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BEGIN:VEVENT
SUMMARY:Daniel Peralta-Salas (ICMAT)
DTSTART;VALUE=DATE-TIME:20201027T150000Z
DTEND;VALUE=DATE-TIME:20201027T160000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/1
DESCRIPTION:Title: The topology of the nodal sets of eigenfunctions and a
problem of Michael Berry.\nby Daniel Peralta-Salas (ICMAT) as part of
Geometric Structures Research Seminar\n\n\nAbstract\nIn 2001\, Sir Michael
Berry conjectured that given any knot there should exist a (complex-value
d) eigenfunction of the harmonic oscillator (or the hydrogen atom) whose n
odal set contains a component of such a knot type. This is a particular in
stance of the following problem: how is the topology of the nodal sets of
eigenfunctions of Schrodinger operators? In this talk I will focus on the
flexibility aspects of the problem: either you construct a suitable Rieman
nian metric adapted to the submanifold you want to realize\, or you consid
er operators with a large group of symmetries (e.g.\, the Laplacian on the
round sphere\, or the harmonic quantum oscillator)\, and exploit the larg
e multiplicity of the high eigenvalues. In particular\, I will show how to
prove Berry's conjecture using an inverse localization property. This tal
k is based on different joint works with A. Enciso\, D. Hartley and F. Tor
res de Lizaur.\n\nSubscribe at https://sites.google.com/view/geometric-str
uctures/ to receive the password by mail.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eero Hakavuori (SISSA)
DTSTART;VALUE=DATE-TIME:20201103T150000Z
DTEND;VALUE=DATE-TIME:20201103T160000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/2
DESCRIPTION:Title: Carnot groups and abnormal dynamics\nby Eero Hakavu
ori (SISSA) as part of Geometric Structures Research Seminar\n\n\nAbstract
\nThe existence of so called abnormal curves is one of the features distin
guishing sub-Riemannian geometry from Riemannian geometry. The need to und
erstand (or avoid) abnormal curves appears in many sub-Riemannian problems
\, such as the regularity of length-minimizing curves and the Sard problem
. Some recent progress in both of these problems has been obtained by stud
ying abnormal curves as trajectories of dynamical systems. In this talk\,
I will present some of the story of abnormal dynamics in the setting of Ca
rnot groups. In particular\, I will cover how to lift an arbitrary traject
ory of an arbitrary polynomial ODE to an abnormal curve in some Carnot gro
up.\n\nPlease register to https://sites.google.com/view/geometric-structur
es/ to get the password\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miruna-Stefana Sorea (SISSA)
DTSTART;VALUE=DATE-TIME:20201117T150000Z
DTEND;VALUE=DATE-TIME:20201117T160000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/3
DESCRIPTION:Title: Disguised toric dynamical systems\nby Miruna-Stefan
a Sorea (SISSA) as part of Geometric Structures Research Seminar\n\n\nAbst
ract\nWe study families of polynomial dynamical systems inspired by bioche
mical reaction networks. We focus on complex balanced mass-action systems\
, which have also been called toric dynamical systems\, by Craciun\, Dicke
nstein\, Shiu and Sturmfels. These systems are known or conjectured to enj
oy very strong dynamical properties\, such as existence and uniqueness of
positive steady states\, local and global stability\, persistence\, and pe
rmanence. We consider the class of disguised toric dynamical systems\, whi
ch contains toric dynamical systems\, and to which all dynamical propertie
s mentioned above extend naturally. We show that\, for some families of re
action networks\, this new class is much larger than the class of toric sy
stems. For example\, for some networks we may even go from an empty locus
of toric systems in parameter space to a positive-measure locus of disguis
ed toric systems. We focus on the characterization of the disguised toric
locus by means of real algebraic geometry. Joint work with Gheorghe Craciu
n and Laura Brustenga i Moncusí.\n\nRegister at https://docs.google.com/f
orms/d/e/1FAIpQLSfOAjTSQWOlb4jcqIkLNo1Qz2tQHMBGs13XmlVmtaRpIFE1wA/viewform
\nto get the password for the talk\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raman Sanyal (Frankfurt)
DTSTART;VALUE=DATE-TIME:20201124T150000Z
DTEND;VALUE=DATE-TIME:20201124T160000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/4
DESCRIPTION:Title: Normally inscribable polytopes\, routed trajectories\,
and reflection arrangements\nby Raman Sanyal (Frankfurt) as part of Ge
ometric Structures Research Seminar\n\n\nAbstract\nSteiner posed the quest
ion if any 3-dimensional polytope had a realization with vertices on a sph
ere. Steinitz constructed the first counter examples and Rivin gave a comp
lete complete answer to Steiner's question. In dimensions 4 and up\, the U
niversality Theorem renders the question for inscribable combinatorial typ
es hopeless. In this talk\, I will address the following refined question:
Given a polytope P\, is there a continuous deformation of P into an inscr
ibed polytope that keeps corresponding faces parallel?\nThis question has
strong ties to deformations of Delaunay subdivisions and ideal hyperbolic
polyhedra and its study reveals a rich interplay of algebra\, geometry\, a
nd combinatorics. In the first part of the talk\, I will discuss relations
to routed trajectories of particles in a ball and reflection groupoids an
d show that that the question is polynomial time decidable.\nIn the second
part of the talk\, we will focus on class of zonotopes\, that is\, polyto
pes representing hyperplane arrangements. It turns out that inscribable zo
notopes are rare and intimately related to reflection groups and Grunbaum'
s quest for simplicial arrangements. This is based on joint work with Seb
astian Manecke.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gal Binyamini (Weizmann Institute of Science)
DTSTART;VALUE=DATE-TIME:20201201T140000Z
DTEND;VALUE=DATE-TIME:20201201T150000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/5
DESCRIPTION:Title: Cylindrical decomposition in real and complex geometry<
/a>\nby Gal Binyamini (Weizmann Institute of Science) as part of Geometric
Structures Research Seminar\n\n\nAbstract\nThe decomposition of a set int
o "cylinders" in one of the fundamental tools of semi-algebraic geometry (
as well as subanalytic geometry and o-minimal geometry). Defined by means
of intervals\, these cylinders are an essentially real-geometric construct
.\nIn a recent paper wit Novikov we introduce a notion of "complex cells"\
, that form a complexification of real cylinders. It turns out that such c
omplex cells admit a rich hyperbolic geometry\, which is not directly visi
ble in their real counterparts. I will sketch some of this theory\, and ho
w it can be used to prove some new results in real geometry (for instance
a sharpening of the Yomdin-Gromov lemma).\n\nPlease subscribe to https://s
ites.google.com/view/geometric-structures/registration-form\nto receive th
e password\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maurizia Rossi (University of Milano-Bicocca)
DTSTART;VALUE=DATE-TIME:20201207T150000Z
DTEND;VALUE=DATE-TIME:20201207T160000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/6
DESCRIPTION:Title: Geometrical properties of random eigenfunctions\nby
Maurizia Rossi (University of Milano-Bicocca) as part of Geometric Struct
ures Research Seminar\n\n\nAbstract\nIn this talk we deal with the geometr
y of random eigenfunctions on manifolds (the round sphere\, the standard f
lat torus\, the Euclidean plane...) motivated by both Yau's conjecture and
Berry's ansatz. In particular\, we investigate the asymptotic behavior (i
n the high-energy limit) of the so-called nodal length for random spherica
l harmonics and (un)correlation phenomena between the latter and other Lip
schitz-Killing curvatures of their excursion sets at any level.\nThis talk
is mainly based on joint works with V. Cammarota\, D. Marinucci\, I. Nour
din\, G. Peccati and I. Wigman.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lev Buhovsky (Tel Aviv University)
DTSTART;VALUE=DATE-TIME:20201215T150000Z
DTEND;VALUE=DATE-TIME:20201215T160000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/7
DESCRIPTION:Title: Critical points of eigenfunctions\nby Lev Buhovsky
(Tel Aviv University) as part of Geometric Structures Research Seminar\n\n
\nAbstract\nOn a closed Riemannian manifold\, the Courant nodal domain the
orem gives an upper bound on the number of nodal domains of n-th eigenfunc
tion of the Laplacian. In contrast to that\, there does not exist such bou
nd on the number of isolated critical points of an eigenfunction. I will t
ry to sketch a proof of the existence of a Riemannian metric on the 2-dime
nsional torus\, whose Laplacian has infinitely many eigenfunctions\, each
of which has infinitely many isolated critical points. Based on a joint wo
rk with A. Logunov and M. Sodin.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olga Paris-Romaskevich (Institut de Mathématiques de Marseille)
DTSTART;VALUE=DATE-TIME:20210126T150000Z
DTEND;VALUE=DATE-TIME:20210126T160000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/8
DESCRIPTION:Title: Tiling billiards in periodic tilings by equal triangles
(and quadrilaterals)\nby Olga Paris-Romaskevich (Institut de Mathéma
tiques de Marseille) as part of Geometric Structures Research Seminar\n\n\
nAbstract\nI will make an elementary introduction to tiling billiards —
model of a light moving through a tiling under refraction laws.\nThis clas
s of dynamical systems is new to mathematicians\, simple to define as well
as connected to already existing areas of research such as ergodic theory
of interval exchange transformations and Novikov's problem on plane secti
ons of 3-periodic surfaces.\n\nI hope you will love it as much as I love i
t !\n\n(Not a very hard) Homework before the talk :\n\nWatch a following 5
-MIN movie (here is a link to Youtube) by a wonderful mathematician and an
imator Ofir David.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessandro Tamai (University of Trieste)
DTSTART;VALUE=DATE-TIME:20210112T150000Z
DTEND;VALUE=DATE-TIME:20210112T160000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/9
DESCRIPTION:Title: Singular solutions spaces of rolling balls problem\
nby Alessandro Tamai (University of Trieste) as part of Geometric Structur
es Research Seminar\n\n\nAbstract\nThe "Rolling Balls Model"\, the model d
escribing a pair of spheres of different ray rolling one on another withou
t slipping or twisting\, is a classical example of sub-Riemannian problem.
