BEGIN:VCALENDAR
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BEGIN:VEVENT
SUMMARY:Daniel Peralta-Salas (ICMAT)
DTSTART:20201027T150000Z
DTEND:20201027T160000Z
DTSTAMP:20260405T094319Z
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 p
art of Geometric Structures Research Seminar\n\n\nAbstract\nIn 2001\, Sir
Michael Berry conjectured that given any knot there should exist a (comple
x-valued) eigenfunction of the harmonic oscillator (or the hydrogen atom)
whose nodal set contains a component of such a knot type. This is a partic
ular instance of the following problem: how is the topology of the nodal s
ets of eigenfunctions of Schrodinger operators? In this talk I will focus
on the flexibility aspects of the problem: either you construct a suitable
Riemannian metric adapted to the submanifold you want to realize\, or you
consider operators with a large group of symmetries (e.g.\, the Laplacian
on the round sphere\, or the harmonic quantum oscillator)\, and exploit t
he large multiplicity of the high eigenvalues. In particular\, I will show
how to prove Berry's conjecture using an inverse localization property. T
his talk is based on different joint works with A. Enciso\, D. Hartley and
F. Torres de Lizaur.\n\nSubscribe at https://sites.google.com/view/geomet
ric-structures/ to receive the password by mail.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eero Hakavuori (SISSA)
DTSTART:20201103T150000Z
DTEND:20201103T160000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/2
DESCRIPTION:Title: Carnot groups and abnormal dynamics\nby Eero
Hakavuori (SISSA) as part of Geometric Structures Research Seminar\n\n\nA
bstract\nThe existence of so called abnormal curves is one of the features
distinguishing sub-Riemannian geometry from Riemannian geometry. The need
to understand (or avoid) abnormal curves appears in many sub-Riemannian p
roblems\, such as the regularity of length-minimizing curves and the Sard
problem. Some recent progress in both of these problems has been obtained
by studying abnormal curves as trajectories of dynamical systems. In this
talk\, I will present some of the story of abnormal dynamics in the settin
g of Carnot groups. In particular\, I will cover how to lift an arbitrary
trajectory of an arbitrary polynomial ODE to an abnormal curve in some Car
not group.\n\nPlease register to https://sites.google.com/view/geometric-s
tructures/ to get the password\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miruna-Stefana Sorea (SISSA)
DTSTART:20201117T150000Z
DTEND:20201117T160000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/3
DESCRIPTION:Title: Disguised toric dynamical systems\nby Miruna
-Stefana Sorea (SISSA) as part of Geometric Structures Research Seminar\n\
n\nAbstract\nWe study families of polynomial dynamical systems inspired by
biochemical reaction networks. We focus on complex balanced mass-action s
ystems\, which have also been called toric dynamical systems\, by Craciun\
, Dickenstein\, Shiu and Sturmfels. These systems are known or conjectured
to enjoy very strong dynamical properties\, such as existence and uniquen
ess of positive steady states\, local and global stability\, persistence\,
and permanence. We consider the class of disguised toric dynamical system
s\, which contains toric dynamical systems\, and to which all dynamical pr
operties mentioned above extend naturally. We show that\, for some familie
s of reaction networks\, this new class is much larger than the class of t
oric systems. 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
disguised toric systems. We focus on the characterization of the disguised
toric locus by means of real algebraic geometry. Joint work with Gheorghe
Craciun and Laura Brustenga i Moncusí.\n\nRegister at https://docs.googl
e.com/forms/d/e/1FAIpQLSfOAjTSQWOlb4jcqIkLNo1Qz2tQHMBGs13XmlVmtaRpIFE1wA/v
iewform\nto get the password for the talk\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raman Sanyal (Frankfurt)
DTSTART:20201124T150000Z
DTEND:20201124T160000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/4
DESCRIPTION:Title: Normally inscribable polytopes\, routed trajecto
ries\, and reflection arrangements\nby Raman Sanyal (Frankfurt) as par
t of Geometric Structures Research Seminar\n\n\nAbstract\nSteiner posed th
e question if any 3-dimensional polytope had a realization with vertices o
n a sphere. Steinitz constructed the first counter examples and Rivin gave
a complete complete answer to Steiner's question. In dimensions 4 and up\
, the Universality Theorem renders the question for inscribable combinator
ial types hopeless. In this talk\, I will address the following refined qu
estion: Given a polytope P\, is there a continuous deformation of P into a
n inscribed polytope that keeps corresponding faces parallel?\nThis questi
on has strong ties to deformations of Delaunay subdivisions and ideal hype
rbolic polyhedra and its study reveals a rich interplay of algebra\, geome
try\, and combinatorics. In the first part of the talk\, I will discuss re
lations to routed trajectories of particles in a ball and reflection group
oids and 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\,
polytopes representing hyperplane arrangements. It turns out that inscrib
able zonotopes are rare and intimately related to reflection groups and Gr
unbaum's quest for simplicial arrangements. This is based on joint work w
ith Sebastian Manecke.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gal Binyamini (Weizmann Institute of Science)
DTSTART:20201201T140000Z
DTEND:20201201T150000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/5
DESCRIPTION:Title: Cylindrical decomposition in real and complex ge
ometry\nby Gal Binyamini (Weizmann Institute of Science) as part of Ge
ometric Structures Research Seminar\n\n\nAbstract\nThe decomposition of a
set into "cylinders" in one of the fundamental tools of semi-algebraic geo
metry (as well as subanalytic geometry and o-minimal geometry). Defined by
means of intervals\, these cylinders are an essentially real-geometric co
nstruct.\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 complex cells admit a rich hyperbolic geometry\, which is not direct
ly visible in their real counterparts. I will sketch some of this theory\,
and how it can be used to prove some new results in real geometry (for in
stance a sharpening of the Yomdin-Gromov lemma).\n\nPlease subscribe to ht
tps://sites.google.com/view/geometric-structures/registration-form\nto rec
eive the password\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maurizia Rossi (University of Milano-Bicocca)
DTSTART:20201207T150000Z
DTEND:20201207T160000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/6
DESCRIPTION:Title: Geometrical properties of random eigenfunctions<
/a>\nby Maurizia Rossi (University of Milano-Bicocca) as part of Geometric
Structures Research Seminar\n\n\nAbstract\nIn this talk we deal with the
geometry of random eigenfunctions on manifolds (the round sphere\, the sta
ndard flat torus\, the Euclidean plane...) motivated by both Yau's conject
ure and Berry's ansatz. In particular\, we investigate the asymptotic beha
vior (in the high-energy limit) of the so-called nodal length for random s
pherical harmonics and (un)correlation phenomena between the latter and ot
her Lipschitz-Killing curvatures of their excursion sets at any level.\nTh
is talk is mainly based on joint works with V. Cammarota\, D. Marinucci\,
I. Nourdin\, G. Peccati and I. Wigman.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lev Buhovsky (Tel Aviv University)
DTSTART:20201215T150000Z
DTEND:20201215T160000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/7
DESCRIPTION:Title: Critical points of eigenfunctions\nby Lev Bu
hovsky (Tel Aviv University) as part of Geometric Structures Research Semi
nar\n\n\nAbstract\nOn a closed Riemannian manifold\, the Courant nodal dom
ain theorem gives an upper bound on the number of nodal domains of n-th ei
genfunction of the Laplacian. In contrast to that\, there does not exist s
uch bound on the number of isolated critical points of an eigenfunction. I
will try to sketch a proof of the existence of a Riemannian metric on the
2-dimensional torus\, whose Laplacian has infinitely many eigenfunctions\
, each of which has infinitely many isolated critical points. Based on a j
oint work with A. Logunov and M. Sodin.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olga Paris-Romaskevich (Institut de Mathématiques de Marseille)
DTSTART:20210126T150000Z
DTEND:20210126T160000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/8
DESCRIPTION:Title: Tiling billiards in periodic tilings by equal tr
iangles (and quadrilaterals)\nby Olga Paris-Romaskevich (Institut de M
athématiques de Marseille) as part of Geometric Structures Research Semin
ar\n\n\nAbstract\nI will make an elementary introduction to tiling billiar
ds — model of a light moving through a tiling under refraction laws.\nTh
is class 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 plan
e sections 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 foll
owing 5-MIN movie (here is a link to Youtube) by a wonderful mathematician
and animator Ofir David.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessandro Tamai (University of Trieste)
DTSTART:20210112T150000Z
DTEND:20210112T160000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/9
DESCRIPTION:Title: Singular solutions spaces of rolling balls probl
em\nby Alessandro Tamai (University of Trieste) as part of Geometric S
tructures Research Seminar\n\n\nAbstract\nThe "Rolling Balls Model"\, the
model describing a pair of spheres of different ray rolling one on another
without slipping or twisting\, is a classical example of sub-Riemannian p
roblem. The symmetries of the distribution associated with the system depe
nd on the 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 o
f the ratio\, also on the singular solutions related to the problem.\nIn t
his talk we show how it is possible to describe the spaces of such singula
r solutions in a geometric way\, as a family of 5-dimensional manifolds de
pending on the ratio. For rational values of the ratio such manifolds have
a structure of SO(2)-principal bundles which are not topologically distin
guished by their homology\, homotopy and de Rham cohomology groups. In add
ition\, we show that for integer values of the ratio the configuration man
ifold of the problem is a branched covering of each of such manifolds and
how the covering maps associated allow to relate them with another known f
amily of topological spaces\, the lens spaces.\n\nThis talk is based on th
e research works developed in my master thesis at University of Trieste\,
under the supervision of the professor A.Agrachev.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kathlén Kohn (Royal Institute of Technology (KTH))
DTSTART:20210119T150000Z
DTEND:20210119T160000Z
DTSTAMP:20260405T094319Z
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 Res
earch Seminar\n\n\nAbstract\nThis talk brings many areas together: discret
e geometry\, statistics\, intersection theory\, classical algebraic geomet
ry\, geometric modeling\, and physics. First\, we recall the definition of
the adjoint of a polytope given by Warren in 1996 in the context of geome
tric modeling. He defined this polynomial to generalize barycentric coordi
nates from simplices to arbitrary polytopes. Secondly\, we show how this p
olynomial appears in statistics. It is the numerator of a generating funct
ion over all moments of the uniform probability distribution on a polytope
. Thirdly\, we prove the conjecture that the adjoint is the unique polynom
ial of minimal degree which vanishes on the non-faces of a simple polytope
. In addition\, we see that the adjoint appears as the central piece in Se
gre classes of monomial schemes\, and in the study of scattering amplitude
s in particle physics. Finally\, we observe that adjoints of polytopes are
special cases of the classical notion of adjoints of divisors. Since the
adjoint of a simple polytope is unique\, the corresponding divisors have u
nique canonical curves. In the case of three-dimensional polytopes\, we sh
ow that these divisors are either K3 - or elliptic surfaces.\nThis talk is
based on joint works with Kristian Ranestad\, Boris Shapiro and Bernd Stu
rmfels.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noémie Combe (Max Planck Institute)
DTSTART:20210202T150000Z
DTEND:20210202T160000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/11
DESCRIPTION:Title: Complement of the discriminant variety\, Gauss
–skizze operads and hidden symmetries\nby Noémie Combe (Max Planck
Institute) as part of Geometric Structures Research Seminar\n\n\nAbstract\
nIn this talk\, the configuration space of marked points on the complex pl
ane is considered. We investigate a decomposition of this space by so-call
ed Gauss-skizze i.e. a class of graphs being forests. These Gauss-skizze\,
reminiscent of Grothendieck's dessins d'enfant\, provide a totally differ
ent real geometric insight on this complex configuration space\, which und
er the light of classical complex geometry tools\, remains invisible. Topo
logically speak- ing\, this stratification is shown to be a Goresky–MacP
herson stratification.\nWe prove that for Gauss-skizze\, classical tools f
rom deformation theory\, ruled by a Maurer--Cartan equation can be used on
ly locally.\nWe show as well\, that the deformation of the Gauss-skizze is
governed by a Hamilton--Jacobi differential equation.\nFinally\, a Gauss-
skizze operad is introduced which can be seen as an enriched Fulton--MacPh
erson operad\, topologically equivalent to the little 2-disc operad.\nThe
combinatorial flavour of this tool allows not only a new interpretation of
the moduli space of genus 0 curves with n marked points\, but gives a ver
y geometric understanding of the Grothendieck--Teichmuller group.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erlend Grong (University of Bergen)
DTSTART:20210209T151500Z
DTEND:20210209T161500Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/12
DESCRIPTION:Title: On the equivalence problem in sub-Riemannian ge
