obligatory \nintersections with Lagrangian sub
manifolds which doesn't come from \nmere topology. Since then several othe
r examples for Lagrangian barriers \nhave been discovered. In this joint w
ork with Richard Hind and Yaron \nOstrover\, we introduce the first exampl
e (as far as we know) of Symplectic \nBarriers\, a symplectic rigidity com
ing from obligatory intersections of \nsymplectic embeddings with symplect
ic submanifolds (and in particular \nnot Lagrangian).\n
LOCATION:https://researchseminars.org/talk/GDS/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Viktor L. Ginzburg (University of California\, Santa Cruz)
DTSTART;VALUE=DATE-TIME:20230419T111000Z
DTEND;VALUE=DATE-TIME:20230419T120000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/79
DESCRIPTION:Title: Top
ological Entropy of Reeb Flows\, Barcodes and Floer Theory\nby Viktor
L. Ginzburg (University of California\, Santa Cruz) as part of Geometry an
d Dynamics seminar\n\n\nAbstract\nTopological entropy is one of the fundam
ental invariants of a dynamical \nsystem\, measuring its complexity. In th
is talk\, we focus on connections \nbetween the topological entropy of a H
amiltonian dynamical system\, e.g.\, \na Hamiltonian diffeomorphism or a R
eeb or geodesic flow\, and its \nSymplectic/Floer homology. We recall the
definition of barcode entropy — \na Floer theoretic counterpart of topol
ogical entropy — and discuss \npossible ways to extend it to Reeb flows.
The talk is based on joint \nwork with Erman Cineli\, Basak Gurel and Mar
co Mazzucchelli.\n
LOCATION:https://researchseminars.org/talk/GDS/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Başak Z. Gürel (University of Central Florida)
DTSTART;VALUE=DATE-TIME:20230419T121000Z
DTEND;VALUE=DATE-TIME:20230419T130000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/80
DESCRIPTION:Title: On
the volume of Lagrangian submanifolds\nby Başak Z. Gürel (University
of Central Florida) as part of Geometry and Dynamics seminar\n\n\nAbstrac
t\nWe will discuss the continuity property of the surface area of Lagrangi
an \nsubmanifolds\, or to be more precise its lower semi-continuity with r
espect \nto the gamma-norm\, and connections with integral geometry\, Floe
r theory \nand barcodes. The talk is based on joint work with Erman Cineli
and \nViktor Ginzburg.\n
LOCATION:https://researchseminars.org/talk/GDS/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shmuel Weinberger (University of Chicago)
DTSTART;VALUE=DATE-TIME:20230503T111000Z
DTEND;VALUE=DATE-TIME:20230503T123000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/81
DESCRIPTION:Title: Tor
sion\, L^2 cohomology and complexity\nby Shmuel Weinberger (University
of Chicago) as part of Geometry and Dynamics seminar\n\n\nAbstract\nAtiya
h introduced real valued L^2 betti numbers as a way of\nunderstanding the
(usually infinite dimensional) cohomology of\nuniversal covers of finite c
omplexes. As far as anyone knows these\nare always integers for torsion f
ree fundamental group\, but for groups\nwith torsion very much more exotic
possibilities arise.\n\nWe will use this and an invariant of Cheeger and
Gromov to see that\nwhenever an oriented smooth manifold of dimension 4k+3
has torsion in\nits fundamental group\, there are many other manifolds ho
motopy\nequivalent but not diffeomorphic to it and that in the known\nsitu
ations where betti numbers can be irrational there is even an\ninfinitely
generated group of such! And\, I will also use this\ninvariant to explain
how many simplices (roughly) it takes to build a\nstandard Lens space. T
his is based on old work with Stanley Chang\,\nand recent work with Geunho
Lim.\n
LOCATION:https://researchseminars.org/talk/GDS/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gleb Smirnov (University of Geneva)
DTSTART;VALUE=DATE-TIME:20230510T111000Z
DTEND;VALUE=DATE-TIME:20230510T120000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/82
DESCRIPTION:Title: Lag
rangian rigidity in K3 surfaces\nby Gleb Smirnov (University of Geneva
) as part of Geometry and Dynamics seminar\n\n\nAbstract\nSheridan-Smith a
nd Entov-Verbitsky show that every Maslov-zero Lagrangian \ntorus in a K3
surface has a nontrivial and primitive homology class. \nIn this talk\, we
prove the "nontrivial" part of their theorem with a \ndifferent method an
d the converse result.\n
LOCATION:https://researchseminars.org/talk/GDS/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcelo R. R. Alves (University of Antwerp)
DTSTART;VALUE=DATE-TIME:20230510T121000Z
DTEND;VALUE=DATE-TIME:20230510T130000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/83
DESCRIPTION:Title: C^0
-stability of topological entropy for 3-dimensional Reeb flows\nby Mar
celo R. R. Alves (University of Antwerp) as part of Geometry and Dynamics
seminar\n\n\nAbstract\nThe C^0-distance on the space of contact forms on a