The symmetries of the distribution associated with the system depend on t
he ratio of the rays and radically change when the ratio equals 3. Indeed\
, for this value of the ratio (and only for this value) it extends to the
exceptional simple Lie group G2 which acts\, still for this value of the r
atio\, also on the singular solutions related to the problem.\nIn this tal
k we show how it is possible to describe the spaces of such singular solut
ions in a geometric way\, as a family of 5-dimensional manifolds depending
on the ratio. For rational values of the ratio such manifolds have a stru
cture of SO(2)-principal bundles which are not topologically distinguished
by their homology\, homotopy and de Rham cohomology groups. In addition\,
we show that for integer values of the ratio the configuration manifold o
f the problem is a branched covering of each of such manifolds and how the
covering maps associated allow to relate them with another known family o
f topological spaces\, the lens spaces.\n\nThis talk is based on the resea
rch works developed in my master thesis at University of Trieste\, under t
he supervision of the professor A.Agrachev.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kathlén Kohn (Royal Institute of Technology (KTH))
DTSTART;VALUE=DATE-TIME:20210119T150000Z
DTEND;VALUE=DATE-TIME:20210119T160000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/10
DESCRIPTION:Title: The adjoint of a polytope\nby Kathlén Kohn (Royal
Institute of Technology (KTH)) as part of Geometric Structures Research S
eminar\n\n\nAbstract\nThis talk brings many areas together: discrete geome
try\, statistics\, intersection theory\, classical algebraic geometry\, ge
ometric modeling\, and physics. First\, we recall the definition of the ad
joint of a polytope given by Warren in 1996 in the context of geometric mo
deling. He defined this polynomial to generalize barycentric coordinates f
rom simplices to arbitrary polytopes. Secondly\, we show how this polynomi
al appears in statistics. It is the numerator of a generating function ove
r all moments of the uniform probability distribution on a polytope. Third
ly\, we prove the conjecture that the adjoint is the unique polynomial of
minimal degree which vanishes on the non-faces of a simple polytope. In ad
dition\, we see that the adjoint appears as the central piece in Segre cla
sses of monomial schemes\, and in the study of scattering amplitudes in pa
rticle physics. Finally\, we observe that adjoints of polytopes are specia
l cases of the classical notion of adjoints of divisors. Since the adjoint
of a simple polytope is unique\, the corresponding divisors have unique c
anonical curves. In the case of three-dimensional polytopes\, we show that
these divisors are either K3 - or elliptic surfaces.\nThis talk is based
on joint works with Kristian Ranestad\, Boris Shapiro and Bernd Sturmfels.
\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noémie Combe (Max Planck Institute)
DTSTART;VALUE=DATE-TIME:20210202T150000Z
DTEND;VALUE=DATE-TIME:20210202T160000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/11
DESCRIPTION:Title: Complement of the discriminant variety\, Gauss–skizz
e operads and hidden symmetries\nby Noémie Combe (Max Planck Institut
e) as part of Geometric Structures Research Seminar\n\n\nAbstract\nIn this
talk\, the configuration space of marked points on the complex plane is c
onsidered. We investigate a decomposition of this space by so-called Gauss
-skizze i.e. a class of graphs being forests. These Gauss-skizze\, reminis
cent of Grothendieck's dessins d'enfant\, provide a totally different real
geometric insight on this complex configuration space\, which under the l
ight of classical complex geometry tools\, remains invisible. Topologicall
y speak- ing\, this stratification is shown to be a Goresky–MacPherson s
tratification.\nWe prove that for Gauss-skizze\, classical tools from defo
rmation theory\, ruled by a Maurer--Cartan equation can be used only local
ly.\nWe show as well\, that the deformation of the Gauss-skizze is governe
d by a Hamilton--Jacobi differential equation.\nFinally\, a Gauss-skizze o
perad is introduced which can be seen as an enriched Fulton--MacPherson op
erad\, topologically equivalent to the little 2-disc operad.\nThe combinat
orial flavour of this tool allows not only a new interpretation of the mod
uli space of genus 0 curves with n marked points\, but gives a very geomet
ric understanding of the Grothendieck--Teichmuller group.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erlend Grong (University of Bergen)
DTSTART;VALUE=DATE-TIME:20210209T151500Z
DTEND;VALUE=DATE-TIME:20210209T161500Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/12
DESCRIPTION:Title: On the equivalence problem in sub-Riemannian geometry<
/a>\nby Erlend Grong (University of Bergen) as part of Geometric Structure
s Research Seminar\n\n\nAbstract\nIn mathematics\, we are always intereste
d in understanding when two objects are essentially the same. For the cont
ext of geometric structures\, such as Riemannian and sub-Riemannian manifo
lds\, "essentially the same" means being connected by an isometry.\n\n\nFo
r a Riemannian geometry\, the central object measuring the local obstructi
on to the existence of an isometry is the curvature tensor of the Levi-Civ
ita connection. We want to show that similar objects can be found on sub-R
iemannian manifolds with constant nilpotentization\, based on the work of
T. Morimoto.\n\nWe will show explicit formulas for a canonical choice of g
rading and connection for sub-Riemannian manifolds in some explicit cases.
\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olga Paris-Romaskevich (Institut de Mathématiques de Marseille)
DTSTART;VALUE=DATE-TIME:20210216T151500Z
DTEND;VALUE=DATE-TIME:20210216T161500Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/13
DESCRIPTION:Title: Tiling billiards in periodic tilings by equal triangle
s (and quadrilaterals)\nby Olga Paris-Romaskevich (Institut de Mathém
atiques de Marseille) as part of Geometric Structures Research Seminar\n\n
\nAbstract\nI will make an elementary introduction to tiling billiards —
model of a light moving through a tiling under refraction laws.\nThis cla
ss of dynamical systems is new to mathematicians\, simple to define as wel
l as connected to already existing areas of research such as ergodic theor
y of interval exchange transformations and Novikov's problem on plane sect
ions of 3-periodic surfaces.\n\nI hope you will love it as much as I love
it !\n\n(Not a very hard) Homework before the talk :\n\nWatch a following
5-MIN movie (here is a link to Youtube) by a wonderful mathematician and a
nimator Ofir David.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Clayton Shonkwiler (Colorado State University)
DTSTART;VALUE=DATE-TIME:20210223T151500Z
DTEND;VALUE=DATE-TIME:20210223T161500Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/14
DESCRIPTION:Title: The (Symplectic) Geometry of Spaces of Frames\nby
Clayton Shonkwiler (Colorado State University) as part of Geometric Struct
ures Research Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Akos Matszangosz (Alfréd Rényi Institute of Mathematics)
DTSTART;VALUE=DATE-TIME:20210302T151500Z
DTEND;VALUE=DATE-TIME:20210302T161500Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/15
DESCRIPTION:Title: Cohomology rings of real flag manifolds\nby Akos M
atszangosz (Alfréd Rényi Institute of Mathematics) as part of Geometric
Structures Research Seminar\n\n\nAbstract\nThe cohomology ring of a comple
x (partial) flag manifold has two classical descriptions\; a topological o
ne (via characteristic classes) and a geometric one (via Schubert classes)
. Similar descriptions are well-known for real flag manifolds X with mod 2
coefficients. In this talk I will discuss some aspects of what can be sai
d with rational\, or integer coefficients. Namely\, I will consider questi
ons of the following type:\n1) Which Schubert varieties represent an integ
er cohomology class?\n\n2) What are their structure constants?\n\n3) What
can be said about torsion in $H^*(X\;\\Z)$?\n\nI will also discuss some ap
plications of the ring structure to real Schubert calculus.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Khazhgali Kozhasov (Technische Universität Braunschweig)
DTSTART;VALUE=DATE-TIME:20210309T151500Z
DTEND;VALUE=DATE-TIME:20210309T161500Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/16
DESCRIPTION:Title: On minimality of determinantal varieties\nby Khazh
gali Kozhasov (Technische Universität Braunschweig) as part of Geometric
Structures Research Seminar\n\n\nAbstract\nMinimal submanifolds are mathem
atical abstractions of soap films: they minimize the Riemannian volume loc
ally around every point. Finding minimal algebraic hypersurfaces in 𝑅
𝑛 for each n is a long-standing open problem posed by Hsiang. In 2010 T
kachev gave a partial solution to this problem showing that the hypersurfa
ce of n x n real matrices of corank one is minimal. I will discuss the fol
lowing generalization of this fact to all determinantal matrix varieties:
for any m\, n and rThe average condition number of different problems\, f
rom a geometric perspective\nby Carlos Beltrán (Universidad de Cantab
ria) as part of Geometric Structures Research Seminar\n\n\nAbstract\nI wil
l present the condition number of problems from a general perspective as a
measure of the stability of problems. Then I will discuss how does this c
ondition number look and interact with other mathematical concepts in diff
erent problems which are very basic but are still full of mysteries: polyn
omial solving\, eigenvalue/eigenvector problems or tensor decomposition pr
oblems. All the material will be presented for a general audience. Differe
nt parts of what will be presented has been done with different authors\,
for example the tensor decomposition part has been done with Paul Breiding
and Nick Vannieuwenhoven. Check the following video for our result in 2 m
inutes:\nhttps://www.teamco.unican.es/portfolio-item/pencil-based-algorith
ms-for-tensor-rank-decomposition-are-not-stable/\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Lotz (Warwick University)
DTSTART;VALUE=DATE-TIME:20210323T151500Z
DTEND;VALUE=DATE-TIME:20210323T161500Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/18
DESCRIPTION:Title: Concentration of Measure in Integral Geometry\nby
Martin Lotz (Warwick University) as part of Geometric Structures Research
Seminar\n\n\nAbstract\nIntrinsic volumes are fundamental geometric invaria
nts that include the Euler characteristic and the volume. Important result
s in integral geometry relate the intrinsic volumes of random projections\
, intersections\, and sums of convex bodies to those of the individual vol
umes. We present a new interpretations of classic results\, based on the o
bservation that intrinsic volumes (both in spherical and Euclidean setting
s) concentrate around certain indices. One consequence is\, for example\,
that as the dimension of a subspace varies\, the average intrinsic volume
polynomial of a random projection of a convex body to this subspace is as
large as possible or is negligible\, and the exact location of the transit
ion between these two cases can be expressed in terms of a summary paramet
er associated with the convex body. Similar phase transitions appear in re
lated problems\, including the rotation mean formula\, the slicing (Crofto
n) formula\, and the kinematic formula. This is joint work with Joel Tropp
.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugenii Shustin (Tel-Aviv University)
DTSTART;VALUE=DATE-TIME:20210406T141500Z
DTEND;VALUE=DATE-TIME:20210406T151500Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/19
DESCRIPTION:Title: Expressive geometry\nby Eugenii Shustin (Tel-Aviv
University) as part of Geometric Structures Research Seminar\n\n\nAbstract
\nWe review two so-called expressive models\, morsifications of real plane
curve singularities introduced in 70s by A'Campo and Gusein-Zade\, and re
al affine expressive curves. These models are characterized by the propert
y that their underlining polynomial has the smallest number of critical po
ints allowed by the topology of the real point set. The classification of
these objects is tightly related to the mutational equivalence of the corr
esponding quivers (which in turn naturally appear in the theory of cluster
algebras). We discuss various problems in the geometry of morsifications
and expressive curves\, including related objects like planar divides\, li
nks of singularities and links of curves at infinity\, combinatorics of qu
ivers. Based on joint works with S. Fomin\, P. Pylyavskyy\, D. Thurston.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miruna-Stefana Sorea (SISSA)
DTSTART;VALUE=DATE-TIME:20210330T141500Z
DTEND;VALUE=DATE-TIME:20210330T151500Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/20
DESCRIPTION:Title: Poincaré-Reeb trees of real Milnor fibres\nby Mir
una-Stefana Sorea (SISSA) as part of Geometric Structures Research Seminar
\n\n\nAbstract\nWe study the real Milnor fibre of real bivariate polynomia
l functions vanishing at the origin\, with an isolated local minimum at th
is point. We work in a neighbourhood of the origin in which its non-zero l
evel sets are smooth Jordan curves. Whenever the origin is a Morse critica
l point\, the sufficiently small levels become boundaries of convex disks.