ometry\nby Erlend Grong (University of Bergen) as part of Geometric St
ructures Research Seminar\n\n\nAbstract\nIn mathematics\, we are always in
terested in understanding when two objects are essentially the same. For t
he context of geometric structures\, such as Riemannian and sub-Riemannian
manifolds\, "essentially the same" means being connected by an isometry.\
n\n\nFor a Riemannian geometry\, the central object measuring the local ob
struction to the existence of an isometry is the curvature tensor of the L
evi-Civita connection. We want to show that similar objects can be found o
n sub-Riemannian manifolds with constant nilpotentization\, based on the w
ork of T. Morimoto.\n\nWe will show explicit formulas for a canonical choi
ce of grading and connection for sub-Riemannian manifolds in some explicit
cases.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olga Paris-Romaskevich (Institut de Mathématiques de Marseille)
DTSTART:20210216T151500Z
DTEND:20210216T161500Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/13
DESCRIPTION:Title: Tiling billiards in periodic tilings by equal t
riangles (and quadrilaterals)\nby Olga Paris-Romaskevich (Institut de
Mathématiques de Marseille) as part of Geometric Structures Research Semi
nar\n\n\nAbstract\nI will make an elementary introduction to tiling billia
rds — model of a light moving through a tiling under refraction laws.\nT
his class of dynamical systems is new to mathematicians\, simple to define
as well as connected to already existing areas of research such as ergodi
c theory of interval exchange transformations and Novikov's problem on pla
ne sections 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 fol
lowing 5-MIN movie (here is a link to Youtube) by a wonderful mathematicia
n and animator Ofir David.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Clayton Shonkwiler (Colorado State University)
DTSTART:20210223T151500Z
DTEND:20210223T161500Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/14
DESCRIPTION:Title: The (Symplectic) Geometry of Spaces of Frames\nby Clayton Shonkwiler (Colorado State University) as part of Geometric
Structures Research Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Akos Matszangosz (Alfréd Rényi Institute of Mathematics)
DTSTART:20210302T151500Z
DTEND:20210302T161500Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/15
DESCRIPTION:Title: Cohomology rings of real flag manifolds\nby
Akos Matszangosz (Alfréd Rényi Institute of Mathematics) as part of Geo
metric Structures Research Seminar\n\n\nAbstract\nThe cohomology ring of a
complex (partial) flag manifold has two classical descriptions\; a topolo
gical one (via characteristic classes) and a geometric one (via Schubert c
lasses). Similar descriptions are well-known for real flag manifolds X wit
h mod 2 coefficients. In this talk I will discuss some aspects of what can
be said with rational\, or integer coefficients. Namely\, I will consider
questions of the following type:\n1) Which Schubert varieties represent a
n integer 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 applications of the ring structure to real Schubert calculus.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Khazhgali Kozhasov (Technische Universität Braunschweig)
DTSTART:20210309T151500Z
DTEND:20210309T161500Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/16
DESCRIPTION:Title: On minimality of determinantal varieties\nb
y Khazhgali Kozhasov (Technische Universität Braunschweig) as part of Geo
metric Structures Research Seminar\n\n\nAbstract\nMinimal submanifolds are
mathematical abstractions of soap films: they minimize the Riemannian vol
ume locally around every point. Finding minimal algebraic hypersurfaces in
𝑅𝑛 for each n is a long-standing open problem posed by Hsiang. In 2
010 Tkachev gave a partial solution to this problem showing that the hyper
surface of n x n real matrices of corank one is minimal. I will discuss th
e following generalization of this fact to all determinantal matrix variet
ies: for any m\, n and rThe average condition number of different probl
ems\, from a geometric perspective\nby Carlos Beltrán (Universidad de
Cantabria) as part of Geometric Structures Research Seminar\n\n\nAbstract
\nI will present the condition number of problems from a general perspecti
ve as a measure of the stability of problems. Then I will discuss how does
this condition number look and interact with other mathematical concepts
in different problems which are very basic but are still full of mysteries
: polynomial solving\, eigenvalue/eigenvector problems or tensor decomposi
tion problems. All the material will be presented for a general audience.
Different parts of what will be presented has been done with different aut
hors\, for example the tensor decomposition part has been done with Paul B
reiding and Nick Vannieuwenhoven. Check the following video for our result
in 2 minutes:\nhttps://www.teamco.unican.es/portfolio-item/pencil-based-a
lgorithms-for-tensor-rank-decomposition-are-not-stable/\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Lotz (Warwick University)
DTSTART:20210323T151500Z
DTEND:20210323T161500Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/18
DESCRIPTION:Title: Concentration of Measure in Integral Geometry\nby Martin Lotz (Warwick University) as part of Geometric Structures Re
search Seminar\n\n\nAbstract\nIntrinsic volumes are fundamental geometric
invariants that include the Euler characteristic and the volume. Important
results in integral geometry relate the intrinsic volumes of random proje
ctions\, intersections\, and sums of convex bodies to those of the individ
ual volumes. We present a new interpretations of classic results\, based o
n the observation that intrinsic volumes (both in spherical and Euclidean
settings) concentrate around certain indices. One consequence is\, for exa
mple\, 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
transition between these two cases can be expressed in terms of a summary
parameter associated with the convex body. Similar phase transitions appea
r in related problems\, including the rotation mean formula\, the slicing
(Crofton) formula\, and the kinematic formula. This is joint work with Joe
l Tropp.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugenii Shustin (Tel-Aviv University)
DTSTART:20210406T141500Z
DTEND:20210406T151500Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/19
DESCRIPTION:Title: Expressive geometry\nby Eugenii Shustin (Te
l-Aviv University) as part of Geometric Structures Research Seminar\n\n\nA
bstract\nWe review two so-called expressive models\, morsifications of rea
l plane curve singularities introduced in 70s by A'Campo and Gusein-Zade\,
and real affine expressive curves. These models are characterized by the
property that their underlining polynomial has the smallest number of crit
ical points allowed by the topology of the real point set. The classificat
ion of these objects is tightly related to the mutational equivalence of t
he corresponding quivers (which in turn naturally appear in the theory of
cluster algebras). We discuss various problems in the geometry of morsific
ations and expressive curves\, including related objects like planar divid
es\, links of singularities and links of curves at infinity\, combinatoric
s of quivers. Based on joint works with S. Fomin\, P. Pylyavskyy\, D. Thur
ston.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miruna-Stefana Sorea (SISSA)
DTSTART:20210330T141500Z
DTEND:20210330T151500Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/20
DESCRIPTION:Title: Poincaré-Reeb trees of real Milnor fibres\
nby Miruna-Stefana Sorea (SISSA) as part of Geometric Structures Research
Seminar\n\n\nAbstract\nWe study the real Milnor fibre of real bivariate po
lynomial functions vanishing at the origin\, with an isolated local minimu
m at this point. We work in a neighbourhood of the origin in which its non
-zero level sets are smooth Jordan curves. Whenever the origin is a Morse
critical point\, the sufficiently small levels become boundaries of convex
disks. Otherwise\, they may fail to be convex\, as was shown by Coste.\n\
nIn order to measure the non-convexity of the level curves\, we introduce
a new combinatorial object\, called the Poincaré-Reeb tree\, and show tha
t locally the shape stabilises and that no spiralling phenomena occur near
the origin. Our main objective is to characterise all topological types o
f asymptotic Poincaré-Reeb trees. To this end\, we construct a family of
polynomials with non-Morse strict local minimum at the origin\, realising
a large class of such trees.\n\nAs a preliminary step\, we reduce the prob
lem to the univariate case\, via the interplay between the polar curve and
its discriminant. Here we give a new and constructive proof of the existe
nce of Morse polynomials whose associated permutation (the so-called "Arno
ld snake") is separable\, using tools inspired from Ghys's work.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Galuppi (University of Trieste)
DTSTART:20210413T141500Z
DTEND:20210413T151500Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/21
DESCRIPTION:Title: Signature tensors of paths\nby Francesco Ga
luppi (University of Trieste) as part of Geometric Structures Research Sem
inar\n\n\nAbstract\nI'm interested in connections between algebraic geomet
ry and other branches of math. In stochastic analysis\, a standard method
to study a path is to work with its signature. This is a sequence of tenso
rs that encode information of the path in a compact form. When the path va
ries\, such signatures parametrize an algebraic variety in the tensor spac
e. My goal is to study the geometry of such varieties and to link it to pr
operties of certain classes of paths.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emil Horobert (Sapientia Hungarian University of Transylvania)
DTSTART:20210420T141500Z
DTEND:20210420T151500Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/22
DESCRIPTION:Title: The critical curvature degree of an algebraic v
ariety\nby Emil Horobert (Sapientia Hungarian University of Transylvan
ia) as part of Geometric Structures Research Seminar\n\n\nAbstract\nThis t
opic is about the complexity involved in the computation of the reach in a
rbitrary dimensions and in particular the computation of the critical sphe
rical curvature points of an arbitrary algebraic variety. We present prope
rties of the critical spherical curvature points as well as an algorithm f
or computing them.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Draisma (Universität Bern)
DTSTART:20210427T141500Z
DTEND:20210427T151500Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/23
DESCRIPTION:Title: Infinite-dimensional geometry with symmetry
\nby Jan Draisma (Universität Bern) as part of Geometric Structures Resea
rch Seminar\n\n\nAbstract\nMost theorems in finite-dimensional algebraic g
eometry 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.\, ideals in C[x_1\,x_2\,...] that are preserved under all variable per
mutations do satisfy the ascending chain condition.\nThis phenomenon is re
levant in pure and applied mathematics\, since many algebraic models come
in infinite families with highly symmetric infinite-dimensional limits. He
re the symmetry is typically captured by either the infinite symmetric gro
up or the infinite general linear group. Theorems about the limit imply un
iform behaviour of the members of the family.\nI will present older and ne
w results in this area\, along with applications to algebraic statistics\,
tensor decomposition\, and algebraic combinatorics.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boulos El Hilany (Johann Radon Institute for Computational and App
lied Mathematics\, Linz)
DTSTART:20210518T141500Z
DTEND:20210518T151500Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/24
DESCRIPTION:Title: Computing efficiently the non-properness set of
polynomial maps on the plane\nby Boulos El Hilany (Johann Radon Insti
tute for Computational and Applied Mathematics\, Linz) as part of Geometri
c Structures Research Seminar\n\n\nAbstract\nI will present new mathematic
al and computational tools to develop a complete and efficient algorithm f
or computing the set of non-properness of polynomial maps in the complex (
and real) plane. In particular\, this is a subset of the plane where a dom
inant polynomial map as above is not proper. The algorithm takes into acco
unt the sparsity of polynomials\, and the genericness of the coefficients
as it depends on their Newton polytopes. As a byproduct it provides a fine
r representation of the set of non-properness as a union of algebraic or s
emi-algebraic sets\, that correspond to edges of the Newton polytopes\, wh
ich is of independent interest. This is a joint work with Elias Tsigaridas
.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Damien Gayet (Université Grenoble I)
DTSTART:20210525T141500Z
DTEND:20210525T151500Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/25
DESCRIPTION:Title: Asymptotic topology of random excursion sets\nby Damien Gayet (Université Grenoble I) as part of Geometric Structure
s Research Seminar\n\n\nAbstract\nLet f be a smooth random Gaussian field
over the 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-b
alls. I will explain that in average\, this intuition is true. After reca
lling the historical background of this subject\, and will present the id
eas of the proof\, which holds on (deterministic) Morse theory and a contr
ol of random critical points of given index.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michele Stecconi (Université de Nantes)
DTSTART:20210504T141500Z
DTEND:20210504T151500Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/26
DESCRIPTION:Title: Semicontinuity of Betti numbers: A little surge
ry cannot kill homology\nby Michele Stecconi (Université de Nantes) a
s part of Geometric Structures Research Seminar\n\n\nAbstract\nA consequen
ce of Thom Isotopy Lemma is that the set of solutions of a regular smooth
equation is stable under C^1-small perturbations (it remains isotopic to t
he original one)\, but what happens if the perturbation is just C^0-small?