contact manifold has \nbeen studied recently by different authors. It can
be thought of as an \nanalogue for Reeb flows of the Hofer metric on the
space of Hamiltonian \ndiffeomorphisms. In this talk\, I will explain some
recent progress on \nthe stability properties of the topological entropy
with respect to this \ndistance. This is joint work with Lucas Dahinden\,
Matthias Meiwes and \nAbror Pirnapasov.\n
LOCATION:https://researchseminars.org/talk/GDS/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joé Brendel (Tel Aviv University)
DTSTART;VALUE=DATE-TIME:20230517T111000Z
DTEND;VALUE=DATE-TIME:20230517T123000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/84
DESCRIPTION:Title: Lag
rangian product tori in $S^2 \\times S^2$\nby Joé Brendel (Tel Aviv U
niversity) as part of Geometry and Dynamics seminar\n\n\nAbstract\nA Lagra
ngian product torus in $S^2 \\times S^2$ is a Lagrangian \ntorus obtained
by taking a product of circles. The main goal of this \ntalk is to give a
symplectic classification of product tori and \nillustrate that interestin
g things can happen in case the symplectic \nform is non-monotone. We make
a detour through toric geometry and \ndiscuss the more general classifica
tion question of toric fibres. If \ntime permits\, we will discuss related
questions and some applications. \nThis is partially based on joint work
with Joontae Kim.\n
LOCATION:https://researchseminars.org/talk/GDS/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lenya Ryzhik (Stanford University)
DTSTART;VALUE=DATE-TIME:20230531T111000Z
DTEND;VALUE=DATE-TIME:20230531T123000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/85
DESCRIPTION:Title: Dif
fusion of learning models\nby Lenya Ryzhik (Stanford University) as pa
rt of Geometry and Dynamics seminar\n\n\nAbstract\nThe notion of diffusion
of knowledge goes at least as far back to \nChapter 1 of the "Pickwick Pa
pers". However\, its mathematical modeling \nin macroeconomics is much mor
e recent. We will discuss some models \nproposed by R. Lucas and B. Moll a
bout ten years ago.\nVarious versions lead to the mean field games type PD
E and also \ninfinite-dimensional optimal control Hamilton-Jacobi problems
. We will \ndiscuss the little mathematical progress but mostly focus on t
he \nmodeling and open questions aspects.\n
LOCATION:https://researchseminars.org/talk/GDS/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hyunmoon Kim (University of Toronto\, Tel Aviv University)
DTSTART;VALUE=DATE-TIME:20230607T111000Z
DTEND;VALUE=DATE-TIME:20230607T123000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/86
DESCRIPTION:Title: The
real orbits of complex Lagrangian Grassmannians\nby Hyunmoon Kim (Uni
versity of Toronto\, Tel Aviv University) as part of Geometry and Dynamics
seminar\n\n\nAbstract\nThe Riemann sphere can be broken up into three orb
its of SL(2\, R)\, as \ntwo open hemispheres and a great circle. We will d
iscuss a generalization \nof this phenomenon in complex Lagrangian Grassma
nnians of higher \ndimensions under the action of the real symplectic grou
p. We will \ngive formulas for the number of orbits\, incidence relations\
, and \ntheir dimensions. We will also show homotopy equivalences between
\nthese orbits and some other Grassmannian objects\, and if time permits\,
\na strategy to compute their homology.\n
LOCATION:https://researchseminars.org/talk/GDS/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lev Birbrair (The Federal University of Ceará and Jagiellonian Un
iversity)
DTSTART;VALUE=DATE-TIME:20230614T111000Z
DTEND;VALUE=DATE-TIME:20230614T123000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/87
DESCRIPTION:by Lev Birbrair (The Federal University of Ceará and Jagiello
nian University) as part of Geometry and Dynamics seminar\n\n\nAbstract\nI
am going to describe the first attempt of outer Lipschitz Classification
\nof germs of Semialgebraic Surfaces. We show how the classification \nque
stion can be solved for a special case - the surfaces\, obtained as \na un
ion of two Normally Embedded Hölder triangles.\n
LOCATION:https://researchseminars.org/talk/GDS/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Nemirovski (Steklov Mathematical Institute and Ruhr Univers
ity Bochum)
DTSTART;VALUE=DATE-TIME:20230621T111000Z
DTEND;VALUE=DATE-TIME:20230621T123000Z
DTSTAMP;VALUE=DATE-TIME:20240715T184236Z
UID:GDS/88
DESCRIPTION:Title: Leg
endrian links and déjà vu moments\nby Stefan Nemirovski (Steklov Mat
hematical Institute and Ruhr University Bochum) as part of Geometry and Dy
namics seminar\n\n\nAbstract\nLegendrian links in the space of null geodes
ics of a spacetime\ncan be used to detect "déjà vu moments"\, i.e. diffe
rent instances\nat which an observer receives the same light ray. In the t
alk\,\nI'll discuss the relevant class of Legendrian links and some\nensui
ng open problems.\n
LOCATION:https://researchseminars.org/talk/GDS/88/
END:VEVENT
END:VCALENDAR