Otherwise\, they may fail to be convex\, as was shown by Coste.\n\nIn ord
er to measure the non-convexity of the level curves\, we introduce a new c
ombinatorial object\, called the Poincaré-Reeb tree\, and show that local
ly the shape stabilises and that no spiralling phenomena occur near the or
igin. Our main objective is to characterise all topological types of asymp
totic Poincaré-Reeb trees. To this end\, we construct a family of polynom
ials with non-Morse strict local minimum at the origin\, realising a large
class of such trees.\n\nAs a preliminary step\, we reduce the problem to
the univariate case\, via the interplay between the polar curve and its di
scriminant. Here we give a new and constructive proof of the existence of
Morse polynomials whose associated permutation (the so-called "Arnold snak
e") is separable\, using tools inspired from Ghys's work.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Galuppi (University of Trieste)
DTSTART;VALUE=DATE-TIME:20210413T141500Z
DTEND;VALUE=DATE-TIME:20210413T151500Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/21
DESCRIPTION:Title: Signature tensors of paths\nby Francesco Galuppi (
University of Trieste) as part of Geometric Structures Research Seminar\n\
n\nAbstract\nI'm interested in connections between algebraic geometry and
other branches of math. In stochastic analysis\, a standard method to stud
y a path is to work with its signature. This is a sequence of tensors that
encode information of the path in a compact form. When the path varies\,
such signatures parametrize an algebraic variety in the tensor space. My g
oal is to study the geometry of such varieties and to link it to propertie
s of certain classes of paths.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emil Horobert (Sapientia Hungarian University of Transylvania)
DTSTART;VALUE=DATE-TIME:20210420T141500Z
DTEND;VALUE=DATE-TIME:20210420T151500Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/22
DESCRIPTION:Title: The critical curvature degree of an algebraic variety<
/a>\nby Emil Horobert (Sapientia Hungarian University of Transylvania) as
part of Geometric Structures Research Seminar\n\n\nAbstract\nThis topic is
about the complexity involved in the computation of the reach in arbitrar
y dimensions and in particular the computation of the critical spherical c
urvature points of an arbitrary algebraic variety. We present properties o
f the critical spherical curvature points as well as an algorithm for comp
uting them.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Draisma (Universität Bern)
DTSTART;VALUE=DATE-TIME:20210427T141500Z
DTEND;VALUE=DATE-TIME:20210427T151500Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/23
DESCRIPTION:Title: Infinite-dimensional geometry with symmetry\nby Ja
n Draisma (Universität Bern) as part of Geometric Structures Research Sem
inar\n\n\nAbstract\nMost theorems in finite-dimensional algebraic geometry
break down in infinite dimensions---for instance\, the polynomial ring C[
x_1\,x_2\,...] is not Noetherian. However\, it turns out that some results
do survive when a sufficiently large symmetry group is imposed\; e.g.\, i
deals in C[x_1\,x_2\,...] that are preserved under all variable permutatio
ns do satisfy the ascending chain condition.\nThis phenomenon is relevant
in pure and applied mathematics\, since many algebraic models come in infi
nite families with highly symmetric infinite-dimensional limits. Here the
symmetry is typically captured by either the infinite symmetric group or t
he infinite general linear group. Theorems about the limit imply uniform b
ehaviour of the members of the family.\nI will present older and new resul
ts in this area\, along with applications to algebraic statistics\, tensor
decomposition\, and algebraic combinatorics.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boulos El Hilany (Johann Radon Institute for Computational and App
lied Mathematics\, Linz)
DTSTART;VALUE=DATE-TIME:20210518T141500Z
DTEND;VALUE=DATE-TIME:20210518T151500Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/24
DESCRIPTION:Title: Computing efficiently the non-properness set of polyno
mial maps on the plane\nby Boulos El Hilany (Johann Radon Institute fo
r Computational and Applied Mathematics\, Linz) as part of Geometric Struc
tures Research Seminar\n\n\nAbstract\nI will present new mathematical and
computational tools to develop a complete and efficient algorithm for comp
uting the set of non-properness of polynomial maps in the complex (and rea
l) plane. In particular\, this is a subset of the plane where a dominant p
olynomial map as above is not proper. The algorithm takes into account the
sparsity of polynomials\, and the genericness of the coefficients as it d
epends on their Newton polytopes. As a byproduct it provides a finer repre
sentation of the set of non-properness as a union of algebraic or semi-alg
ebraic sets\, that correspond to edges of the Newton polytopes\, which is
of independent interest. This is a joint work with Elias Tsigaridas.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Damien Gayet (Université Grenoble I)
DTSTART;VALUE=DATE-TIME:20210525T141500Z
DTEND;VALUE=DATE-TIME:20210525T151500Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/25
DESCRIPTION:Title: Asymptotic topology of random excursion sets\nby D
amien Gayet (Université Grenoble I) as part of Geometric Structures Resea
rch Seminar\n\n\nAbstract\nLet f be a smooth random Gaussian field over th
e unit ball of R^n. It is very natural\nto imagine that for a high level u
\, {f>u} is mainly composed of small components homeomorphic to n-balls. I
will explain that in average\, this intuition is true. After recalling t
he historical background of this subject\, and will present the ideas of
the proof\, which holds on (deterministic) Morse theory and a control of r
andom critical points of given index.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michele Stecconi (Université de Nantes)
DTSTART;VALUE=DATE-TIME:20210504T141500Z
DTEND;VALUE=DATE-TIME:20210504T151500Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/26
DESCRIPTION:Title: Semicontinuity of Betti numbers: A little surgery cann
ot kill homology\nby Michele Stecconi (Université de Nantes) as part
of Geometric Structures Research Seminar\n\n\nAbstract\nA consequence of T
hom Isotopy Lemma is that the set of solutions of a regular smooth equatio
n is stable under C^1-small perturbations (it remains isotopic to the orig
inal one)\, but what happens if the perturbation is just C^0-small? In thi
s case\, the topology of the set of solution may change. However\, it turn
s out that the Homology groups cannot "decrease". In this talk I will pres
ent such result and some related examples and applications. This theorem i
s useful in those contexts where the price to pay to approximate something
in C^1 is higher than in C^0. For instance in the search for quantitative
bounds (here the price can be the degree of an algebraic approximation) o
r in combination with Eliashberg's and Mishachev's holonomic approximation
Theorem (which is C^0 at most).\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julian Sahasrabudhe (University of Cambridge)
DTSTART;VALUE=DATE-TIME:20210511T141500Z
DTEND;VALUE=DATE-TIME:20210511T151500Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/27
DESCRIPTION:Title: Anti-concentration and the geometry of polynomials
\nby Julian Sahasrabudhe (University of Cambridge) as part of Geometric St
ructures Research Seminar\n\n\nAbstract\nLet X be a random variable taking
values in {0\,...\,n} with standard deviation sigma and let f_X be its pr
obability generating function. Pemantle conjectured that if sigma is large
and f_X has no roots close to 1 in the complex plane then X must approxim
ate a normal distribution. In this talk\, I will discuss the resolution of
Pemantle's conjecture and its application to prove a conjecture of Ghosh\
, Liggett and Pemantle by proving a multivariate central limit theorem for
\, so called\, strong Rayleigh distributions. I will also touch on some mo
re recent work connecting anti-concentration for random variables with the
zeros of their probability generating functions.\n \nThis talk is based o
n joint work with Marcus Michelen.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ursula Ludwig (Universität Duisburg-Essen and MPIM Bonn)
DTSTART;VALUE=DATE-TIME:20210601T141500Z
DTEND;VALUE=DATE-TIME:20210601T151500Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/28
DESCRIPTION:Title: The Witten deformation on singular spaces\nby Ursu
la Ludwig (Universität Duisburg-Essen and MPIM Bonn) as part of Geometric
Structures Research Seminar\n\n\nAbstract\nIn his seminal paper “Supers
ymmetry and Morse theory” (Journal Diff. Geom. 1982) Witten\, inspired b
y ideas from quantum field theory\, gave a new analytic proof of the famou
s Morse inequalities. The Witten deformation plays an important role in th
e generalisation by Bismut and Zhang of the comparison theorem between ana
lytic and topological torsion of a smooth compact manifold\, aka Cheeger-M
u ̈ller theorem.\nThe aim of this talk is to explain the generalisation o
f the Witten deformation to certain singular spaces. We will explain the c
ase of singular spaces with conical singularities equipped with a radial M
orse function as well as the case of singular algebraic complex curves equ
ipped with a stratified Morse function in the sense of Goresky and MacPher
son. A first result in both situations is the proof of the Morse inequalit
ies for the L2-cohomology (or equivalently the intersection cohomology). A
much stronger result is the generalisation of the comparison between the
so called Witten complex and an appropriate singular Morse-Thom-Smale comp
lex.\n\nIn the first part of this talk\, I will give a gentle introduction
to the Witten deformation for a smooth compact manifold.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Kahle (The Ohio State University)
DTSTART;VALUE=DATE-TIME:20210608T141500Z
DTEND;VALUE=DATE-TIME:20210608T151500Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/29
DESCRIPTION:Title: Configurations spaces of particles: homological solid\
, liquid\, and gas\nby Matthew Kahle (The Ohio State University) as pa
rt of Geometric Structures Research Seminar\n\n\nAbstract\nConfiguration s
paces of points in the plane are well studied and the topology of such spa
ces is well understood. But what if you replace points by particles with s
ome positive thickness\, and put them in a container with boundaries? It s
eems like not much is known. To mathematicians\, this is a natural general
ization of the configuration space of points\, perhaps interesting for its
own sake. But is also important from the point of view of physics––ph
ysicists might call such a space the "phase space" or "energy landscape" f
or a hard-spheres system. Since hard-spheres systems are observed experime
ntally to undergo phase transitions (analogous to water changing into ice)
\, it would be quite interesting to understand topological underpinnings o
f such transitions.\nWe have just started to understand the homology of th