In this case\, the topology of the set of solution may change. However\,
it turns out that the Homology groups cannot "decrease". In this talk I wi
ll present such result and some related examples and applications. This th
eorem is useful in those contexts where the price to pay to approximate so
mething in C^1 is higher than in C^0. For instance in the search for quant
itative bounds (here the price can be the degree of an algebraic approxima
tion) or in combination with Eliashberg's and Mishachev's holonomic approx
imation Theorem (which is C^0 at most).\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julian Sahasrabudhe (University of Cambridge)
DTSTART:20210511T141500Z
DTEND:20210511T151500Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/27
DESCRIPTION:Title: Anti-concentration and the geometry of polynomi
als\nby Julian Sahasrabudhe (University of Cambridge) as part of Geome
tric Structures 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 probability generating function. Pemantle conjectured that if sigma i
s large and f_X has no roots close to 1 in the complex plane then X must a
pproximate a normal distribution. In this talk\, I will discuss the resolu
tion of Pemantle's conjecture and its application to prove a conjecture of
Ghosh\, Liggett and Pemantle by proving a multivariate central limit theo
rem for\, so called\, strong Rayleigh distributions. I will also touch on
some more recent work connecting anti-concentration for random variables w
ith the zeros of their probability generating functions.\n \nThis talk is
based on joint work with Marcus Michelen.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ursula Ludwig (Universität Duisburg-Essen and MPIM Bonn)
DTSTART:20210601T141500Z
DTEND:20210601T151500Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/28
DESCRIPTION:Title: The Witten deformation on singular spaces\n
by Ursula Ludwig (Universität Duisburg-Essen and MPIM Bonn) as part of Ge
ometric Structures Research Seminar\n\n\nAbstract\nIn his seminal paper
“Supersymmetry and Morse theory” (Journal Diff. Geom. 1982) Witten\, i
nspired by ideas from quantum field theory\, gave a new analytic proof of
the famous Morse inequalities. The Witten deformation plays an important r
ole in the generalisation by Bismut and Zhang of the comparison theorem be
tween analytic and topological torsion of a smooth compact manifold\, aka
Cheeger-Mu ̈ller theorem.\nThe aim of this talk is to explain the general
isation of the Witten deformation to certain singular spaces. We will expl
ain the case of singular spaces with conical singularities equipped with a
radial Morse function as well as the case of singular algebraic complex c
urves equipped with a stratified Morse function in the sense of Goresky an
d MacPherson. A first result in both situations is the proof of the Morse
inequalities for the L2-cohomology (or equivalently the intersection cohom
ology). A much stronger result is the generalisation of the comparison bet
ween the so called Witten complex and an appropriate singular Morse-Thom-S
male complex.\n\nIn the first part of this talk\, I will give a gentle int
roduction to the Witten deformation for a smooth compact manifold.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Kahle (The Ohio State University)
DTSTART:20210608T141500Z
DTEND:20210608T151500Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/29
DESCRIPTION:Title: Configurations spaces of particles: homological
solid\, liquid\, and gas\nby Matthew Kahle (The Ohio State University
) as part of Geometric Structures Research Seminar\n\n\nAbstract\nConfigur
ation spaces of points in the plane are well studied and the topology of s
uch spaces is well understood. But what if you replace points by particles
with some positive thickness\, and put them in a container with boundarie
s? It seems like not much is known. To mathematicians\, this is a natural
generalization of the configuration space of points\, perhaps interesting
for its own sake. But is also important from the point of view of physics
––physicists might call such a space the "phase space" or "energy land
scape" for a hard-spheres system. Since hard-spheres systems are observed
experimentally to undergo phase transitions (analogous to water changing i
nto ice)\, it would be quite interesting to understand topological underpi
nnings of such transitions.\nWe have just started to understand the homolo
gy of these configuration spaces\, and based on our results so far we sugg
est working definitions of "homological solid\, liquid\, and gas". This is
joint work with a number of collaborators\, including Hannah Alpert\, Ulr
ich Bauer\, Kelly Spendlove\, and Robert MacPherson.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boulos El Hilany (Johann Radon Institute for Computational and App
lied Mathematics\, Linz)
DTSTART:20210615T141500Z
DTEND:20210615T151500Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/30
DESCRIPTION:Title: Computing efficiently the non-properness set of
polynomial maps on the plane\nby Boulos El Hilany (Johann Radon Insti
tute for Computational and Applied Mathematics\, Linz) as part of Geometri
c Structures Research Seminar\n\n\nAbstract\nI will present new mathematic
al and computational tools to develop a complete and efficient algorithm f
or computing the set of non-properness of polynomial maps in the complex (
and real) plane. In particular\, this is a subset of the plane where a dom
inant polynomial map as above is not proper. The algorithm takes into acco
unt the sparsity of polynomials\, and the genericness of the coefficients
as it depends on their Newton polytopes. As a byproduct it provides a fine
r representation of the set of non-properness as a union of algebraic or s
emi-algebraic sets\, that correspond to edges of the Newton polytopes\, wh
ich is of independent interest. This is a joint work with Elias Tsigaridas
.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hamza Ounesli (SISSA and ICTP)
DTSTART:20210622T141500Z
DTEND:20210622T151500Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/31
DESCRIPTION:Title: Minimal entropy of geometric 3-manifolds\nb
y 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 ent
ropy. In this seminar we will investigate this question in dimension 3\, p
recisely\, we will prove that geometrizeable 3-manifolds with zero simplic
ial volume admits a metric of minimal entropy\, then we will show that clo
sed 3-manifolds admitting a geometric structure modelled on H^3\, Sol or t
he universal cover of PSL(2\,R) do not have a metric of minimal entropy wh
ich reveals in fact a chaotic aspect of negative curvature!\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yosef Yomdin (Weizzmann Institute of Science)
DTSTART:20210629T141500Z
DTEND:20210629T151500Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/32
DESCRIPTION:Title: Estimating high order derivatives of a function
through geometry and topology of its zero set\nby Yosef Yomdin (Weizz
mann Institute of Science) as part of Geometric Structures Research Semina
r\n\n\nAbstract\nAn order d rigidity inequality for a smooth function f is
an explicit lower bound for the (d+1)-st derivatives of f\, which holds\,
if f exhibits certain patterns\, forbidden for polynomials of degree d.\n
We discuss some recent results in this direction\, which use as an input t
he ``density'' of the zero set Z of f\, or\, in contrast\, its topology. I
n particular\, we interpret in terms of rigidity inequalities some recent
results of Lerario and Stecconi\, comparing topology of smooth transversal
singularities\, and of their polynomial approximations.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paolo Antonini (Università del Salento)
DTSTART:20210706T120000Z
DTEND:20210706T130000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/33
DESCRIPTION:Title: Infinite dimensional grassmannians\, quantum st
ates and optimal transport\nby Paolo Antonini (Università del Salento
) as part of Geometric Structures Research Seminar\n\n\nAbstract\nIn this
seminar we report on a recent work in collaboration with F. Cavalletti whe
re we develop the basic theory of optimal transport for the quantum states
of the C*-algebra of the compact operators on a (separable) Hilbert space
.\n \nAs usual\, states are interpreted as the noncommutative replacement
of probability measures\; via the spectral theorem applied to their densit
y matrices\, we associate to states discrete measures on the grassmannian
of the finite dimensional subspaces. In this way we can treat them as ordi
nary probability measures and develop the theory of optimal transport.\n \
nThe metric geometry of the grassmannian\, as an infinite dimensional mani
fold plays a decisive role and part of the talk will be devoted to describ
ing its rich structure. Notably the grassmannian is an Alexandrov space wi
th non negative curvature.\n \nFinally we will interpret pure normal state
s of the tensor product $H\\otimes H$ as families of transport maps. This
idea leads to the possibility of giving a definition of the Wasserstein co
st for such objects.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yassine El Maazouz (UC Berkeley)
DTSTART:20211111T130000Z
DTEND:20211111T150000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/34
DESCRIPTION:Title: Local fields: Gaussian measures and random proc
esses\nby Yassine El Maazouz (UC Berkeley) as part of Geometric Struct
ures Research Seminar\n\n\nAbstract\nGaussian measures on Banach spaces ov
er local fields can be defined and constructed by exploiting the orthogona
lity structures of such spaces. We discuss these constructions and their m
erit by exhibiting the interesting properties of the objects they produce.
Since these probabilistic objects also have a rich algebraic structure\,
interesting questions and problems arise.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniele Tiberio (SISSA\, Trieste)
DTSTART:20211125T130000Z
DTEND:20211125T150000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/35
DESCRIPTION:Title: The entropy Morse-Sard Theorem I\nby Daniel
e Tiberio (SISSA\, Trieste) as part of Geometric Structures Research Semin
ar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniele Tiberio (SISSA\, Trieste)
DTSTART:20211202T130000Z
DTEND:20211202T150000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/36
DESCRIPTION:Title: The entropy Morse-Sard Theorem II\nby Danie
le Tiberio (SISSA\, Trieste) as part of Geometric Structures Research Semi
nar\n\n\nAbstract\nIn these series of three seminars\, we will present a p
roof of the classical Morse-Sard Theorem\, based on results from semialgeb
raic geometry. It is a bit long\, but it also gives a bound on the so-call
ed entropy dimension of the set of critical values of a smooth function de
fined 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\;
December 9.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniele Tiberio (SISSA\, Trieste)
DTSTART:20211216T130000Z
DTEND:20211216T150000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/38
DESCRIPTION:Title: The entropy Morse-Sard Theorem III\nby Dani
ele Tiberio (SISSA\, Trieste) as part of Geometric Structures Research Sem
inar\n\n\nAbstract\nIn these series of three seminars\, we will present a
proof of the classical Morse-Sard Theorem\, based on results from semialge
braic geometry. It is a bit long\, but it also gives a bound on the so-cal
led entropy dimension of the set of critical values of a smooth function d
efined 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\;
December 16.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David TEWODROSE (Nantes Université)
DTSTART:20220224T130000Z
DTEND:20220224T150000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/39
DESCRIPTION:Title: Kato limit spaces\nby David TEWODROSE (Nant
es Université) as part of Geometric Structures Research Seminar\n\n\nAbst
ract\nConsider a sequence of Riemannian manifolds. Assume that this sequen
ce converges\, in the measured Gromov-Hausdorff sense\, to a possibly non-
smooth metric measure space. What are the properties of this limit space?