ese configuration spaces\, and based on our results so far we suggest work
ing definitions of "homological solid\, liquid\, and gas". This is joint w
ork with a number of collaborators\, including Hannah Alpert\, Ulrich Baue
r\, Kelly Spendlove\, and Robert MacPherson.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boulos El Hilany (Johann Radon Institute for Computational and App
lied Mathematics\, Linz)
DTSTART;VALUE=DATE-TIME:20210615T141500Z
DTEND;VALUE=DATE-TIME:20210615T151500Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/30
DESCRIPTION:Title: Computing efficiently the non-properness set of polyno
mial maps on the plane\nby Boulos El Hilany (Johann Radon Institute fo
r Computational and Applied Mathematics\, Linz) as part of Geometric Struc
tures Research Seminar\n\n\nAbstract\nI will present new mathematical and
computational tools to develop a complete and efficient algorithm for comp
uting the set of non-properness of polynomial maps in the complex (and rea
l) plane. In particular\, this is a subset of the plane where a dominant p
olynomial map as above is not proper. The algorithm takes into account the
sparsity of polynomials\, and the genericness of the coefficients as it d
epends on their Newton polytopes. As a byproduct it provides a finer repre
sentation of the set of non-properness as a union of algebraic or semi-alg
ebraic sets\, that correspond to edges of the Newton polytopes\, which is
of independent interest. This is a joint work with Elias Tsigaridas.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hamza Ounesli (SISSA and ICTP)
DTSTART;VALUE=DATE-TIME:20210622T141500Z
DTEND;VALUE=DATE-TIME:20210622T151500Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/31
DESCRIPTION:Title: Minimal entropy of geometric 3-manifolds\nby Hamza
Ounesli (SISSA and ICTP) as part of Geometric Structures Research Seminar
\n\n\nAbstract\nFor a closed smooth manifold M it's natural to ask whether
there exists a Riemannian metric which has minimal topological entropy. I
n this seminar we will investigate this question in dimension 3\, precisel
y\, we will prove that geometrizeable 3-manifolds with zero simplicial vol
ume admits a metric of minimal entropy\, then we will show that closed 3-m
anifolds admitting a geometric structure modelled on H^3\, Sol or the univ
ersal cover of PSL(2\,R) do not have a metric of minimal entropy which rev
eals in fact a chaotic aspect of negative curvature!\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yosef Yomdin (Weizzmann Institute of Science)
DTSTART;VALUE=DATE-TIME:20210629T141500Z
DTEND;VALUE=DATE-TIME:20210629T151500Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/32
DESCRIPTION:Title: Estimating high order derivatives of a function throug
h geometry and topology of its zero set\nby Yosef Yomdin (Weizzmann In
stitute of Science) as part of Geometric Structures Research Seminar\n\n\n
Abstract\nAn order d rigidity inequality for a smooth function f is an exp
licit lower bound for the (d+1)-st derivatives of f\, which holds\, if f e
xhibits certain patterns\, forbidden for polynomials of degree d.\nWe disc
uss some recent results in this direction\, which use as an input the ``de
nsity'' of the zero set Z of f\, or\, in contrast\, its topology. In parti
cular\, we interpret in terms of rigidity inequalities some recent results
of Lerario and Stecconi\, comparing topology of smooth transversal singul
arities\, and of their polynomial approximations.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paolo Antonini (Università del Salento)
DTSTART;VALUE=DATE-TIME:20210706T120000Z
DTEND;VALUE=DATE-TIME:20210706T130000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/33
DESCRIPTION:Title: Infinite dimensional grassmannians\, quantum states an
d optimal transport\nby Paolo Antonini (Università del Salento) as pa
rt of Geometric Structures Research Seminar\n\n\nAbstract\nIn this seminar
we report on a recent work in collaboration with F. Cavalletti where we d
evelop the basic theory of optimal transport for the quantum states of the
C*-algebra of the compact operators on a (separable) Hilbert space.\n \nA
s usual\, states are interpreted as the noncommutative replacement of prob
ability measures\; via the spectral theorem applied to their density matri
ces\, we associate to states discrete measures on the grassmannian of the
finite dimensional subspaces. In this way we can treat them as ordinary pr
obability measures and develop the theory of optimal transport.\n \nThe me
tric geometry of the grassmannian\, as an infinite dimensional manifold pl
ays a decisive role and part of the talk will be devoted to describing its
rich structure. Notably the grassmannian is an Alexandrov space with non
negative curvature.\n \nFinally we will interpret pure normal states of th
e tensor product $H\\otimes H$ as families of transport maps. This idea le
ads to the possibility of giving a definition of the Wasserstein cost for
such objects.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yassine El Maazouz (UC Berkeley)
DTSTART;VALUE=DATE-TIME:20211111T130000Z
DTEND;VALUE=DATE-TIME:20211111T150000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/34
DESCRIPTION:Title: Local fields: Gaussian measures and random processes\nby Yassine El Maazouz (UC Berkeley) as part of Geometric Structures Re
search Seminar\n\n\nAbstract\nGaussian measures on Banach spaces over loca
l fields can be defined and constructed by exploiting the orthogonality st
ructures of such spaces. We discuss these constructions and their merit by
exhibiting the interesting properties of the objects they produce. Since
these probabilistic objects also have a rich algebraic structure\, interes
ting questions and problems arise.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniele Tiberio (SISSA\, Trieste)
DTSTART;VALUE=DATE-TIME:20211125T130000Z
DTEND;VALUE=DATE-TIME:20211125T150000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/35
DESCRIPTION:Title: The entropy Morse-Sard Theorem I\nby Daniele Tiber
io (SISSA\, Trieste) as part of Geometric Structures Research Seminar\n\nA
bstract: TBA\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniele Tiberio (SISSA\, Trieste)
DTSTART;VALUE=DATE-TIME:20211202T130000Z
DTEND;VALUE=DATE-TIME:20211202T150000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/36
DESCRIPTION:Title: The entropy Morse-Sard Theorem II\nby Daniele Tibe
rio (SISSA\, Trieste) as part of Geometric Structures Research Seminar\n\n
\nAbstract\nIn these series of three seminars\, we will present a proof of
the classical Morse-Sard Theorem\, based on results from semialgebraic ge
ometry. It is a bit long\, but it also gives a bound on the so-called entr
opy dimension of the set of critical values of a smooth function defined o
n a closed ball of R^n. This proof is due to Yomdin and Comte.\n\n\n*This
consists of a series of three lectures: November 25\; December 2\; Decembe
r 9.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniele Tiberio (SISSA\, Trieste)
DTSTART;VALUE=DATE-TIME:20211216T130000Z
DTEND;VALUE=DATE-TIME:20211216T150000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/38
DESCRIPTION:Title: The entropy Morse-Sard Theorem III\nby Daniele Tib
erio (SISSA\, Trieste) as part of Geometric Structures Research Seminar\n\
n\nAbstract\nIn these series of three seminars\, we will present a proof o
f the classical Morse-Sard Theorem\, based on results from semialgebraic g
eometry. It is a bit long\, but it also gives a bound on the so-called ent
ropy dimension of the set of critical values of a smooth function defined
on a closed ball of R^n. This proof is due to Yomdin and Comte.\n\n\n*This
consists of a series of three lectures: November 25\; December 2\; Decemb
er 16.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David TEWODROSE (Nantes Université)
DTSTART;VALUE=DATE-TIME:20220224T130000Z
DTEND;VALUE=DATE-TIME:20220224T150000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/39
DESCRIPTION:Title: Kato limit spaces\nby David TEWODROSE (Nantes Univ
ersité) as part of Geometric Structures Research Seminar\n\n\nAbstract\nC
onsider a sequence of Riemannian manifolds. Assume that this sequence conv
erges\, in the measured Gromov-Hausdorff sense\, to a possibly non-smooth
metric measure space. What are the properties of this limit space? In a se
ries of celebrated works from the nineties\, Cheeger and Colding addressed
this question under the assumption of a uniform lower bound on the Ricci
curvature of the manifolds. This has led to the fruitful development of a
synthetic theory of Ricci curvature lower bounds. In this talk\, I will pr
esent a couple of joint works with Gilles Carron (Nantes Université) and
Ilaria Mondello (Université de Créteil) where we relax the uniform Ricci
lower bound assumption and work in the context of a weaker uniform Kato-t
ype assumption\, namely that the part of the lowest eigenvalue of the Ricc
i tensor lying under a certain threshold belongs to a given Kato class. Un
der this assumption which authorizes the Ricci curvature to degenerate to
- infinity but in a « heat-kernel controlled » way\, we show that most r
esults of Cheeger and Colding are still true\, including rectifiability on
which I shall focus.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexis AUMONIER (University of Copenhagen)
DTSTART;VALUE=DATE-TIME:20220317T130000Z
DTEND;VALUE=DATE-TIME:20220317T150000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/41
DESCRIPTION:Title: An h-principle for complements of discriminants\nb
y Alexis AUMONIER (University of Copenhagen) as part of Geometric Structur
es Research Seminar\n\n\nAbstract\nIn classical algebraic geometry\, discr
iminants appear naturally in various moduli spaces as the loci parametrisi
ng degenerate objects. The motivating example for this talk is the locus o
f singular sections of a line bundle on a smooth projective complex variet
y\, the complement of which is a moduli space of smooth hypersurfaces.\nI
will present an approach to studying the homology of such moduli spaces of
non-singular algebraic sections via algebro-topological tools. The main i
dea is to prove an "h-principle" which translates the problem into a purel
y homotopical one.\n\nI shall explain how to talk effectively about singul
ar sections of vector bundles and what an h-principle is. To demonstrate t
he usefulness of homotopical methods\, and using a bit of rational homotop
y theory\, we will prove together a homological stability result for modul
i spaces of smooth hypersurfaces of increasing degree.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea MONDINO (University of Oxford)
DTSTART;VALUE=DATE-TIME:20220331T120000Z
DTEND;VALUE=DATE-TIME:20220331T140000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/42
DESCRIPTION:Title: Minimal boundaries in non-smooth spaces with Ricci Cur
vature bounded below\nby Andrea MONDINO (University of Oxford) as part
of Geometric Structures Research Seminar\n\n\nAbstract\nThe goal of the s
eminar is to report on recent joint work with Daniele Semola. Motivated by
a question of Gromov to establish a “synthetic regularity theory" for m