In a series of celebrated works from the nineties\, Cheeger and Colding ad
dressed this question under the assumption of a uniform lower bound on the
Ricci curvature of the manifolds. This has led to the fruitful developmen
t of a synthetic theory of Ricci curvature lower bounds. In this talk\, I
will present a couple of joint works with Gilles Carron (Nantes Universit
é) and Ilaria Mondello (Université de Créteil) where we relax the unifo
rm Ricci lower bound assumption and work in the context of a weaker unifor
m Kato-type assumption\, namely that the part of the lowest eigenvalue of
the Ricci tensor lying under a certain threshold belongs to a given Kato c
lass. Under this assumption which authorizes the Ricci curvature to degene
rate to - infinity but in a « heat-kernel controlled » way\, we show tha
t most results of Cheeger and Colding are still true\, including rectifiab
ility on which I shall focus.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexis AUMONIER (University of Copenhagen)
DTSTART:20220317T130000Z
DTEND:20220317T150000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/41
DESCRIPTION:Title: An h-principle for complements of discriminants
\nby Alexis AUMONIER (University of Copenhagen) as part of Geometric S
tructures Research Seminar\n\n\nAbstract\nIn classical algebraic geometry\
, discriminants appear naturally in various moduli spaces as the loci para
metrising degenerate objects. The motivating example for this talk is the
locus of singular sections of a line bundle on a smooth projective complex
variety\, the complement of which is a moduli space of smooth hypersurfac
es.\nI will present an approach to studying the homology of such moduli sp
aces of non-singular algebraic sections via algebro-topological tools. The
main idea is to prove an "h-principle" which translates the problem into
a purely homotopical one.\n\nI shall explain how to talk effectively about
singular sections of vector bundles and what an h-principle is. To demons
trate the usefulness of homotopical methods\, and using a bit of rational
homotopy theory\, we will prove together a homological stability result fo
r moduli spaces of smooth hypersurfaces of increasing degree.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea MONDINO (University of Oxford)
DTSTART:20220331T120000Z
DTEND:20220331T140000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/42
DESCRIPTION:Title: Minimal boundaries in non-smooth spaces with Ri
cci Curvature bounded below\nby Andrea MONDINO (University of Oxford)
as part of Geometric Structures Research Seminar\n\n\nAbstract\nThe goal o
f the seminar is to report on recent joint work with Daniele Semola. Motiv
ated by a question of Gromov to establish a “synthetic regularity theory
" for minimal surfaces in non-smooth ambient spaces\, we address the quest
ion in the setting of non-smooth spaces satisfying Ricci curvature lower b
ounds in a synthetic sense via optimal transport. The talk is meant to be
accessibile also to non specialists.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davide BARILARI (Università degli Studi di Padova)
DTSTART:20220421T120000Z
DTEND:20220421T140000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/43
DESCRIPTION:Title: Bakry–Émery curvature and sub-Riemannian geo
metry\nby Davide BARILARI (Università degli Studi di Padova) as part
of Geometric Structures Research Seminar\n\n\nAbstract\nIn this talk we di
scuss some generalization of comparison theorems involving Bakry Émery cu
rvature in sub-Riemannian geometry. In particular we will focus on compari
son theorems for distortion coefficients appearing in geometric interpolat
ion inequalities\, such as the Brunn-Minkovski inequality. The model space
s for comparison are variational problems coming from optimal control theo
ry.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessandro PORTALURI (University of Torino)
DTSTART:20220324T130000Z
DTEND:20220324T150000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/44
DESCRIPTION:Title: Spectral stability\, spectral flow and circular
relative equilibria for the Newtonian n-body problem\nby Alessandro
PORTALURI (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
periodic solutions are provided by circular relative equilibria (RE)\, n
amely solutions in which each body rigidly rotates about the center of mas
s and the configuration of the whole system is constant in time and centr
al configuration. A classical problem in celestial mechanics aims at re
lating the (in-)stability properties of a (RE) to the index properties of
the central configuration generating it. \n\nIn this talk\, we discuss so
me sufficient \nconditions that imply the spectral instability of planar
and non-planar (RE) generated by a central configuration. \n\nThe key ing
redients are a new formula that allows to compute the spectral flow of a
path of symmetric matrices having degenerate starting point\, and \na symp
lectic decomposition of the phase space of the linearized Hamiltonian syst
em along a given (RE) which allows us \nto rule out the uninteresting par
t of the dynamics corresponding to the translational and (partially) to th
e rotational symmetry of the problem. \n\nThis talk is based on a recent j
oint work with Prof. Dr. Luca Asselle (Ruhr Universit\\"at Bochum\, Germa
ny) and Prof. Dr. Li Wu (Shandong University\, Jinan\, China).\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arthur RENAUDINEAU (Université de Lille)
DTSTART:20220512T120000Z
DTEND:20220512T140000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/45
DESCRIPTION:Title: Real structures on tropical varieties\nby A
rthur RENAUDINEAU (Université de Lille) as part of Geometric Structures R
esearch Seminar\n\n\nAbstract\nWe will propose a definition of a real stru
cture on a non-singular projective tropical variety. This definition takes
its inspiration from the Viro's patchworking theorem. In the local settin
g\, we will prove that such a structure on a matroidal fan is equivalent t
o an orientation on the underlying matroid. We will then generalize Viro's
theorem to this setting. This is a joint work with Johannes Rau and Kris
Shaw.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlos BELTRAN (Universidad de Cantabria)
DTSTART:20220526T120000Z
DTEND:20220526T140000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/47
DESCRIPTION:Title: Smale’s 7th problem: an overview\nby Carl
os BELTRAN (Universidad de Cantabria) as part of Geometric Structures Rese
arch Seminar\n\n\nAbstract\nSmale’s 7th problem demands for an algorithm
to find finite collections of points in the 2-sphere\, in such a way that
they minimize some energy that one may think of as the classical electros
tatic potential. This beautiful problem (which is the computational versio
n of a problem posed by J. J. Thomson\, the discoverer of the electron) ha
s attracted the attention of dozens of researchers and\, although it is co
nsidered extremely difficult\, the hope for solving it has not vanished. I
n this talk I will present the problem from a general perspective\, showin
g its relations with other questions\, mentioning the most important resul
ts obtained to the date and posing several open questions in the path to t
he total solution. The talk will be directed for a general audience.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea ROSANA (SISSA\, Trieste)
DTSTART:20220428T120000Z
DTEND:20220428T140000Z
DTSTAMP:20260405T094319Z
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 Ge
ometric Structures Research Seminar\n\n\nAbstract\nThe aim of these talks
is to show that the (rescaled) zeroes of Hermite polynomials and the (resc
aled) eigenvalues of matrices in the Gaussian Orthogonal Ensemble share th
e same asymptotic distribution\, i.e. the semi-circle law of radius \\sqrt
(2). We address this problem through logarithmic potential theory.\n\nWe b
egin by showing how we can interpret the zeroes of orthogonal polynomials
as equilibrium configurations for the electrostatic Stieltjes model on the
real line\, which serves as a motivation for their study. We then introdu
ce logarithmic potential and energy of a measure with respect to an extern
al potential. Under suitable hypothesis on such potential\, we show the ex
istence and uniqueness of a minimizing measure for the energy\, which we c
all the equilibrium measure. A characterization of such equilibrium measur
es is also provided. We end the talk briefly discussing the equilibrium me
asure for a Gaussian potential.\n\nThe tools we developed here will be use
d in the second talk to address our starting problem.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea ROSANA (SISSA\, Trieste)
DTSTART:20220505T120000Z
DTEND:20220505T140000Z
DTSTAMP:20260405T094319Z
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 Ge
ometric Structures Research Seminar\n\n\nAbstract\nWe introduce the probab
ility measure associated to the zeroes of Hermite polynomials and discuss
how a rescaling is necessary in order to get convergence (in the weak star
topology). Using the tools from logarithmic potential theory from previou
s talk\, we show convergence of this measure to the semi-circular law. We
then introduce Gaussian Ensambles and the empirical and statistical eigenv
alue distributions for hermitian matrices in these ensambles. We show how
these ensambles fit in a more general framework and we discuss the general
ized Wigner theorem\, highlighting a parallelism with Laplace asymptotic m
ethod. From this we get as a corollary the convergence of the (rescaled) s
tatistical eigenvalue distribution for GOE matrices to the semi-circular l
aw.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul BREIDING (MPI MiS (Max Planck Institute for Mathematics in th
e Sciences))
DTSTART:20220609T120000Z
DTEND:20220609T140000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/51
DESCRIPTION:Title: Facet Volumes of Polytopes\nby Paul BREIDIN
G (MPI MiS (Max Planck Institute for Mathematics in the Sciences)) as part
of Geometric 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)-dimensi
onal volumes of its facets. For instance\, every triangle defines three le
nghts\; every tetrahedron defines four areas.\nWe study the space of all s
uch vectors. We show that for fixed integers d\\geq 2 and n\\geq d+1 the c
onfiguration space of all facet volume vectors of all d-polytopes in R^d w
ith n facets is a full dimensional cone in R^n\, and we describe this cone
in terms of inequalities. For tetrahedra this is a cone over a regular oc
tahedron.\nJoint work with Pavle Blagojevic and Alexander Heaton.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Zelenko (Texas A&M University)
DTSTART:20220616T120000Z
DTEND:20220616T140000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/52
DESCRIPTION:Title: Morse inequalities for eigenvalue branches of g
eneric families of self-adjoint matrices\nby Igor Zelenko (Texas A&M U
niversity) as part of Geometric Structures Research Seminar\n\n\nAbstract\
nThe eigenvalue branches of families of self-adjoint matrices are not smoo
th at points corresponding to repeated eigenvalues (called diabolic points
or Dirac points). Generalizing the notion of critical points as points fo
r which the homotopical type of (local) sub-level set changes after the pa
ssage through the corresponding value\, in the case of the generic family
we give an effective criterion for a diabolic point to be critical for tho
se branches and compute the contribution of each such critical point to th
e Morse polynomial of each branch\, getting the appropriate Morse inequali
ties as a byproduct of the theory. These contributions are expressed in te
rms of the homologies of Grassmannians. The motivation comes from the Floq
uet-Bloch theory of Schroedinger equations with periodic potential and oth
er problems in Mathematical Physics. The talk is based on the joint work w
ith Gregory Berkolaiko.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tim Laux (Hausdorff Center for Mathematics in Bonn)
DTSTART:20220627T140000Z
DTEND:20220627T160000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/53
DESCRIPTION:Title: The large-data limit of the MBO scheme for data
clustering\nby Tim Laux (Hausdorff Center for Mathematics in Bonn) as
part of Geometric Structures Research Seminar\n\n\nAbstract\nThe MBO sche
me is an efficient scheme used for data clustering\, the task of partition
ing a given dataset into several clusters. In this talk\, I will present a
rigorous analysis of the MBO scheme for data clustering in the large-data
limit. Each iteration of the MBO scheme corresponds to one step of implic
it gradient descent for the thresholding energy on the similarity graph of
the dataset. For a subset of the nodes of the graph\, the thresholding en
ergy is the amount of heat transferred from the subset to its complement.
It is then natural to think that outcomes of the MBO scheme are (local) mi
nimizers of this energy. We prove that the algorithm is consistent\, in th
e sense that these (local) minimizers converge to minimizers of a suitably
weighted optimal partition problem. This is joint work with Jona Lelmi (U
Bonn).\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Georges Comte (Université Savoie Mont-Blanc)
DTSTART:20220728T120000Z
DTEND:20220728T140000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/54
DESCRIPTION:Title: Motivic Vitushkin's invariants\nby Georges
Comte (Université Savoie Mont-Blanc) as part of Geometric Structures Rese
arch Seminar\n\n\nAbstract\nI will explain how\, in a joint work with Imma
nuel Halupczok (Düsseldorf Univ.)\, we define in definable nonarchimedean
geometry a sequence of invariants which is the counterpart in this contex
t of the sequence of Vituskin's invariants in real geometry. For this we u
se the theory of t-stratification in its uniform version. \nWe also defin
e a notion of preorder on the ring of motivic constructible functions\, wh
ich is compatible with motivic integration. As in the real case\, our inva
riants are related to a notion of metric entropy.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Sykes (Masaryk University)
DTSTART:20221027T080000Z
DTEND:20221027T090000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/56
DESCRIPTION:Title: Absolute parallelism constructions for 2-nondeg
enerate CR hypersurfaces\nby David Sykes (Masaryk University) as part
of Geometric Structures Research Seminar\n\n\nAbstract\nThe talk will intr
oduce and demonstrate through examples a Tanaka-theoretic general method (
developed in joint work with Igor Zelenko) for solving local equivalence p
roblems applicable to a broad class of 2-nondegenerate hypersurface-type C
R manifolds\, namely to all such structures that are uniquely determined b
y the geometry naturally induced on their associated Levi leaf space. We w
ill apply the general method to an instructive family of CR hypersurfaces
in complex 6-space\, reducing their local equivalence problem to one of ab
solute parallelisms that we explicitly construct in local coordinates. The
talk will also review further applications of the general method\, applic
ations to estimating symmetry group dimensions and to classifications of h
omogeneous structures.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ching-Peng Huang (Brown University)
DTSTART:20221117T130000Z
DTEND:20221117T150000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/57
DESCRIPTION:Title: Brownian motion under the Bures-Wasserstein geo
metry\nby Ching-Peng Huang (Brown University) as part of Geometric Str
uctures Research Seminar\n\n\nAbstract\nThe Bures-Wasserstein geometry of
positive definite matrices is closely related to the optimal transport of
Gaussian measures and has several applications such as in optimization and
physics. We present a detailed formula of the Brownian motion under such
geometry\, which has an extra mean curvature drift term and is reminiscent
of well-studied stochastic processes such as Dyson's Brownian\, suggestin
g broader framework of matrix geometry for these processes. Moreover\, we
investigate ideas utilizing the mean curvature drift term to design a cont
rol system.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pawel Nurowski (Center for Theoretical Physics\, Warsaw)
DTSTART:20220913T120000Z
DTEND:20220913T140000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/58
DESCRIPTION:Title: What is a para-CR structure of type (k\,r\,s) a
nd why it describes geometry of ODEs and PDEs of finite type\nby Pawel
Nurowski (Center for Theoretical Physics\, Warsaw) as part of Geometric S
tructures Research Seminar\n\n\nAbstract\nI will talk about a geometry of
manifolds equipped with a pair of integrable vector distributions. Such ge
ometry is suitable to describe a geometry of a large class of Partial Diff
erential Equations (PDEs) considered modulo various types of changes of va
riables. This class of PDEs is called `the finite type'\, meaning that the
ir space of solutions is finite dimensional. I will illustrate the para-CR
structure of type (k\,r\,s) geometry with a few examples having applicati
ons in theoretical physics.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey Podobryaev (Control Processes Research Center\, Program Sys
tems Institute of RAS)
DTSTART:20221110T130000Z
DTEND:20221110T150000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/59
DESCRIPTION:Title: Attainable sets for step 2 free Carnot groups w
ith non-negative controls and inequalities for independent random variable
s\nby Alexey Podobryaev (Control Processes Research Center\, Program S
ystems Institute of RAS) as part of Geometric Structures Research Seminar\
n\n\nAbstract\nIn recent works H.Abels and E.B.Vinberg considered free nil
potent Lie\nsemigroups and suggested a probability interpretaion of such s
emigroups\nof step 2. With a help of an algebraic method they obtained an
explicit\ndescription of the step 2 rank 3 free nilpotant Lie semigroup. T
his\nresult implies some non trivial inequalities for a system of three\ni
ndependent 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 r
egard these free nilpotent Lie semigroups as attainable sets for\nsome con
trol systems. We describe the boundary of the attainable set\nwith a help
of first and second order optimality conditions. It turns\nout that the cu
rved faces of the attainable set consist of the ends of\noptimal trajector
ies with the number of control switching corresponding\nto the face dimens
ion. We give an explicit answer in the case of rank 3\nand upper bounds fo
r the number for control switchings in the case of\nrank 4.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valentino Magnani (University of Pisa)
DTSTART:20221215T130000Z
DTEND:20221215T150000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/61
DESCRIPTION:Title: Surface area on sub-Riemannian measure manifold
s\nby Valentino Magnani (University of Pisa) as part of Geometric Stru
ctures Research Seminar\n\n\nAbstract\nWe present an area formula in equir
egular sub-Riemannian measure manifolds. The perimeter measure of a smooth
bounded open set is related to the spherical measure of its boundary\, us
ing the sub-Riemannian distance. To perform the intrinsic blow-up at the b
oundary new difficulties appear\, that also involve the nilpotent approxim
ation of the sub-Riemannian manifold. The density of the perimeter measure
naturally arises as a geometric invariant that can be explicitly related
to different objects\, like the nilpotent approximation\, the tangent Riem
annian metric and the shape of the tangent unit ball. The area formula for
the perimeter measure is achieved by showing that this invariant is equal
to the Federer density. These results are a joint work with Sebastiano Do
n (Brescia University).\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kenshiro Tashiro (Tohoku University)
DTSTART:20230119T130000Z
DTEND:20230119T150000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/62
DESCRIPTION:Title: Systolic inequality and volume of the unit ball
in Carnot groups\nby Kenshiro Tashiro (Tohoku University) as part of
Geometric Structures Research Seminar\n\n\nAbstract\nRoughly speaking\, a
systolic inequality on a length measure space asserts that the minimal len
gth 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
inequalities hold for (a class of) Riemannian manifolds and Alexandrov sp
aces with the constants depending only on the Hausdorff dimension.\nWe pro
ved the systolic inequality on quotient spaces of Carnot groups\, which is
a class of closed sub-Riemannian manifolds\, with the constant depending
only on the Hausdorff dimension. Actually it is equivalent to give a unifo
rm lower bound of volume of the unit ball in Carnot groups of a given Haus
dorff dimension.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuri Sachkov (Program Systems Institute\, Russian Academy of Scien
ce)
DTSTART:20230216T130000Z
DTEND:20230216T150000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/63
DESCRIPTION:Title: Sub-Lorentzian problem on the Heisenberg group
(Yu. Sachkov\, E. Sachkova)\nby Yuri Sachkov (Program Systems Institut
e\, Russian Academy of Science) as part of Geometric Structures Research S
eminar\n\n\nAbstract\nThe sub-Riemannian problem on the Heisenberg group i
s 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 circle.\nThe talk will be devoted to its natural variation\, the time-o
ptimal problem with a hyperbola as a set of control parameters.\nThis vari
ation is the sub-Lorentzian problem on the Heisenberg group.\n\nFor this p
roblem we will describe the following results:\n1) The reachable set from
the identity of the group\,\n2) Pontryagin maximum principle\, parameteriz
ation of extremal trajectories\, exponential mapping\,\n3) Diffeomorphic p
roperty of the exponential mapping\, its inverse\,\n4) Optimality of extre
mal trajectories\, optimal synthesis\,\n5) Sub-Lorentzian distance\,\n6) S
ub-Lorentzian spheres of positive and zero radii.\nResults 1)\, 2) were ob
tained by M.Grochowski (2006)\, the rest results are new.\n\nThe talk will
be based on the work \nhttps://arxiv.org/abs/2208.04073\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Zelenko (Texas A&M Univerisity)
DTSTART:20230407T090000Z
DTEND:20230407T110000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/64
DESCRIPTION:Title: Gromov's h-principle for corank two distributio
n of odd rank with maximal first Kronecker index\nby Igor Zelenko (Tex
as A&M Univerisity) as part of Geometric Structures Research Seminar\n\n\n
Abstract\nWhile establishing various versions of the h-principle for conta
ct\ndistributions (Eliashberg (1989) in dimension 3\, Borman-\nEliashberg
-Murphy (2015) in arbitrary dimension\, and even-contact\ncontact (D. Mc
Duff\, 1987) distributions are among the most remarkable\nadvances in di
fferential topology in the last four decades\, very little\nis known about
analogous results for other classes of distributions\,\ne.g. generic dist
ributions of corank 2 or higher. The smallest\ndimensional nontrivial case
of corank 2 distributions are Engel\ndistributions\, i.e. the maximally n
onholonomic rank 2 distributions on\n$4$-manifolds. This case is highly no
ntrivial and was treated recently\nby Casals-Pérez-del Pino-Presas (2017)
and Casals-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
-principle for corank 2\ndistribution of arbitrary odd rank satisfying a n
atural generic\nassumption on the associated pencil of skew-symmetric form
s. During the\ntalk I will try to give all the necessary background relate
d to the\nmethod of convex integration in principle. This is the joint wor
k with\nMilan Jovanovic\, Javier Martinez-Aguinaga\, and Alvaro del Pino.
\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brendan Guilfoyle (Munster Technological University)
DTSTART:20230302T130000Z
DTEND:20230302T150000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/65
DESCRIPTION:Title: From CT Scans to four-manifold topology\nby
Brendan Guilfoyle (Munster Technological University) as part of Geometric
Structures Research Seminar\n\n\nAbstract\nIntegration over lines is the
mathematical basis of many modern methods of tomography\, including Comput
erized Tomography scans. In this talk\, a recent geometrization using inde
finite metrics of signature (2\,2) is presented of the seminal work of Fri
tz John on the problem. The contemporary mathematical background is 4-mani
fold topology and the use of neutral metrics to explore co-dimension two p
roblems.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomasso Rossi (Institut für Angewandte Mathematik\, Universität
Bonn)
DTSTART:20230519T090000Z
DTEND:20230519T110000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/66
DESCRIPTION:Title: First-order heat content asymptotics on RCD(K\,
N) spaces\nby Tomasso Rossi (Institut für Angewandte Mathematik\, Uni
versität Bonn) as part of Geometric Structures Research Seminar\n\n\nAbst
ract\nWe study the small-time asymptotics of the heat content associated w
ith a bounded open set when the ambient space is an RCD(K\,N) metric measu
re space. By adapting a technique due to Savo\, we establish the existence
of a first-order asymptotic expansion\, under a regularity condition for
the boundary of the domain that we call measured interior geodesic conditi
on. We carefully study such a condition\, relating it to the properties of
the disintegration associated with the signed distance function from the
boundary. This is a joint work with Emanuele Caputo.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lev Birbrair (Universidade Federal do Ceará & Jagiellonian Univer
sity)
DTSTART:20230601T090000Z
DTEND:20230601T110000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/68
DESCRIPTION:Title: Lipschitz Geometry of Germs of Real Surfaces\nby Lev Birbrair (Universidade Federal do Ceará & Jagiellonian Universi
ty) as part of Geometric Structures Research Seminar\n\n\nAbstract\nLipsch
itz Geometry is now an intensively developed part of Singularity Theory.\n
I am going to make an introductory talk on the subject. I am going to exp
lain\nthe general directions of Lipschitz geometry (inner\, outer and ambi
ent)\non the example of germs of Real Semialgebraic Surfaces.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samuël Borza (SISSA\, Trieste\, Italy)
DTSTART:20230615T120000Z
DTEND:20230615T140000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/69
DESCRIPTION:Title: MCP and geodesic dimension of sub-Finsler Heise
nberg groups\nby Samuël Borza (SISSA\, Trieste\, Italy) as part of Ge
ometric Structures Research Seminar\n\n\nAbstract\nWe will discuss the Hei
senberg group equipped with an $\\ell^p$-sub-Finsler metric. We will explo
re its geometry through the corresponding (Finsler) isoperimetric problem.
Subsequently\, we will analyse these spaces as metric measure spaces\, co
nsidering whether the measure contraction property holds. Furthermore\, we
will also compute their geodesic dimension. It will become apparent how t
he answers to these questions are controlled by the value of p (and its H
ölder conjugate q). This value determines whether the $\\ell^p$-sub-Finsl
er metric is branching or not\, whether it possesses a negligible cut locu
s\, and whether its geodesics are sufficiently smooth or not. Joint work w
ith K. Tashiro.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paweł Nurowski (Center for Theoretical Physics\, Warsaw\, Poland)
DTSTART:20230904T090000Z
DTEND:20230904T110000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/70
DESCRIPTION:Title: Exceptional real Lie algebras $f_4$ and $e_6$ v
ia contactifications\nby Paweł Nurowski (Center for Theoretical Physi
cs\, Warsaw\, Poland) as part of Geometric Structures Research Seminar\n\n
\nAbstract\nIn Cartan's PhD thesis\, there is a formula defining a certain
rank 8 vector distribution in dimension 15\, whose algebra of authomorphi
sm is the split real form of the simple exceptional complex Lie algebra $f
_4$. Cartan's formula is written in the standard Cartesian coordinates in
$\\mathbb{R}^{15}$. In the talk I will explain how to find analogous formu
la for the flat models of any bracket generating distribution $D$ whose sy
mbol algebra $n(D)$ is constant and 2-step graded\, $n(D) = n−2 \\oplus
n−1$. I will use the general formula to provide other distributions with
symmetries being real forms of simple exceptional Lie algebras $f_4$ and
$e_6$.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cyril Letrouit (CNRS\, Laboratoire de Mathématiques d'Orsay)
DTSTART:20240111T130000Z
DTEND:20240111T150000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/71
DESCRIPTION:Title: Nodal sets of eigenfunctions of sub-Laplacians<
/a>\nby Cyril Letrouit (CNRS\, Laboratoire de Mathématiques d'Orsay) as p
art of Geometric Structures Research Seminar\n\n\nAbstract\nNodal sets of
eigenfunctions of elliptic operators on compact manifolds have been studie
d extensively over the past decades. In a recent work\, we initiated the s
tudy of nodal sets of eigenfunctions of hypoelliptic operators on compact
manifolds\, focusing on sub-Laplacians (e.g. on compact quotients of the H
eisenberg group). Our results show that nodal sets behave in an anisotropi
c way which can be analyzed with standard tools from sub-Riemannian geomet
ry such as sub-Riemannian dilations\, nilpotent approximation and desingul
arization at singular points. This is a joint work with S. Eswarathasan.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giovanni Russo (SISSA)
DTSTART:20240123T130000Z
DTEND:20240123T140000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/72
DESCRIPTION:Title: Nearly Kähler metrics and torus symmetry\n
by Giovanni Russo (SISSA) as part of Geometric Structures Research Seminar
\n\n\nAbstract\nNearly Kähler manifolds are Riemannian spaces equipped wi
th an almost complex structure of special type. In dimension six\, nearly
Kähler metrics are Einstein with positive scalar curvature\, and have int
eresting connections with G2 and spin geometry. At present there are very
few compact examples\, which are either homogeneous or of cohomogeneity on
e. \n\nIn this talk I will explain a theory of nearly Kähler six-manifold
s with two-torus symmetry. The torus-action yields a multi-moment map\, wh
ich we use as a Morse function to understand the structure of the whole ma
nifold. In particular\, we show how the local geometry of a nearly Kähler
six-manifold can be recovered from three-dimensional data\, and discuss c
onnections with GKM theory.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniele Tiberio (SISSA)
DTSTART:20240130T130000Z
DTEND:20240130T150000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/73
DESCRIPTION:Title: Sard theorems in infinite dimensions and applic
ations to sub-Riemannian geometry\nby Daniele Tiberio (SISSA) as part
of Geometric Structures Research Seminar\n\nLecture held in SISSA Main Bui
lding.\n\nAbstract\nThe Sard conjecture in sub-Riemannian geometry claims
that the set of critical values of the endpoint maps has measure zero. The
se are smooth maps which take values in the manifold\, but they are define
d on infinite dimensional domains. I will present recent Sard-type theorem
s 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 Profess
or Antonio Lerario and Professor Luca Rizzi.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yosef Yomdin (Weizmann Institute of Science)
DTSTART:20240611T120000Z
DTEND:20240611T140000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/74
DESCRIPTION:Title: Super-resolution\, classical Moment Theory\, an
d some Real Algebraic Geometry\nby Yosef Yomdin (Weizmann Institute of
Science) as part of Geometric Structures Research Seminar\n\nLecture held
in Room 005 - SISSA Main Building.\n\nAbstract\nWe consider the problem o
f reconstruction of “spike-train” signals\n\\[\nF(x) = \\sum_{j=1}^d
a_j \\delta(x-x_j)\,\n\\]\nwhich are linear combinations of shifted delta-
functions\, from noisy Moment measurements\n\\[\nm_k(F) = \\int F(x) x^k d
x = \\sum_{j=1}^d a_j x_j^k.\n\\]\nThis is equivalent to solving the so-c
alled Prony 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 unknowns $(a_j\, x_j)\, \\ j = 1\,…\,d.$\n\nOur goal is to underst
and the “intrinsic geometry” of the error amplification in the reconst
ruction process\, stressing the case where the nodes $x_j$ nearly collide.