inimal surfaces in non-smooth ambient spaces\, we address the question in
the setting of non-smooth spaces satisfying Ricci curvature lower bounds i
n a synthetic sense via optimal transport. The talk is meant to be accessi
bile also to non specialists.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davide BARILARI (Università degli Studi di Padova)
DTSTART;VALUE=DATE-TIME:20220421T120000Z
DTEND;VALUE=DATE-TIME:20220421T140000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/43
DESCRIPTION:Title: Bakry–Émery curvature and sub-Riemannian geometry\nby Davide BARILARI (Università degli Studi di Padova) as part of Geom
etric Structures Research Seminar\n\n\nAbstract\nIn this talk we discuss s
ome generalization of comparison theorems involving Bakry Émery curvature
in sub-Riemannian geometry. In particular we will focus on comparison the
orems for distortion coefficients appearing in geometric interpolation ine
qualities\, such as the Brunn-Minkovski inequality. The model spaces for c
omparison are variational problems coming from optimal control theory.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessandro PORTALURI (University of Torino)
DTSTART;VALUE=DATE-TIME:20220324T130000Z
DTEND;VALUE=DATE-TIME:20220324T150000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/44
DESCRIPTION:Title: Spectral stability\, spectral flow and circular relati
ve equilibria for the Newtonian n-body problem\nby Alessandro PORTALU
RI (University of Torino) as part of Geometric Structures Research Seminar
\n\n\nAbstract\nFor the Newtonian (gravitational) $n$-body problem in the
Euclidean $d$-dimensional space\, $d\\ge 2$\, the simplest possible period
ic solutions are provided by circular relative equilibria (RE)\, namely s
olutions in which each body rigidly rotates about the center of mass and t
he configuration of the whole system is constant in time and central con
figuration. A classical problem in celestial mechanics aims at relating
the (in-)stability properties of a (RE) to the index properties of the cen
tral configuration generating it. \n\nIn this talk\, we discuss some suf
ficient \nconditions that imply the spectral instability of planar and non
-planar (RE) generated by a central configuration. \n\nThe key ingredient
s are a new formula that allows to compute the spectral flow of a path of
symmetric matrices having degenerate starting point\, and \na symplectic
decomposition of the phase space of the linearized Hamiltonian system alon
g a given (RE) which allows us \nto rule out the uninteresting part of th
e dynamics corresponding to the translational and (partially) to the rotat
ional symmetry of the problem. \n\nThis talk is based on a recent joint wo
rk with Prof. Dr. Luca Asselle (Ruhr Universit\\"at Bochum\, Germany) a
nd Prof. Dr. Li Wu (Shandong University\, Jinan\, China).\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arthur RENAUDINEAU (Université de Lille)
DTSTART;VALUE=DATE-TIME:20220512T120000Z
DTEND;VALUE=DATE-TIME:20220512T140000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/45
DESCRIPTION:Title: Real structures on tropical varieties\nby Arthur R
ENAUDINEAU (Université de Lille) as part of Geometric Structures Research
Seminar\n\n\nAbstract\nWe will propose a definition of a real structure o
n a non-singular projective tropical variety. This definition takes its in
spiration from the Viro's patchworking theorem. In the local setting\, we
will prove that such a structure on a matroidal fan is equivalent to an or
ientation on the underlying matroid. We will then generalize Viro's theore
m to this setting. This is a joint work with Johannes Rau and Kris Shaw.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlos BELTRAN (Universidad de Cantabria)
DTSTART;VALUE=DATE-TIME:20220526T120000Z
DTEND;VALUE=DATE-TIME:20220526T140000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/47
DESCRIPTION:Title: Smale’s 7th problem: an overview\nby Carlos BELT
RAN (Universidad de Cantabria) as part of Geometric Structures Research Se
minar\n\n\nAbstract\nSmale’s 7th problem demands for an algorithm to fin
d finite collections of points in the 2-sphere\, in such a way that they m
inimize some energy that one may think of as the classical electrostatic p
otential. This beautiful problem (which is the computational version of a
problem posed by J. J. Thomson\, the discoverer of the electron) has attra
cted the attention of dozens of researchers and\, although it is considere
d extremely difficult\, the hope for solving it has not vanished. In this
talk I will present the problem from a general perspective\, showing its r
elations with other questions\, mentioning the most important results obta
ined to the date and posing several open questions in the path to the tota
l solution. The talk will be directed for a general audience.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea ROSANA (SISSA\, Trieste)
DTSTART;VALUE=DATE-TIME:20220428T120000Z
DTEND;VALUE=DATE-TIME:20220428T140000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/49
DESCRIPTION:Title: Equilibrium measures and logarithmic potential theory
(Part 1 of 2)\nby Andrea ROSANA (SISSA\, Trieste) as part of Geometric
Structures Research Seminar\n\n\nAbstract\nThe aim of these talks is to s
how that the (rescaled) zeroes of Hermite polynomials and the (rescaled) e
igenvalues of matrices in the Gaussian Orthogonal Ensemble share the same
asymptotic distribution\, i.e. the semi-circle law of radius \\sqrt(2). We
address this problem through logarithmic potential theory.\n\nWe begin by
showing how we can interpret the zeroes of orthogonal polynomials as equi
librium configurations for the electrostatic Stieltjes model on the real l
ine\, which serves as a motivation for their study. We then introduce loga
rithmic potential and energy of a measure with respect to an external pote
ntial. Under suitable hypothesis on such potential\, we show the existence
and uniqueness of a minimizing measure for the energy\, which we call the
equilibrium measure. A characterization of such equilibrium measures is a
lso provided. We end the talk briefly discussing the equilibrium measure f
or a Gaussian potential.\n\nThe tools we developed here will be used in th
e second talk to address our starting problem.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea ROSANA (SISSA\, Trieste)
DTSTART;VALUE=DATE-TIME:20220505T120000Z
DTEND;VALUE=DATE-TIME:20220505T140000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/50
DESCRIPTION:Title: Equilibrium measures and logarithmic potential theory
(Part 2 of 2)\nby Andrea ROSANA (SISSA\, Trieste) as part of Geometric
Structures Research Seminar\n\n\nAbstract\nWe introduce the probability m
easure associated to the zeroes of Hermite polynomials and discuss how a r
escaling is necessary in order to get convergence (in the weak star topolo
gy). Using the tools from logarithmic potential theory from previous talk\
, we show convergence of this measure to the semi-circular law. We then in
troduce Gaussian Ensambles and the empirical and statistical eigenvalue di
stributions for hermitian matrices in these ensambles. We show how these e
nsambles fit in a more general framework and we discuss the generalized Wi
gner theorem\, highlighting a parallelism with Laplace asymptotic method.
From this we get as a corollary the convergence of the (rescaled) statisti
cal eigenvalue distribution for GOE matrices to the semi-circular law.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul BREIDING (MPI MiS (Max Planck Institute for Mathematics in th
e Sciences))
DTSTART;VALUE=DATE-TIME:20220609T120000Z
DTEND;VALUE=DATE-TIME:20220609T140000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/51
DESCRIPTION:Title: Facet Volumes of Polytopes\nby Paul BREIDING (MPI
MiS (Max Planck Institute for Mathematics in the Sciences)) as part of Geo
metric Structures Research Seminar\n\n\nAbstract\nWe consider what we call
facet volume vectors of polytopes. Every full-dimensional polytope in R^d
with n facets defines n positive real numbers: the n (d-1)-dimensional vo
lumes of its facets. For instance\, every triangle defines three lenghts\;
every tetrahedron defines four areas.\nWe study the space of all such vec
tors. We show that for fixed integers d\\geq 2 and n\\geq d+1 the configur
ation space of all facet volume vectors of all d-polytopes in R^d with n f
acets is a full dimensional cone in R^n\, and we describe this cone in ter
ms of inequalities. For tetrahedra this is a cone over a regular octahedro
n.\nJoint work with Pavle Blagojevic and Alexander Heaton.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Zelenko (Texas A&M University)
DTSTART;VALUE=DATE-TIME:20220616T120000Z
DTEND;VALUE=DATE-TIME:20220616T140000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/52
DESCRIPTION:Title: Morse inequalities for eigenvalue branches of generic
families of self-adjoint matrices\nby Igor Zelenko (Texas A&M Universi
ty) as part of Geometric Structures Research Seminar\n\n\nAbstract\nThe ei
genvalue branches of families of self-adjoint matrices are not smooth at p
oints corresponding to repeated eigenvalues (called diabolic points or Dir
ac points). Generalizing the notion of critical points as points for which
the homotopical type of (local) sub-level set changes after the passage t
hrough the corresponding value\, in the case of the generic family we give
an effective criterion for a diabolic point to be critical for those bran
ches and compute the contribution of each such critical point to the Morse
polynomial of each branch\, getting the appropriate Morse inequalities as
a byproduct of the theory. These contributions are expressed in terms of
the homologies of Grassmannians. The motivation comes from the Floquet-Blo
ch theory of Schroedinger equations with periodic potential and other prob
lems in Mathematical Physics. The talk is based on the joint work with Gre
gory Berkolaiko.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tim Laux (Hausdorff Center for Mathematics in Bonn)
DTSTART;VALUE=DATE-TIME:20220627T140000Z
DTEND;VALUE=DATE-TIME:20220627T160000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/53
DESCRIPTION:Title: The large-data limit of the MBO scheme for data cluste
ring\nby Tim Laux (Hausdorff Center for Mathematics in Bonn) as part o
f Geometric Structures Research Seminar\n\n\nAbstract\nThe MBO scheme is a
n efficient scheme used for data clustering\, the task of partitioning a g
iven dataset into several clusters. In this talk\, I will present a rigoro
us analysis of the MBO scheme for data clustering in the large-data limit.
Each iteration of the MBO scheme corresponds to one step of implicit grad
ient descent for the thresholding energy on the similarity graph of the da
taset. For a subset of the nodes of the graph\, the thresholding energy is
the amount of heat transferred from the subset to its complement. It is t
hen natural to think that outcomes of the MBO scheme are (local) minimizer
s of this energy. We prove that the algorithm is consistent\, in the sense
that these (local) minimizers converge to minimizers of a suitably weight
ed optimal partition problem. This is joint work with Jona Lelmi (U Bonn).