We study the geometry of the system above\, independently of a specific r
econstruction algorithm.\n\n \nWe construct a growing chain of algebraic s
ub-varieties $Y_q$ (which we call Prony varieties) in the space of the par
ameters $(a_j\, x_j)$\, which accurately control the rate of the error amp
lification. These sub-varieties $Y_q$ can be reconstructed from the noisy
moment measurements with a significantly better accuracy than the amplitud
es $a_j$ and the nodes $x_j$ themselves. This opens a possibility to apply
adaptive reconstruction algorithms\, subordinated to the chain of the Pro
ny varieties $Y_q$. We show that this approach in many cases provides high
er reconstruction accuracy than the standard ones.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Beschastnyi (INRIA\, Nice)
DTSTART:20240220T130000Z
DTEND:20240220T150000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/75
DESCRIPTION:Title: Symplectic geometry for boundary conditions of
Grushin operators\nby Ivan Beschastnyi (INRIA\, Nice) as part of Geome
tric Structures Research Seminar\n\nLecture held in SISSA Main Building.\n
\nAbstract\nIn this talk I will explain how to construct self-adjoint exte
nsions for a class of differential operators on Grushin manifolds. The mai
n tool will be a natural bijection between self-adjoint extensions and Lag
rangian subspaces of some symplectic space. I will illustrate the techniqu
e first via a full classification of self-adjoint extensions of a Schroedi
nger operator with inverse square potential\, and then explain what can be
said in the case of Grushin manifolds. This is a joint work with H. Quan.
\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michele Motta (SISSA)
DTSTART:20240206T130000Z
DTEND:20240206T150000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/76
DESCRIPTION:Title: Lyapunov exponents of linear switched systems\nby Michele Motta (SISSA) as part of Geometric Structures Research Semi
nar\n\nLecture held in room 133 - SISSA Main Building.\n\nAbstract\nIn app
lications\, there are many systems whose dynamics can be influenced by dis
crete events. For instance\, a power switch turned on and off\, a thermost
at turning the heat on and off\, a car running on a street with some ice h
ere and there. Such systems are called switched systems.\n\nAs for classic
al dynamical systems\, stability for this class of systems is a very impor
tant issue. A natural way to measure the stability is to use Lyapunov expo
nents. \nIn this talk\, I will show how to compute exact Lyapunov exponent
s for a simple class of switched systems. This problem can be reduced to a
n Optimal Control Problem. Applying Pontryagin Maximum Principle\, one can
find all extremals for this problem and then choose among them the optima
l one. This is a joint work with Prof. A. A. Agrachev.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valentino Magnani (Pisa)
DTSTART:20240213T130000Z
DTEND:20240213T150000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/77
DESCRIPTION:Title: Area of intrinsic graphs in homogeneous groups<
/a>\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 as
sumes that the map generating the intrinsic graph is continuously intrinsi
cally differentiable. The important novelty lies in the notion of Jacobian
\, which is built by the auxiliary Euclidean distance. The introduction of
this Jacobian allows the spherical factor to appear in the area formula a
nd enables explicit computations. This is joint work with Francesca Corni
(University of Bologna).\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Armin Rainer (Wien)
DTSTART:20240227T130000Z
DTEND:20240227T150000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/78
DESCRIPTION:Title: On the semialgebraic Whitney extension problem<
/a>\nby Armin Rainer (Wien) as part of Geometric Structures Research Semin
ar\n\nLecture held in room 133 -SISSA Main Building.\n\nAbstract\nIn 1934\
, Whitney raised the question of how one can decide whether a function $f$
defined on a closed subset $X$ of $\\mathbb R^n$ is the restriction of a
$C^m$ function 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 discuss a related conjecture: if a semialgebraic function $f : X \\t
o \\mathbb R$ has a $C^m$ extension to $\\mathbb R^n$\, then it has a sem
ialgebraic $C^m$ extension. In particular\, I will show that the $C^{1\,\\
omega}$ case of the conjecture is true (in a uniformly bounded way)\, for
each semialgebraic modulus of continuity $\\omega$. The proof is based o
n the existence of semialgebraic Lipschitz selections for certain affine-s
et valued maps. This is joint work with Adam Parusinski.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Rosana (SISSA)
DTSTART:20240305T090000Z
DTEND:20240305T100000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/79
DESCRIPTION:Title: The Grassmann Distance Degree\nby Andrea Ro
sana (SISSA) as part of Geometric Structures Research Seminar\n\nLecture h
eld 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 prob
lem. 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
Distance Degree (EDD). Then we will try to mimic this construction for Gr
assmannians when the subset is a subvariety. After explaining why the tech
niques used in the previous case fail\, we will be able to define an analo
gue of the EDD\, which we call Grassmann Distance Degree. In the last part
we will focus on the case where the subvariety is a simple Schubert varie
ty\, finding an interesting connection between the geometry of the problem
and Eckart-Young theorem.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giuseppe Pipoli (Università degli Studi dell'Aquila)
DTSTART:20240409T120000Z
DTEND:20240409T140000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/80
DESCRIPTION:Title: Vanishing theorems for minimal stable hypersurf
aces\nby Giuseppe Pipoli (Università degli Studi dell'Aquila) as part
of Geometric Structures Research Seminar\n\nLecture held in room 133 - SI
SSA Main Building.\n\nAbstract\nWe will discuss some topological obstructi
ons to the existence of stable minimal hypersurfaces. In particular\, we w
ill show the non-existence of nontrivial harmonic $p$-forms and nontrivial
harmonic spinors on stable minimal hypersurfaces under suitable curvature
assumptions of the ambient manifold. This talk is based on a upcoming joi
nt work with Francesco Bei (Sapienza\, Università di Roma).\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joe Hoisington (Max Planck Institute for Mathematics)
DTSTART:20240507T120000Z
DTEND:20240507T140000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/81
DESCRIPTION:Title: Energy-minimizing mappings of real and complex
projective spaces\nby Joe Hoisington (Max Planck Institute for Mathema
tics) as part of Geometric Structures Research Seminar\n\nLecture held in
room 133 - SISSA Main Building.\n\nAbstract\nWe will show that\, in any ho
motopy class of mappings from complex projective space to a Riemannian man
ifold\, the infimum of the energy is proportional to the infimal area in t
he class of mappings of the 2-sphere representing the induced homomorphism
on the second homotopy group. We will also give a related estimate for t
he infimum of the energy in a homotopy class of mappings of real projectiv
e space\, and we will discuss several results and questions about energy-m
inimizing maps and their metric properties.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mattia Magnabosco (Oxford)
DTSTART:20240312T130000Z
DTEND:20240312T150000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/82
DESCRIPTION:Title: Failure of the curvature-dimension condition in
sub-Finsler manifolds\nby Mattia Magnabosco (Oxford) as part of Geome
tric Structures Research Seminar\n\nLecture held in SISSA Main Building.\n
\nAbstract\nThe Lott–Sturm–Villani curvature-dimension condition $\\ma
thsf{CD}(K\,N)$ provides a synthetic notion for a metric measure space to
have curvature bounded from below by $K$ and dimension bounded from above
by $N$. It has been recently proved that this condition does not hold in a
ny sub-Riemannian manifold equipped with a positive smooth measure\, for e
very choice of the parameters $K$ and $N$. In this talk\, we investigate t
he validity of the analogous result for sub-Finsler manifolds\, providing
two results in this direction. On the one hand\, we show that the $\\maths
f{CD}$ condition fails in sub-Finsler manifolds equipped with a smooth str
ongly convex norm and with a positive smooth measure. On the other hand\,
we prove that\, on the sub-Finsler Heisenberg group\, the same result hold
s for every reference norm. Additionally\, we show that the validity of th
e measure contraction property $\\mathsf{MCP}(K\,N)$ on the sub-Finsler He
isenberg group depends on the regularity of the reference norm.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tommaso Rossi (Paris)
DTSTART:20240319T130000Z
DTEND:20240319T150000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/83
DESCRIPTION:Title: Weyl's tube formula in sub-Riemannian geometry<
/a>\nby Tommaso Rossi (Paris) as part of Geometric Structures Research Sem
inar\n\nLecture held in SISSA Main Building.\n\nAbstract\nWe study the vol
ume of a tube around a submanifold in sub-Riemannian geometry. Firstly\, w
e show that the volume of the tube around a non-characteristic submanifold
of class $C^2$ is either smooth or real-analytic for small radii\, depend
ing on the regularity of the underlying manifold\, and we establish a Weyl
's tube formula. Secondly\, we investigate Weyl's invariance theorem in su
b-Riemannian geometry: we show that two curves in the Heisenberg group wit
h the same Reeb angle have the same Weyl's tube formula. This is a joint w
ork with T. Bossio and L. Rizzi.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugenio Bellini (Milano Bicocca)
DTSTART:20240326T130000Z
DTEND:20240326T150000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/84
DESCRIPTION:Title: Geometry and topology of 3D-contact sub-Riemann
ian manifolds\nby Eugenio Bellini (Milano Bicocca) as part of Geometri
c Structures Research Seminar\n\nLecture held in room 133 - SISSA Main Bui
lding.\n\nAbstract\nA contact structure on a three dimensional manifold is
a plane field satisfying a non-integrability condition. The topological p
roperties of such structures are often subtle and difficult to detect. Ind
eed\, even the simple statement that there are two different contact struc
tures on $\\mathbb{R}^3$ is highly non-trivial to prove. In this talk I wi
ll describe some recent results concerning the relations between contact t
opology and sub-Riemannian geometry. The focus will be on tightness questi
ons\, both semi-local and global\, and on geometric detection of overtwist
ed disks. In particular I will present a contac version of Hadamard theore
m: the universal cover of any negatively curved normal contact manifold is
the Heisenberg group. This is a joint work with A. Agrachev\, S. Baranzin
i and L. Rizzi.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giorgio Saracco (University of Florence)
DTSTART:20240618T120000Z
DTEND:20240618T140000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/85
DESCRIPTION:Title: Existence of minimizers of Cheeger's functional
among convex sets\nby Giorgio Saracco (University of Florence) as par
t of Geometric Structures Research Seminar\n\nLecture held in SISSA Main B
uilding.\n\nAbstract\nGiven any open\, bounded set in $\\mathbb{R}^N$\, th
e Cheeger inequality states that its first eigenvalue of the Dirichlet $p$
-Laplacian is suitably bounded from below by the $p$-th power of the so-ca
lled Cheeger constant of the set. A natural question is whether this inequ
ality is sharp and if the infimum of the ratio of these two quantities is
attained (at least when restricting to suitable classes of competitors) by
some set.\n\nParini proved existence of minimizers among convex sets in t
he linear case $p=2$\, limitedly to the planar case $N=2$. The result was
later extended to general $p$ by Briani—Buttazzo—Prinari\, still for $
N=2$. They conjecture that existence of minimizers among convex sets shoul
d hold regardless of the dimension. Together with Aldo Pratelli\, we posit
ively solve the conjecture. The proof exploits a criterion proved by Ftouh
i paired with some cylindrical estimate on the Cheeger constant.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Felix Rydell (KTH Royal Institute of Technology)
DTSTART:20240521T120000Z
DTEND:20240521T140000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/86
DESCRIPTION:Title: Nearest Point Problems in Computer Vision\n
by Felix Rydell (KTH Royal Institute of Technology) as part of Geometric S
tructures Research Seminar\n\nLecture held in room 133 - SISSA Main Buildi
ng.\n\nAbstract\nStructure-from-Motion in Computer Vision aims to create 3
D models of objects based on 2D images. The first step in this pipeline is
to identify key features in each image and match these across the differe
nt views. After having estimated the camera parameters\, world features ar
e obtained by triangulation\, which refers to finding the world features t
hat best correspond to the matched image features. This is done by minimiz
ing the distance between the data and our mathematical model\; it is a nea
rest point problem. The number of complex solutions to the associated crit
ical equations given general data is the Euclidean distance degree\, which
measures the complexity of this optimization problem. In this talk\, we d
escribe the algebra and geometry that arises in Structure-from-Motion and
discuss the associated nearest point problems and Euclidean distance degre
es.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michele Stecconi (University Of Luxembourg)
DTSTART:20240604T120000Z
DTEND:20240604T140000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/87
DESCRIPTION:Title: Sobolev-Malliavin regularity of the nodal volum
e\nby Michele Stecconi (University Of Luxembourg) as part of Geometric
Structures Research Seminar\n\nLecture held in room 133 - SISSA Main Buil
ding.\n\nAbstract\nConsider the $(d-1)$-volume $V(f)$ of the level set of
a smooth function $f$ on a compact Riemannian manifold of arbitrary dimens
ion $d$. We show that\, if restricted to a generic finite dimensional vect
or space of smooth functions\, the functional $f \\mapsto V(f)$ belongs to
an appropriate Sobolev space. A fundamental ingredient is to understand t
he Sobolev regularity of the function $t\\mapsto V(f-t)$ that expresses th
e volume of the level $t$ of a "typical" Morse function.\n\nThis result ca
n be stated more naturally in the language of a Gaussian random field $f$\
, in which case $V(f)$ is a random variable and being Sobolev (Malliavin)
implies that its law has an absolutely continuous component.\nThis was an
open question in the 2 dimensional case: both the differentiability and th
e regularity of the law of the nodal length were unknown.\n\nThe result I
will present 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
constant 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 Gi
ovanni Peccati.)\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ludovic Rifford (Laboratoire J.A. Dieudonné\, Université Côte d
'Azur\, Nice)
DTSTART:20241212T130000Z
DTEND:20241212T150000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/88
DESCRIPTION:Title: Minimal rank Sard Conjecture in sub-Riemannian
geometry\nby Ludovic Rifford (Laboratoire J.A. Dieudonné\, Universit
é Côte d'Azur\, Nice) as part of Geometric Structures Research Seminar\n
\nLecture held in SISSA Main Building - room 005.\n\nAbstract\nWe present
a proof of the minimal rank Sard conjecture in the analytic category under
an additional assumption on the subanalytic abnormal distribution. This r
esult establishes that from a given point the set of points accessible thr
ough singular horizontal curves of minimal rank\, which corresponds to the
rank of the distribution\, has Lebesgue measure zero. The minimal rank Sa
rd Conjecture is equivalent to the Sard Conjecture for co-rank 1 distribut
ions.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Korobkov (Fudan University\, Shanghai\, China\, and Sobole
v Institute of Mathematics\, Novosibirsk\, Russia)
DTSTART:20250121T130000Z
DTEND:20250121T150000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/89
DESCRIPTION:Title: From the theorems of Morse\, Sard\, Dubovitskii
and Federer to the Luzin N-property: the story so far.\nby Mikhail Ko
robkov (Fudan University\, Shanghai\, China\, and Sobolev Institute of Mat
hematics\, Novosibirsk\, Russia) as part of Geometric Structures Research
Seminar\n\nLecture held in SISSA Main Building - Room 133.\n\nAbstract\nTh
e talk is based on the recent joint survey paper~[1]. Here we demonstrate
a universal synthesis of all the above-mentioned analytic phenomena for co
ntinuous mappings of Holder and Sobolev classes. This concludes the long-
time research started with our previous joint papers with Jean Bourgain (2
013\, 2015).\n\n[1] Ferone A.\, Korobkov M.V.\, Kristensen J.: From the th
eorems of Morse\, Sard\, Dubovitskii and Federer to the Luzin N-property:
the story so far // Pure and Applied Functional Analysis\, vol.9 (2024)\,
no.2\, 441--467\, http://yokohamapublishers.jp/online2/oppafa/vol9/p441.ht
ml\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessandro Socionovo (Sorbonne Universitè)
DTSTART:20250206T130000Z
DTEND:20250206T150000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/90
DESCRIPTION:Title: Non-smooth sub-Riemannian length minimizing cur
ves\nby Alessandro Socionovo (Sorbonne Universitè) as part of Geometr
ic Structures Research Seminar\n\nLecture held in SISSA Main Building - Ro
om 005.\n\nAbstract\nWe present the first examples of nonsmooth sub-Rieman
nian length minimizing curves. The length minimizer with the lowest regula
rity within these examples is of class $C^2\\setminus C^3$. The singularit
y is at a boundary point. The result is sharp in the sense that we can pro
ve that\, within these examples\, it is not possible to find a minimizer o
f class $C^1\\setminus C^2$. This is an ongoing research project with Y. C
hitour\, F. Jean\, R. Monti\, L. Rifford\, L. Sacchelli\, and M. Sigalotti
.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ye Zhang (Okinawa Institute of Science and Technology)
DTSTART:20250225T130000Z
DTEND:20250225T150000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/91
DESCRIPTION:Title: Semiconcavity results of squared sub-Riemannian
distance on the Heisenberg group and applications to PDEs\nby Ye Zhan
g (Okinawa Institute of Science and Technology) as part of Geometric Struc
tures Research Seminar\n\nLecture held in SISSA Main Building - Room 136.\
n\nAbstract\nOn Euclidean spaces\, the squared distance function $|\\cdot|
^2$ is a convex function as well as a semiconcave function. When it comes
to the simplest sub-Riemannian manifold\, the Heisenberg group\, due to th
e appearance of the cut locus and the abnormal set\, the squared sub-Riema
nnian distance cannot be locally semiconcave nor locally semiconvex. Howev
er\, if we consider the correponding weaker horizontal convexity (or h-con
vexity in short) on Heisenberg group instead\, it turns out that the h-sem
iconcavity holds for the squared sub-Riemannian distance but the h-semicon
vexity still fails. We will also provide two applications of our results t
o PDEs. This talk is based on joint works with Federica Dragoni (Cardiff U
niversity)\, Qing Liu (OIST)\, and Xiaodan Zhou (OIST).\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pepijn Roos Hoefgeest (KTH)
DTSTART:20250218T130000Z
DTEND:20250218T150000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/92
DESCRIPTION:Title: Christoffel polynomials for Topological Data An
alysis\nby Pepijn Roos Hoefgeest (KTH) as part of Geometric Structures
Research Seminar\n\nLecture held in SISSA Main Building - room 136.\n\nAb
stract\nIn topological data analysis\, persistent homology has been widely
used to study the geometry of point clouds in $\\mathbb{R}^n$. Unfortunat
ely\, standard methods are very sensitive to outliers\, and their computat
ional complexity depends badly on the number of data points. In this talk
we will present a novel persistence module\, based on recent applications
of Christoffel-Darboux kernels in the context of statistical data analysis
and geometric inference. Our approach is robust to outliers and can be co
mputed in time linear in the number of data points. We illustrate the bene
fits and limitations of our new module with various numerical examples in
$\\mathbb{R}^n$\, $n=1\,2\,3$.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrei Agrachev (SISSA)
DTSTART:20250306T130000Z
DTEND:20250306T150000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/95
DESCRIPTION:Title: Geometry of osculating curves\nby Andrei Ag
rachev (SISSA) as part of Geometric Structures Research Seminar\n\nLecture
held in SISSA Main Building - Room 005.\n\nAbstract\nSimplest geometric e
xample of a nonholonomic constraint is one for the movement of the tangent
line along a smooth plane curve. We obtain a better contact with the curv
e and more interesting constraints if we substitute tangent lines with "os
culating" algebraic curves of degree n>1. My talk is devoted to the vector
distributions and subriemannian structures raised from these geometric mo
dels\, starting from the osculating conics and cubics.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gianmarco Caldini (Trento)
DTSTART:20250311T130000Z
DTEND:20250311T150000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/96
DESCRIPTION:Title: Optimal smooth approximation of integral cycles
\nby Gianmarco Caldini (Trento) as part of Geometric Structures Resear
ch Seminar\n\nLecture held in SISSA Main Building - 136.\n\nAbstract\nThe
natural question of how much smoother integral currents are with respect t
o their initial definition goes back to the late 1950s and to the origin o
f the theory with the seminal article of Federer and Fleming. In this semi
nar I will explain how closely one can approximate an integral current rep
resenting a given homology class by means of a smooth submanifold. This is
a joint study with Frederick Almgren\, William Browder and Camillo De Lel
lis.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luca Nalon (Fribourg)
DTSTART:20250318T130000Z
DTEND:20250318T150000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/98
DESCRIPTION:Title: Asymptotic sub-Riemannian distances in 2-step n
ilpotent Lie groups\nby Luca Nalon (Fribourg) as part of Geometric Str
uctures Research Seminar\n\nLecture held in SISSA Main Building - 136.\n\n
Abstract\nWe are interested in the large-scale geometric properties of Rie
mannian and sub-Riemannian metrics in 2-step nilpotent Lie groups. Given t
wo left-invariant sub-Riemannian metrics $d_1$ and $d_2$ on a simply conne
cted\, 2-step nilpotent Lie group\, we provide a characterization of the f
ollowing properties in terms of the underlying sub-Riemannian structure:\n
\n1) $d_1$ and $d_2$ are at bounded distance as functions from $G \\times
G$ to $\\mathbb{R}$\,\n\n2) $d_1^2$ and $d_2^2$ are at bounded distance as
functions from $G \\times G$ to $\\mathbb{R}$.\n\nThis characterization i
s based on a novel tecnique we developed to perturb horizontal curves in o
rder to displace their end-points in a prescribed vertical direction. This
talk is based on a joint work with E. Le Donne\, S. Nicolussi Golo\, and
S-Y Ryoo.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucia Tessarolo (Paris)
DTSTART:20250408T140000Z
DTEND:20250408T160000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/99
DESCRIPTION:Title: Schrödinger evolution on surfaces in 3D contac
t sub-Riemannian manifolds\nby Lucia Tessarolo (Paris) as part of Geom
etric Structures Research Seminar\n\nLecture held in SISSA Main Building -
Room 134.\n\nAbstract\nLet $M$ be a 3-dimensional contact sub-Riemannian
manifold and $S$ a surface embedded in $M$.\nSuch a surface inherits a fie
ld of directions that becomes singular at characteristic points. The integ
ral curves of such field define a characteristic foliation $\\mathscr{F}$.