\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Georges Comte (Université Savoie Mont-Blanc)
DTSTART;VALUE=DATE-TIME:20220728T120000Z
DTEND;VALUE=DATE-TIME:20220728T140000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/54
DESCRIPTION:Title: Motivic Vitushkin's invariants\nby Georges Comte (
Université Savoie Mont-Blanc) as part of Geometric Structures Research Se
minar\n\n\nAbstract\nI will explain how\, in a joint work with Immanuel Ha
lupczok (Düsseldorf Univ.)\, we define in definable nonarchimedean geomet
ry a sequence of invariants which is the counterpart in this context of th
e sequence of Vituskin's invariants in real geometry. For this we use the
theory of t-stratification in its uniform version. \nWe also define a not
ion of preorder on the ring of motivic constructible functions\, which is
compatible with motivic integration. As in the real case\, our invariants
are related to a notion of metric entropy.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Sykes (Masaryk University)
DTSTART;VALUE=DATE-TIME:20221027T080000Z
DTEND;VALUE=DATE-TIME:20221027T090000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/56
DESCRIPTION:Title: Absolute parallelism constructions for 2-nondegenerate
CR hypersurfaces\nby David Sykes (Masaryk University) as part of Geom
etric Structures Research Seminar\n\n\nAbstract\nThe talk will introduce a
nd demonstrate through examples a Tanaka-theoretic general method (develop
ed in joint work with Igor Zelenko) for solving local equivalence problems
applicable to a broad class of 2-nondegenerate hypersurface-type CR manif
olds\, namely to all such structures that are uniquely determined by the g
eometry naturally induced on their associated Levi leaf space. We will app
ly the general method to an instructive family of CR hypersurfaces in comp
lex 6-space\, reducing their local equivalence problem to one of absolute
parallelisms that we explicitly construct in local coordinates. The talk w
ill also review further applications of the general method\, applications
to estimating symmetry group dimensions and to classifications of homogene
ous structures.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ching-Peng Huang (Brown University)
DTSTART;VALUE=DATE-TIME:20221117T130000Z
DTEND;VALUE=DATE-TIME:20221117T150000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/57
DESCRIPTION:Title: Brownian motion under the Bures-Wasserstein geometry\nby Ching-Peng Huang (Brown University) as part of Geometric Structures
Research Seminar\n\n\nAbstract\nThe Bures-Wasserstein geometry of positiv
e definite matrices is closely related to the optimal transport of Gaussia
n measures and has several applications such as in optimization and physic
s. We present a detailed formula of the Brownian motion under such geometr
y\, which has an extra mean curvature drift term and is reminiscent of wel
l-studied stochastic processes such as Dyson's Brownian\, suggesting broad
er framework of matrix geometry for these processes. Moreover\, we investi
gate ideas utilizing the mean curvature drift term to design a control sys
tem.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pawel Nurowski (Center for Theoretical Physics\, Warsaw)
DTSTART;VALUE=DATE-TIME:20220913T120000Z
DTEND;VALUE=DATE-TIME:20220913T140000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/58
DESCRIPTION:Title: What is a para-CR structure of type (k\,r\,s) and why
it describes geometry of ODEs and PDEs of finite type\nby Pawel Nurows
ki (Center for Theoretical Physics\, Warsaw) as part of Geometric Structur
es Research Seminar\n\n\nAbstract\nI will talk about a geometry of manifol
ds equipped with a pair of integrable vector distributions. Such geometry
is suitable to describe a geometry of a large class of Partial Differentia
l Equations (PDEs) considered modulo various types of changes of variables
. This class of PDEs is called `the finite type'\, meaning that their spac
e of solutions is finite dimensional. I will illustrate the para-CR struct
ure of type (k\,r\,s) geometry with a few examples having applications in
theoretical physics.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey Podobryaev (Control Processes Research Center\, Program Sys
tems Institute of RAS)
DTSTART;VALUE=DATE-TIME:20221110T130000Z
DTEND;VALUE=DATE-TIME:20221110T150000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/59
DESCRIPTION:Title: Attainable sets for step 2 free Carnot groups with non
-negative controls and inequalities for independent random variables\n
by Alexey Podobryaev (Control Processes Research Center\, Program Systems
Institute of RAS) as part of Geometric Structures Research Seminar\n\n\nAb
stract\nIn recent works H.Abels and E.B.Vinberg considered free nilpotent
Lie\nsemigroups and suggested a probability interpretaion of such semigrou
ps\nof step 2. With a help of an algebraic method they obtained an explici
t\ndescription of the step 2 rank 3 free nilpotant Lie semigroup. This\nre
sult implies some non trivial inequalities for a system of three\nindepend
ent random variables x\, y\, z. For example\, if P(x < y) = 3/5 and\nP(y <
z) = 3/5\, then P(x < z) >= 1/3 (an obvious bound is 1/5).\n\nWe regard t
hese free nilpotent Lie semigroups as attainable sets for\nsome control sy
stems. We describe the boundary of the attainable set\nwith a help of firs
t and second order optimality conditions. It turns\nout that the curved fa
ces of the attainable set consist of the ends of\noptimal trajectories wit
h the number of control switching corresponding\nto the face dimension. We
give an explicit answer in the case of rank 3\nand upper bounds for the n
umber for control switchings in the case of\nrank 4.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valentino Magnani (University of Pisa)
DTSTART;VALUE=DATE-TIME:20221215T130000Z
DTEND;VALUE=DATE-TIME:20221215T150000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/61
DESCRIPTION:Title: Surface area on sub-Riemannian measure manifolds\n
by Valentino Magnani (University of Pisa) as part of Geometric Structures
Research Seminar\n\n\nAbstract\nWe present an area formula in equiregular
sub-Riemannian measure manifolds. The perimeter measure of a smooth bounde
d open set is related to the spherical measure of its boundary\, using the
sub-Riemannian distance. To perform the intrinsic blow-up at the boundary
new difficulties appear\, that also involve the nilpotent approximation o
f the sub-Riemannian manifold. The density of the perimeter measure natura
lly arises as a geometric invariant that can be explicitly related to diff
erent objects\, like the nilpotent approximation\, the tangent Riemannian
metric and the shape of the tangent unit ball. The area formula for the pe
rimeter measure is achieved by showing that this invariant is equal to the
Federer density. These results are a joint work with Sebastiano Don (Bres
cia University).\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kenshiro Tashiro (Tohoku University)
DTSTART;VALUE=DATE-TIME:20230119T130000Z
DTEND;VALUE=DATE-TIME:20230119T150000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/62
DESCRIPTION:Title: Systolic inequality and volume of the unit ball in Car
not groups\nby Kenshiro Tashiro (Tohoku University) as part of Geometr
ic Structures Research Seminar\n\n\nAbstract\nRoughly speaking\, a systoli
c inequality on a length measure space asserts that the minimal length of
non-contractible closed curve is controlled by the product of the (root of
) total measure and a constant depending only on its topology. Such inequa
lities hold for (a class of) Riemannian manifolds and Alexandrov spaces wi
th the constants depending only on the Hausdorff dimension.\nWe proved the
systolic inequality on quotient spaces of Carnot groups\, which is a clas
s of closed sub-Riemannian manifolds\, with the constant depending only on
the Hausdorff dimension. Actually it is equivalent to give a uniform lowe
r bound of volume of the unit ball in Carnot groups of a given Hausdorff d
imension.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuri Sachkov (Program Systems Institute\, Russian Academy of Scien
ce)
DTSTART;VALUE=DATE-TIME:20230216T130000Z
DTEND;VALUE=DATE-TIME:20230216T150000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/63
DESCRIPTION:Title: Sub-Lorentzian problem on the Heisenberg group (Yu. Sa
chkov\, E. Sachkova)\nby Yuri Sachkov (Program Systems Institute\, Rus
sian Academy of Science) as part of Geometric Structures Research Seminar\
n\n\nAbstract\nThe sub-Riemannian problem on the Heisenberg group is well
known\, it is a cornerstone of sub-Riemannian geometry.\nIt can be stated
as a time-optimal problem with a planar set of control parameters\, a circ
le.\nThe talk will be devoted to its natural variation\, the time-optimal
problem with a hyperbola as a set of control parameters.\nThis variation i
s the sub-Lorentzian problem on the Heisenberg group.\n\nFor this problem
we will describe the following results:\n1) The reachable set from the ide
ntity of the group\,\n2) Pontryagin maximum principle\, parameterization o
f extremal trajectories\, exponential mapping\,\n3) Diffeomorphic property
of the exponential mapping\, its inverse\,\n4) Optimality of extremal tra
jectories\, optimal synthesis\,\n5) Sub-Lorentzian distance\,\n6) Sub-Lore
ntzian spheres of positive and zero radii.\nResults 1)\, 2) were obtained
by M.Grochowski (2006)\, the rest results are new.\n\nThe talk will be bas
ed on the work \nhttps://arxiv.org/abs/2208.04073\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Zelenko (Texas A&M Univerisity)
DTSTART;VALUE=DATE-TIME:20230407T090000Z
DTEND;VALUE=DATE-TIME:20230407T110000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/64
DESCRIPTION:Title: Gromov's h-principle for corank two distribution of od
d rank with maximal first Kronecker index\nby Igor Zelenko (Texas A&M
Univerisity) as part of Geometric Structures Research Seminar\n\n\nAbstrac
t\nWhile establishing various versions of the h-principle for contact\ndis
tributions (Eliashberg (1989) in dimension 3\, Borman-\nEliashberg-Murphy
(2015) in arbitrary dimension\, and even-contact\ncontact (D. McDuff\,
1987) distributions are among the most remarkable\nadvances in different
ial topology in the last four decades\, very little\nis known about analog
ous results for other classes of distributions\,\ne.g. generic distributio
ns of corank 2 or higher. The smallest\ndimensional nontrivial case of cor
ank 2 distributions are Engel\ndistributions\, i.e. the maximally nonholon
omic rank 2 distributions on\n$4$-manifolds. This case is highly nontrivia
l and was treated recently\nby Casals-Pérez-del Pino-Presas (2017) and Ca
sals-Pérez-Presas (2017).\nIn my talk\, I will show how to use the method
of contex integration in\norder to establish all versions of the h-princi
ple for corank 2\ndistribution of arbitrary odd rank satisfying a natural
generic\nassumption on the associated pencil of skew-symmetric forms. Duri
ng the\ntalk I will try to give all the necessary background related to th
e\nmethod of convex integration in principle. This is the joint work with\
nMilan Jovanovic\, Javier Martinez-Aguinaga\, and Alvaro del Pino.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brendan Guilfoyle (Munster Technological University)
DTSTART;VALUE=DATE-TIME:20230302T130000Z
DTEND;VALUE=DATE-TIME:20230302T150000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/65
DESCRIPTION:Title: From CT Scans to four-manifold topology\nby Brenda
n Guilfoyle (Munster Technological University) as part of Geometric Struct
ures Research Seminar\n\n\nAbstract\nIntegration over lines is the mathema
tical basis of many modern methods of tomography\, including Computerized
Tomography scans. In this talk\, a recent geometrization using indefinite
metrics of signature (2\,2) is presented of the seminal work of Fritz John
on the problem. The contemporary mathematical background is 4-manifold to
pology and the use of neutral metrics to explore co-dimension two problems
.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomasso Rossi (Institut für Angewandte Mathematik\, Universität
Bonn)
DTSTART;VALUE=DATE-TIME:20230519T090000Z
DTEND;VALUE=DATE-TIME:20230519T110000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/66
DESCRIPTION:Title: First-order heat content asymptotics on RCD(K\,N) spac
es\nby Tomasso Rossi (Institut für Angewandte Mathematik\, Universit
ät Bonn) as part of Geometric Structures Research Seminar\n\n\nAbstract\n
We study the small-time asymptotics of the heat content associated with a
bounded open set when the ambient space is an RCD(K\,N) metric measure spa
ce. By adapting a technique due to Savo\, we establish the existence of a
first-order asymptotic expansion\, under a regularity condition for the bo
undary of the domain that we call measured interior geodesic condition. We
carefully study such a condition\, relating it to the properties of the d
isintegration associated with the signed distance function from the bounda
ry. This is a joint work with Emanuele Caputo.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lev Birbrair (Universidade Federal do Ceará & Jagiellonian Univer
sity)
DTSTART;VALUE=DATE-TIME:20230601T090000Z
DTEND;VALUE=DATE-TIME:20230601T110000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/68
DESCRIPTION:Title: Lipschitz Geometry of Germs of Real Surfaces\nby L
ev Birbrair (Universidade Federal do Ceará & Jagiellonian University) as
part of Geometric Structures Research Seminar\n\n\nAbstract\nLipschitz Geo
metry is now an intensively developed part of Singularity Theory.\nI am go
ing to make an introductory talk on the subject. I am going to explain\nt
he general directions of Lipschitz geometry (inner\, outer and ambient)\no
n the example of germs of Real Semialgebraic Surfaces.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samuël Borza (SISSA\, Trieste\, Italy)
DTSTART;VALUE=DATE-TIME:20230615T120000Z
DTEND;VALUE=DATE-TIME:20230615T140000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/69
DESCRIPTION:Title: MCP and geodesic dimension of sub-Finsler Heisenberg g
roups\nby Samuël Borza (SISSA\, Trieste\, Italy) as part of Geometric
Structures Research Seminar\n\n\nAbstract\nWe will discuss the Heisenberg
group equipped with an $\\ell^p$-sub-Finsler metric. We will explore its
geometry through the corresponding (Finsler) isoperimetric problem. Subseq
uently\, we will analyse these spaces as metric measure spaces\, consideri
ng whether the measure contraction property holds. Furthermore\, we will a
lso compute their geodesic dimension. It will become apparent how the answ
ers to these questions are controlled by the value of p (and its Hölder c
onjugate q). This value determines whether the $\\ell^p$-sub-Finsler metri
c is branching or not\, whether it possesses a negligible cut locus\, and
whether its geodesics are sufficiently smooth or not. Joint work with K. T
ashiro.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paweł Nurowski (Center for Theoretical Physics\, Warsaw\, Poland)
DTSTART;VALUE=DATE-TIME:20230904T090000Z
DTEND;VALUE=DATE-TIME:20230904T110000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/70
DESCRIPTION:Title: Exceptional real Lie algebras $f_4$ and $e_6$ via cont
actifications\nby Paweł Nurowski (Center for Theoretical Physics\, Wa
rsaw\, Poland) as part of Geometric Structures Research Seminar\n\n\nAbstr
act\nIn Cartan's PhD thesis\, there is a formula defining a certain rank 8
vector distribution in dimension 15\, whose algebra of authomorphism is t
he split real form of the simple exceptional complex Lie algebra $f_4$. Ca
rtan's formula is written in the standard Cartesian coordinates in $\\math
bb{R}^{15}$. In the talk I will explain how to find analogous formula for
the flat models of any bracket generating distribution $D$ whose symbol al
gebra $n(D)$ is constant and 2-step graded\, $n(D) = n−2 \\oplus n−1$.