\nIn this talk we analyse the Schrödinger evolution of a particle constr
ained on $\\mathscr{F}$. \nSpecifically\, we define the Schrödinger opera
tor $\\Delta_\\ell$ on each leaf $\\ell$ as the classical "divergence of g
radient"\, where the gradient is the Euclidean gradient along the leaf and
the divergence is taken with respect to the surface measure inherited fro
m the Popp volume\, using the sub-Riemannian normal to the surface. \nWe t
hen study the self-adjointness of the operator $\\Delta_\\ell$ on each lea
f by defining a notion of “essential self-adjointness at a point”\, in
such a way that $\\Delta_\\ell$ will be essentially self-adjoint on the w
hole leaf if and only if it is essentially self-adjoint at both its endpoi
nts. We see how this local property at a characteristic point depends on a
curvature-like invariant at that point. We then discuss self-adjoint exte
nsions of an operator defined on the whole foliation and we construct a sp
ecial family of such extension in a toy model.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Federica Dragoni (Cardiff)
DTSTART:20251009T120000Z
DTEND:20251009T140000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/101
DESCRIPTION:Title: Semiconcavity of the square distance in Carno
t groups\nby Federica Dragoni (Cardiff) as part of Geometric Structure
s Research Seminar\n\nLecture held in SISSA Main Building.\n\nAbstract\nSe
miconcavity and semiconvexity are key regularity properties for functions
with many applications in a broad range of mathematical subjects. The noti
ons of semiconcavity and semiconvexity have been adapted to different geom
etrical contexts\, in particular in sub-Riemannian structures such as Carn
ot groups\, where they turn out to be extremely useful for the study of so
lutions of degenerate PDEs.\n\nIn this talk I will show that\, for a suita
ble class of Carnot groups\, the square Carnot-Carathéodory distance is s
emiconcave\, in the sense of the group\, in the whole space.\n\nI will als
o give some applications to solutions of non-coercive Hamilton-Jacobi equa
tions. Joint work with Qing Liu and Ye Zhang.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugenio Bellini (Università di Padova)
DTSTART:20251016T120000Z
DTEND:20251016T140000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/102
DESCRIPTION:Title: Curvature measures and the sub-Riemannian Gaus
s-Bonnet Theorem\nby Eugenio Bellini (Università di Padova) as part o
f Geometric Structures Research Seminar\n\nLecture held in SISSA Main Buil
ding - Room 133.\n\nAbstract\nIt is not uncommon for curvature to concentr
ate at the singularities of geometric spaces. In this talk\, we show how t
his phenomenon occurs for surfaces immersed in 3D contact sub-Riemannian m
anifolds. Adopting a measure-theoretic viewpoint on the Riemannian approxi
mation scheme\, we prove that the Gaussian curvature measure of such a sur
face is singular and supported on its isolated characteristic points. We i
dentify natural geometric conditions under which this behavior occurs\, na
mely when the surface admits characteristic points of finite order of dege
neracy. This is a joint work with D. Barilari and A. Pinamonti.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steven Flynn (University College London)
DTSTART:20251204T130000Z
DTEND:20251204T150000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/105
DESCRIPTION:Title: A Microlocal Calculus on Filtered Manifolds\nby Steven Flynn (University College London) as part of Geometric Struct
ures Research Seminar\n\nLecture held in SISSA Main Building - Room 133.\n
\nAbstract\nSub-Riemannian geometries arise naturally in quantum mechanics
and control theory\, yet fundamental questions about quantum dynamics rem
ain open\, suggesting that new microlocal tools are needed to extend class
ical results to these singular geometries.\n\nI will present a pseudodiffe
rential calculus for filtered manifolds with operator-valued symbols built
using representation theory of nilpotent groups. The key innovation is an
explicit quantization procedure for noncommutative symbols adapted to the
filtration\, extending the Van Erp-Yuncken calculus while maintaining ess
ential properties: closure under composition\, parametrices\, and Sobolev
continuity.\n\nThis framework enables systematic microlocal analysis on eq
uiregular sub-Riemannian manifolds. This is joint work with Véronique Fis
cher and Clotilde Fermanian-Kammerer.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mattia Magnabosco (University of Oxford)
DTSTART:20251211T130000Z
DTEND:20251211T150000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/106
DESCRIPTION:Title: On the topology of Riemannian manifolds with n
onnegative Ricci curvature and $\\mathsf{RCD}(0\,N)$ spaces\nby Mattia
Magnabosco (University of Oxford) as part of Geometric Structures Researc
h Seminar\n\nLecture held in SISSA Main Building - Room 005.\n\nAbstract\n
The topology of complete noncompact Riemannian manifolds with nonnegative
Ricci curvature has been studied extensively since the earliest developmen
ts of Geometric Analysis. In dimension $3$\, a complete topological classi
fication was only recently achieved by Gang Liu\, with a strategy based on
minimal surfaces methods. They proved that a $3$-dimensional Riemannian m
anifold with nonnegative Ricci curvature either is homeomorphic to $\\math
bb R^3$ or the universal cover splits a line isometrically. In this talk\,
I present an alternative proof of Liu’s classification\, which also wor
ks for nonsmooth $\\mathsf{RCD}(0\,3)$ spaces. Our strategy relies on two
main building blocks with independent interest\, that provide results whic
h are new also in the smooth setting. In particular\, we prove that\, give
n a complete $n$-dimensional Riemannian manifold $(M\,g)$ with nonnegative
Ricci curvature and first Betti number $b_1(M) \\geq n-2$\, the universal
cover splits $\\mathbb R^{n-2}$ isometrically. Moreover\, we show that ev
ery complete oriented $n$-dimensional Riemannian manifold with nonnegative
Ricci curvature has vanishing simplicial volume. \nThis is a joint work w
ith Alessandro Cucinotta and Daniele Semola.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessandro Tamai (SISSA)
DTSTART:20251218T130000Z
DTEND:20251218T150000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/107
DESCRIPTION:Title: Testing the variety hypothesis\nby Alessan
dro Tamai (SISSA) as part of Geometric Structures Research Seminar\n\nLect
ure held in SISSA Main Building - Room 005.\n\nAbstract\nGiven a probabili
ty measure on the unit disk\, we study the problem of deciding whether\, f
or some threshold probability\, this measure is supported near a real alge
braic variety of given dimension and bounded degree. We call this “testi
ng the variety hypothesis”. We prove an upper bound on the so–called
“sample complexity” of this problem and show how it can be reduced to
a semialgebraic decision problem. This is done by studying in a quantitati
ve way the Hausdorff geometry of the space of real algebraic varieties of
a given dimension and degree.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrei Agrachev (SISSA)
DTSTART:20260115T130000Z
DTEND:20260115T150000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/111
DESCRIPTION:Title: Geometry of osculating curves\nby Andrei A
grachev (SISSA) as part of Geometric Structures Research Seminar\n\nLectur
e held in SISSA Main Building - Room 005.\n\nAbstract\nThis talk concerns
the geometry of smooth plane curves. First we fix a space of sample curves
\, this can be the space of lines or circles\, or conics\, cubics\, etc. G
iven a smooth curve\, the osculating line is just the tangent line sliding
along the curve. Other sample spaces provide higher order analogues of th
is picture. Osculating curves are integral curves of a canonical vector di
stribution on the space of pointed sample curves\; it was described in my
talk at the "Geometric Structures" seminar last year.\nIn the new talk\, I
am going to recall the construction of the canonical distribution and the
n focus on the metric aspects of this story.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yaozhong Qiu (Université Paris Nanterre)
DTSTART:20260129T130000Z
DTEND:20260129T150000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/112
DESCRIPTION:Title: Isoperimetric inequalities for subriemannian a
nalogues of the gaussian measure\nby Yaozhong Qiu (Université Paris N
anterre) as part of Geometric Structures Research Seminar\n\nLecture held
in SISSA Main Building - Room 005.\n\nAbstract\nWe propose a family of pro
bability measures defined on a stratified Lie group\, as well as on the Gr
ushin and Heisenberg-Greiner spaces\, which may be considered an analogue
of the gaussian measure. As evidence\, we show such measures satisfy an ap
proximate (up to a constant) isoperimetric inequality\, which is degenerat
e in the sense there is a mismatch between the decay of tails and isoperim
etric profiles\, and we show in two cases the corresponding approximate is
operimetric extremisers can be interpreted as a generalisation of a half-s
pace. Along the way we will discuss some literature surrounding functional
inequalities for probability measures in subriemannian settings\, aspects
of the proof\, and finally a discussion on subsequent questions.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/112/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Zelenko (Texas A&M University)
DTSTART:20251120T130000Z
DTEND:20251120T150000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/113
DESCRIPTION:Title: Local Geometry of Distributions: Symplectifica
tion\, Cartan Prolongation\, and Maximality of Class\nby Igor Zelenko
(Texas A&M University) as part of Geometric Structures Research Seminar\n\
nLecture held in SISSA Main Building - Room 005.\n\nAbstract\nIn 1970\, N.
Tanaka introduced a method for constructing a canonical frame for distrib
utions with constant Tanaka symbol. In 2009\, B. Doubrov and I\, building
on earlier works of A. Agrachev\, R. Gamkrelidze\, and myself\, employed a
symplectification procedure to obtain a canonical frame for distributions
independent of their Tanaka symbol. However\, this required an additional
assumption - the maximality of class of the distribution.\n\nIn a recent
joint work with N. Day\, we proved that all bracket generating rank-2 dist
ributions with 5-dimensional cube are of maximal class at a generic point.
This result allows one to assign a canonical frame at a generic point to
every rank-2 distribution that is not of Goursat type. On the optimal cont
rol side\, this result implies that for bracket-generating rank-2 distribu
tions with 5-dimensional cube\, there exist plenty of abnormal extremal tr
ajectories starting from a generic point.\n\nFurther\, in the rank-2 case\
, I will give an interpretation of the symplectification procedure in term
s of a classical construction known as Cartan prolongation and discuss the
question of the minimal number of iterative Cartan prolongations needed f
or the Tanaka symbols to become unified or finitely unified.\n\nIn contras
t with the rank-2 situation\, we found examples of rank-3 distributions wi
th 6-dimensional square that are not of maximal class. In particular\, I w
ill present a (3\, 8) distribution of non-maximal class whose symmetry alg
ebra has dimension 29 and contains a semidirect sum of the exceptional Lie
algebra $\\mathfrak g_2$ with a copy of its adjoint module.\n\nFinally\,
if time permits\, I will discuss the analogous results for normal geodesic
s in sub-Riemannian geometry and more general geometries\, yielding algebr
aic proofs and extensions of several results of Agrachev that were origina
lly obtained by analytic methods.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/113/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicola Paddeu (Université de Fribourg)
DTSTART:20260416T120000Z
DTEND:20260416T140000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/114
DESCRIPTION:Title: Branching of normal curves in sub-Finsler Lie
groups\nby Nicola Paddeu (Université de Fribourg) as part of Geometri
c Structures Research Seminar\n\nLecture held in SISSA Main Building - Roo
m 005.\n\nAbstract\nWe begin by introducing sub-Finsler Lie groups. We the
n present a version of the Pontryagin Maximum Principle adapted to this se
tting and use it to deduce several properties of normal curves in sub-Fins
ler Lie groups. Finally\, we provide sufficient conditions for the existen
ce of branching of normal curves in sub-Finsler Lie groups endowed with st
rongly convex norms.\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/114/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rotem Assouline (Sorbonne Université)
DTSTART:20260423T120000Z
DTEND:20260423T140000Z
DTSTAMP:20260405T094319Z
UID:Geometric_Structures_SISSA/115
DESCRIPTION:Title: Curvature-Dimension for autonomous Lagrangians
\nby Rotem Assouline (Sorbonne Université) as part of Geometric Struc
tures Research Seminar\n\nLecture held in SISSA Main Building - Room 004.\
n\nAbstract\nIn this talk\, we will see how the celebrated connection betw
een Ricci curvature\, optimal transport\, and geometric inequalities such
as the Brunn-Minkowski inequality\, extends to the setting of autonomous T
onelli Lagrangians on weighted manifolds. As applications\, we will state
a generalization of the horocyclic Brunn-Minkowski inequality to complex h
yperbolic space of arbitrary dimension\, as well as a new Brunn-Minkowski
inequality for contact magnetic geodesics on odd-dimensional spheres. The
main technical tool is a generalization of Klartag's needle decomposition
technique to the Lagrangian setting.\n\nNote the unusual room\n
LOCATION:https://stable.researchseminars.org/talk/Geometric_Structures_SIS
SA/115/
END:VEVENT
END:VCALENDAR