I will use the general formula to provide other distributions with symmet
ries being real forms of simple exceptional Lie algebras $f_4$ and $e_6$.\
n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cyril Letrouit (CNRS\, Laboratoire de Mathématiques d'Orsay)
DTSTART;VALUE=DATE-TIME:20240111T130000Z
DTEND;VALUE=DATE-TIME:20240111T150000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/71
DESCRIPTION:Title: Nodal sets of eigenfunctions of sub-Laplacians\nby
Cyril Letrouit (CNRS\, Laboratoire de Mathématiques d'Orsay) as part of
Geometric Structures Research Seminar\n\n\nAbstract\nNodal sets of eigenfu
nctions of elliptic operators on compact manifolds have been studied exten
sively over the past decades. In a recent work\, we initiated the study of
nodal sets of eigenfunctions of hypoelliptic operators on compact manifol
ds\, focusing on sub-Laplacians (e.g. on compact quotients of the Heisenbe
rg group). Our results show that nodal sets behave in an anisotropic way w
hich can be analyzed with standard tools from sub-Riemannian geometry such
as sub-Riemannian dilations\, nilpotent approximation and desingularizati
on at singular points. This is a joint work with S. Eswarathasan.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giovanni Russo (SISSA)
DTSTART;VALUE=DATE-TIME:20240123T130000Z
DTEND;VALUE=DATE-TIME:20240123T140000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/72
DESCRIPTION:Title: Nearly Kähler metrics and torus symmetry\nby Giov
anni Russo (SISSA) as part of Geometric Structures Research Seminar\n\n\nA
bstract\nNearly Kähler manifolds are Riemannian spaces equipped with an a
lmost complex structure of special type. In dimension six\, nearly Kähler
metrics are Einstein with positive scalar curvature\, and have interestin
g connections with G2 and spin geometry. At present there are very few com
pact examples\, which are either homogeneous or of cohomogeneity one. \n\n
In this talk I will explain a theory of nearly Kähler six-manifolds with
two-torus symmetry. The torus-action yields a multi-moment map\, which we
use as a Morse function to understand the structure of the whole manifold.
In particular\, we show how the local geometry of a nearly Kähler six-ma
nifold can be recovered from three-dimensional data\, and discuss connecti
ons with GKM theory.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniele Tiberio (SISSA)
DTSTART;VALUE=DATE-TIME:20240130T130000Z
DTEND;VALUE=DATE-TIME:20240130T150000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/73
DESCRIPTION:Title: Sard theorems in infinite dimensions and applications
to sub-Riemannian geometry\nby Daniele Tiberio (SISSA) as part of Geom
etric Structures Research Seminar\n\nLecture held in SISSA Main Building.\
n\nAbstract\nThe Sard conjecture in sub-Riemannian geometry claims that th
e set of critical values of the endpoint maps has measure zero. These are
smooth maps which take values in the manifold\, but they are defined on in
finite dimensional domains. I will present recent Sard-type theorems for "
polynomial" functions from a Hilbert space to a finite dimensional space.
As a result\, we provide a partial answer to the Sard conjecture in Carnot
groups. This talk is based on a work in collaboration with Professor Anto
nio Lerario and Professor Luca Rizzi.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yosef Yomdin (Weizmann Institute of Science)
DTSTART;VALUE=DATE-TIME:20240611T120000Z
DTEND;VALUE=DATE-TIME:20240611T140000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/74
DESCRIPTION:Title: Super-resolution\, classical Moment Theory\, and some
Real Algebraic Geometry\nby Yosef Yomdin (Weizmann Institute of Scienc
e) as part of Geometric Structures Research Seminar\n\nLecture held in Roo
m 005 - SISSA Main Building.\n\nAbstract\nWe consider the problem of recon
struction of “spike-train” signals\n\\[\nF(x) = \\sum_{j=1}^d a_j \\d
elta(x-x_j)\,\n\\]\nwhich are linear combinations of shifted delta-functio
ns\, from noisy Moment measurements\n\\[\nm_k(F) = \\int F(x) x^k dx = \\s
um_{j=1}^d a_j x_j^k.\n\\]\nThis is equivalent to solving the so-called P
rony system of algebraic equations\n\\[\n\\sum_{j=1}^d a_i x_j^k = m_k(F
)\, \\qquad k = 0\,1\,…\, 2d-1\,\n\\] \n\nwith respect to the un
knowns $(a_j\, x_j)\, \\ j = 1\,…\,d.$\n\nOur goal is to understand the
“intrinsic geometry” of the error amplification in the reconstruction
process\, stressing the case where the nodes $x_j$ nearly collide. We stu
dy the geometry of the system above\, independently of a specific reconstr
uction algorithm.\n\n \nWe construct a growing chain of algebraic sub-vari
eties $Y_q$ (which we call Prony varieties) in the space of the parameters
$(a_j\, x_j)$\, which accurately control the rate of the error amplificat
ion. These sub-varieties $Y_q$ can be reconstructed from the noisy moment
measurements with a significantly better accuracy than the amplitudes $a_j
$ and the nodes $x_j$ themselves. This opens a possibility to apply adapti
ve reconstruction algorithms\, subordinated to the chain of the Prony vari
eties $Y_q$. We show that this approach in many cases provides higher reco
nstruction accuracy than the standard ones.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Beschastnyi (INRIA\, Nice)
DTSTART;VALUE=DATE-TIME:20240220T130000Z
DTEND;VALUE=DATE-TIME:20240220T150000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/75
DESCRIPTION:Title: Symplectic geometry for boundary conditions of Grushin
operators\nby Ivan Beschastnyi (INRIA\, Nice) as part of Geometric St
ructures Research Seminar\n\nLecture held in SISSA Main Building.\n\nAbstr
act\nIn this talk I will explain how to construct self-adjoint extensions
for a class of differential operators on Grushin manifolds. The main tool
will be a natural bijection between self-adjoint extensions and Lagrangian
subspaces of some symplectic space. I will illustrate the technique first
via a full classification of self-adjoint extensions of a Schroedinger op
erator with inverse square potential\, and then explain what can be said i
n the case of Grushin manifolds. This is a joint work with H. Quan.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michele Motta (SISSA)
DTSTART;VALUE=DATE-TIME:20240206T130000Z
DTEND;VALUE=DATE-TIME:20240206T150000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/76
DESCRIPTION:Title: Lyapunov exponents of linear switched systems\nby
Michele Motta (SISSA) as part of Geometric Structures Research Seminar\n\n
Lecture held in room 133 - SISSA Main Building.\n\nAbstract\nIn applicatio
ns\, there are many systems whose dynamics can be influenced by discrete e
vents. For instance\, a power switch turned on and off\, a thermostat turn
ing the heat on and off\, a car running on a street with some ice here and
there. Such systems are called switched systems.\n\nAs for classical dyna
mical systems\, stability for this class of systems is a very important is
sue. A natural way to measure the stability is to use Lyapunov exponents.
\nIn this talk\, I will show how to compute exact Lyapunov exponents for a
simple class of switched systems. This problem can be reduced to an Optim
al Control Problem. Applying Pontryagin Maximum Principle\, one can find a
ll extremals for this problem and then choose among them the optimal one.
This is a joint work with Prof. A. A. Agrachev.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valentino Magnani (Pisa)
DTSTART;VALUE=DATE-TIME:20240213T130000Z
DTEND;VALUE=DATE-TIME:20240213T150000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/77
DESCRIPTION:Title: Area of intrinsic graphs in homogeneous groups\nby
Valentino Magnani (Pisa) as part of Geometric Structures Research Seminar
\n\nLecture held in SISSA Main Building.\n\nAbstract\nWe introduce an area
formula for computing the spherical measure of an intrinsic graph of any
codimension in an arbitrary homogeneous group. Our approach only assumes t
hat the map generating the intrinsic graph is continuously intrinsically d
ifferentiable. The important novelty lies in the notion of Jacobian\, whic
h is built by the auxiliary Euclidean distance. The introduction of this J
acobian allows the spherical factor to appear in the area formula and enab
les explicit computations. This is joint work with Francesca Corni (Univer
sity of Bologna).\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Armin Rainer (Wien)
DTSTART;VALUE=DATE-TIME:20240227T130000Z
DTEND;VALUE=DATE-TIME:20240227T150000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/78
DESCRIPTION:Title: On the semialgebraic Whitney extension problem\nby
Armin Rainer (Wien) as part of Geometric Structures Research Seminar\n\nL
ecture held in room 133 -SISSA Main Building.\n\nAbstract\nIn 1934\, Whitn
ey raised the question of how one can decide whether a function $f$ define
d on a closed subset $X$ of $\\mathbb R^n$ is the restriction of a $C^m$ f
unction on $\\mathbb R^n$. He gave a characterization in dimension $n=1$.
The problem was fully solved by Fefferman in 2006. In this talk\, I will d
iscuss a related conjecture: if a semialgebraic function $f : X \\to \\mat
hbb R$ has a $C^m$ extension to $\\mathbb R^n$\, then it has a semialgebr
aic $C^m$ extension. In particular\, I will show that the $C^{1\,\\omega}$
case of the conjecture is true (in a uniformly bounded way)\, for each se
mialgebraic modulus of continuity $\\omega$. The proof is based on the e
xistence of semialgebraic Lipschitz selections for certain affine-set valu
ed maps. This is joint work with Adam Parusinski.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Rosana (SISSA)
DTSTART;VALUE=DATE-TIME:20240305T090000Z
DTEND;VALUE=DATE-TIME:20240305T100000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/79
DESCRIPTION:Title: The Grassmann Distance Degree\nby Andrea Rosana (S
ISSA) as part of Geometric Structures Research Seminar\n\nLecture held in
room 136 - SISSA main building.\n\nAbstract\nGiven a space endowed with a
distance\, how can we optimize the distance from a point to a given subset
? In this talk we will explore two different settings for this problem. We
will first focus on the classical Euclidean space were the subset will be
given by an algebraic variety\, leading to the notion of Euclidean Distan
ce Degree (EDD). Then we will try to mimic this construction for Grassmann
ians when the subset is a subvariety. After explaining why the techniques
used in the previous case fail\, we will be able to define an analogue of
the EDD\, which we call Grassmann Distance Degree. In the last part we wil
l focus on the case where the subvariety is a simple Schubert variety\, fi
nding an interesting connection between the geometry of the problem and Ec
kart-Young theorem.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giuseppe Pipoli (Università degli Studi dell'Aquila)
DTSTART;VALUE=DATE-TIME:20240409T120000Z
DTEND;VALUE=DATE-TIME:20240409T140000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/80
DESCRIPTION:Title: Vanishing theorems for minimal stable hypersurfaces\nby Giuseppe Pipoli (Università degli Studi dell'Aquila) as part of Geo
metric Structures Research Seminar\n\nLecture held in room 133 - SISSA Mai
n Building.\n\nAbstract\nWe will discuss some topological obstructions to
the existence of stable minimal hypersurfaces. In particular\, we will sho
w the non-existence of nontrivial harmonic $p$-forms and nontrivial harmon
ic spinors on stable minimal hypersurfaces under suitable curvature assump
tions of the ambient manifold. This talk is based on a upcoming joint work
with Francesco Bei (Sapienza\, Università di Roma).\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joe Hoisington (Max Planck Institute for Mathematics)
DTSTART;VALUE=DATE-TIME:20240507T120000Z
DTEND;VALUE=DATE-TIME:20240507T140000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/81
DESCRIPTION:Title: Energy-minimizing mappings of real and complex project
ive spaces\nby Joe Hoisington (Max Planck Institute for Mathematics) a
s part of Geometric Structures Research Seminar\n\nLecture held in room 13
3 - SISSA Main Building.\n\nAbstract\nWe will show that\, in any homotopy
class of mappings from complex projective space to a Riemannian manifold\,
the infimum of the energy is proportional to the infimal area in the clas
s of mappings of the 2-sphere representing the induced homomorphism on the
second homotopy group. We will also give a related estimate for the infi
mum of the energy in a homotopy class of mappings of real projective space
\, and we will discuss several results and questions about energy-minimizi
ng maps and their metric properties.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mattia Magnabosco (Oxford)
DTSTART;VALUE=DATE-TIME:20240312T130000Z
DTEND;VALUE=DATE-TIME:20240312T150000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/82
DESCRIPTION:Title: Failure of the curvature-dimension condition in sub-Fi
nsler manifolds\nby Mattia Magnabosco (Oxford) as part of Geometric St
ructures Research Seminar\n\nLecture held in SISSA Main Building.\n\nAbstr
act\nThe Lott–Sturm–Villani curvature-dimension condition $\\mathsf{CD
}(K\,N)$ provides a synthetic notion for a metric measure space to have cu
rvature bounded from below by $K$ and dimension bounded from above by $N$.
It has been recently proved that this condition does not hold in any sub-
Riemannian manifold equipped with a positive smooth measure\, for every ch
oice of the parameters $K$ and $N$. In this talk\, we investigate the vali
dity of the analogous result for sub-Finsler manifolds\, providing two res
ults in this direction. On the one hand\, we show that the $\\mathsf{CD}$
condition fails in sub-Finsler manifolds equipped with a smooth strongly c
onvex norm and with a positive smooth measure. On the other hand\, we prov
e that\, on the sub-Finsler Heisenberg group\, the same result holds for e
very reference norm. Additionally\, we show that the validity of the measu
re contraction property $\\mathsf{MCP}(K\,N)$ on the sub-Finsler Heisenber
g group depends on the regularity of the reference norm.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tommaso Rossi (Paris)
DTSTART;VALUE=DATE-TIME:20240319T130000Z
DTEND;VALUE=DATE-TIME:20240319T150000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/83
DESCRIPTION:Title: Weyl's tube formula in sub-Riemannian geometry\nby
Tommaso Rossi (Paris) as part of Geometric Structures Research Seminar\n\
nLecture held in SISSA Main Building.\n\nAbstract\nWe study the volume of
a tube around a submanifold in sub-Riemannian geometry. Firstly\, we show
that the volume of the tube around a non-characteristic submanifold of cla
ss $C^2$ is either smooth or real-analytic for small radii\, depending on
the regularity of the underlying manifold\, and we establish a Weyl's tube
formula. Secondly\, we investigate Weyl's invariance theorem in sub-Riema
nnian geometry: we show that two curves in the Heisenberg group with the s
ame Reeb angle have the same Weyl's tube formula. This is a joint work wit
h T. Bossio and L. Rizzi.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugenio Bellini (Milano Bicocca)
DTSTART;VALUE=DATE-TIME:20240326T130000Z
DTEND;VALUE=DATE-TIME:20240326T150000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/84
DESCRIPTION:Title: Geometry and topology of 3D-contact sub-Riemannian man
ifolds\nby Eugenio Bellini (Milano Bicocca) as part of Geometric Struc
tures Research Seminar\n\nLecture held in room 133 - SISSA Main Building.\
n\nAbstract\nA contact structure on a three dimensional manifold is a plan
e field satisfying a non-integrability condition. The topological properti
es of such structures are often subtle and difficult to detect. Indeed\, e
ven the simple statement that there are two different contact structures o
n $\\mathbb{R}^3$ is highly non-trivial to prove. In this talk I will desc
ribe some recent results concerning the relations between contact topology
and sub-Riemannian geometry. The focus will be on tightness questions\, b
oth semi-local and global\, and on geometric detection of overtwisted disk
s. In particular I will present a contac version of Hadamard theorem: the
universal cover of any negatively curved normal contact manifold is the He
isenberg group. This is a joint work with A. Agrachev\, S. Baranzini and L
. Rizzi.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giorgio Saracco (University of Florence)
DTSTART;VALUE=DATE-TIME:20240618T120000Z
DTEND;VALUE=DATE-TIME:20240618T140000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/85
DESCRIPTION:Title: Existence of minimizers of Cheeger's functional among
convex sets\nby Giorgio Saracco (University of Florence) as part of Ge
ometric Structures Research Seminar\n\nLecture held in SISSA Main Building
.\n\nAbstract\nGiven any open\, bounded set in $\\mathbb{R}^N$\, the Cheeg
er inequality states that its first eigenvalue of the Dirichlet $p$-Laplac
ian is suitably bounded from below by the $p$-th power of the so-called Ch
eeger constant of the set. A natural question is whether this inequality i
s sharp and if the infimum of the ratio of these two quantities is attaine
d (at least when restricting to suitable classes of competitors) by some s
et.\n\nParini proved existence of minimizers among convex sets in the line
ar case $p=2$\, limitedly to the planar case $N=2$. The result was later e
xtended to general $p$ by Briani—Buttazzo—Prinari\, still for $N=2$. T
hey conjecture that existence of minimizers among convex sets should hold
regardless of the dimension. Together with Aldo Pratelli\, we positively s
olve the conjecture. The proof exploits a criterion proved by Ftouhi paire
d with some cylindrical estimate on the Cheeger constant.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Felix Rydell (KTH Royal Institute of Technology)
DTSTART;VALUE=DATE-TIME:20240521T120000Z
DTEND;VALUE=DATE-TIME:20240521T140000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/86
DESCRIPTION:Title: Nearest Point Problems in Computer Vision\nby Feli
x Rydell (KTH Royal Institute of Technology) as part of Geometric Structur
es Research Seminar\n\nLecture held in room 133 - SISSA Main Building.\n\n
Abstract\nStructure-from-Motion in Computer Vision aims to create 3D model
s of objects based on 2D images. The first step in this pipeline is to ide
ntify key features in each image and match these across the different view
s. After having estimated the camera parameters\, world features are obtai
ned by triangulation\, which refers to finding the world features that bes
t correspond to the matched image features. This is done by minimizing the
distance between the data and our mathematical model\; it is a nearest po
int problem. The number of complex solutions to the associated critical eq
uations given general data is the Euclidean distance degree\, which measur
es the complexity of this optimization problem. In this talk\, we describe
the algebra and geometry that arises in Structure-from-Motion and discuss
the associated nearest point problems and Euclidean distance degrees.\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michele Stecconi (University Of Luxembourg)
DTSTART;VALUE=DATE-TIME:20240604T120000Z
DTEND;VALUE=DATE-TIME:20240604T140000Z
DTSTAMP;VALUE=DATE-TIME:20240614T062626Z
UID:Geometric_Structures_SISSA/87
DESCRIPTION:Title: Sobolev-Malliavin regularity of the nodal volume\n
by Michele Stecconi (University Of Luxembourg) as part of Geometric Struct
ures Research Seminar\n\nLecture held in room 133 - SISSA Main Building.\n
\nAbstract\nConsider the $(d-1)$-volume $V(f)$ of the level set of a smoot
h function $f$ on a compact Riemannian manifold of arbitrary dimension $d$
. We show that\, if restricted to a generic finite dimensional vector spac
e of smooth functions\, the functional $f \\mapsto V(f)$ belongs to an app
ropriate Sobolev space. A fundamental ingredient is to understand the Sobo
lev regularity of the function $t\\mapsto V(f-t)$ that expresses the volum
e of the level $t$ of a "typical" Morse function.\n\nThis result can be st
ated more naturally in the language of a Gaussian random field $f$\, in wh
ich case $V(f)$ is a random variable and being Sobolev (Malliavin) implies
that its law has an absolutely continuous component.\nThis was an open qu
estion in the 2 dimensional case: both the differentiability and the regul
arity of the law of the nodal length were unknown.\n\nThe result I will pr
esent completes the picture in that we describe what happens for $d=2$: in
short\, $V(f)$ is Sobolev only if the topology of the zero set is constan
t for all $f$ in the given vector space. Nevertheless\, the law of $V(f)$
has an absolutely continuous component.\n \n(A joint work with Giovanni
Peccati.)\n
LOCATION:https://researchseminars.org/talk/Geometric_Structures_SISSA/87/
END:VEVENT
END:VCALENDAR