Next Meeting
The meeting will take place on Monday, October 6th at the Institut de Mathématiques de Jussieu, Sorbonne Université, Paris in Room 1516-4-13 (4th floor).
Also through zoom using the link:
https://cnrs.zoom.us/j/94996859068?pwd=fnxL2Fz0YhStBoqd836Mx92jcLC2ZB.1
Meeting ID: 949 9685 9068
Passcode: b3bqdb
Schedule
11:30-12:30: Alex Fink (Queen Mary University of London)
Title: TBA
Abstract: TBA
PAST MEETINGS
Meeting
The meeting will take place on Tuesday, July 29th at the Institut de Mathématiques de Jussieu, Sorbonne Université, Paris in Room 1516-4-13 (4th floor).
Also through zoom using the link:
https://cnrs.zoom.us/j/94996859068?pwd=fnxL2Fz0YhStBoqd836Mx92jcLC2ZB.1
Meeting ID: 949 9685 9068
Passcode: b3bqdb
Schedule
11:30-12:30: Lior Silberman (University of British Columbia)
Title: Arithmetic Quantum Unique Ergodicity for hyperbolic spaces
Abstract: I shall discuss joint work with Zvi Shem-Tov on the equidistribution problem for Hecke eigenfunctions on congruence hyperbolic 3- and 4-manifolds.
This problem lies in the intersection of spectral theory, representation theory, number theory, diophantine geometry, homogenous dynamics, etc. I will introduce the problem and some old and new ideas about it, leading to an equidistribution for Hecke--Maass forms on congruence quotients for $SL_2$ over number fields (including hyperbolic 3-manifolds and for hyperbolic four-manifolds.
Meeting
The meeting will take place on Monday, June 30 at the Institut de Mathématiques de Jussieu, Sorbonne Université, Paris in Room 1516-4-13 (4th floor).
Also through zoom using the link:
https://cnrs.zoom.us/j/92318027540?pwd=rduObmTSjxvPWPue3i7aKr3hyUranh.1
Meeting ID: 923 1802 7540
Passcode: RjHzF6
Schedule
11:30-12:30: Veronica Fantini (LMO, Orsay)
Title: Resurgent series from local Calabi-Yau threefolds and arithmetic
Abstract: Formal divergent power series appear in various contexts, and the theory of resurgence introduced by Écalle is a prominent tool to study them. In fact, it associates to a divergent power series a collection of exponentially small corrections with a set of complex numbers known as Stokes constants. In this talk, I will introduce some of the main ideas of resurgence and discuss the arithmetic structure of the Stokes constants of the divergent series associated with locally weighted projective spaces.
14:45-15:45: Eitan Bachmat (Ben-Gurion University)
Title: Combinatorics, geometry and lenses
Abstract: We will explore the connection between combinatorial notions such as the chain polytope and the entropy of a poset, Lorentzian geometry and super lenses in hyperbolic metamaterials.
Meeting
The meeting will take place on Tuesday, May 6 at the Institut de Mathématiques de Jussieu, Sorbonne Université, Paris in Room 1516-4-13 (4th floor).
Also through zoom using the link:
https://cnrs.zoom.us/j/92318027540?pwd=rduObmTSjxvPWPue3i7aKr3hyUranh.1
Meeting ID: 923 1802 7540
Passcode: RjHzF6
Schedule
11:30-12:30: Meral Tosun (Galatasaray University)
Title: Geometric and combinatorial views on singularities
Abstract: We focus on a special class of singularities that allow a polyhedral and
combinatorial description. We show how jet schemes capture fine local data
and lead to a resolution process in this class.
14:45-15:45: Dmitry Mineev ( Bar-Ilan University)
Title: From tropical modifications of Bergman fans to correspondences and flag fans
Abstract: Bergman fans are tropical counterparts of matroids. Strong maps between matroids admit a description as morphisms between Bergman fans. However, taking limits of even the simplest diagrams of matroids requires so-called weak maps, which do not translate to the tropical side. We suggest a fix, generalizing both weak maps of matroids and tropical morphisms, and construct a functor relating the two. We also introduce flag fans as a convenient tool for computations in this extended setting.
16:00-17:00: Christos Tatakis (University of Western Macedonia)
Title: The structure of complete intersection graphs and their planarity.
Abstract:
Let G be a connected, undirected, finite and simple graph. We study the complete intersection property on the toric ideal $I_G$. In general, the toric ideal $I_G$ is complete intersection if and only if it can be generated by h binomials, where h=m-n+1 if G is a bipartite graph or h=m-n if G is not a bipartite graph, where by m we denote the number of the edges of G and by n the number of its vertices. The answer is known in the case of bipartite graphs, i.e. graphs with no odd cycles. In the last years, several useful partial results have been proved and they provide key properties of complete intersection toric ideals of graphs.
We focus on the general case, where G is a random graph and we present a structural theorem which gives us necessary and sufficient conditions in which the toric ideal $I_G$ is complete intersection. Moreover, we characterize with sufficient and necessary conditions the complete intersection graphs which are planar. The talk is based on a joint work with Apostolos Thoma.
Meeting
The meeting will take place on Tuesday, March 4 at the Institut de Mathématiques de Jussieu, Sorbonne Université, Paris in Room 1516-4-13 (4th floor).
Also through zoom using the link:
https://cnrs.zoom.us/j/92318027540?pwd=rduObmTSjxvPWPue3i7aKr3hyUranh.1
Meeting ID: 923 1802 7540
Passcode: RjHzF6
Schedule
11:30-12:30: Carsten Peterson (Sorbonne University)
Title: A degenerate version of Brion's formula
Abstract: Brion's formula says that the continuous (resp. discrete) Fourier-Laplace transform of a polytope $P$ (resp. lattice points in a rational polytope) is equal to the sum of the continuous (resp. discrete) Fourier-Laplace transforms of the tangent cones of the vertices. However, whereas the former is an entire function, each latter function is merely meromorphic with singularities on the dual vectors $\xi$ which are constant on some positive-dimensional face of the polytope (resp. constant on the sublattice parallel to some positive-dimensional face). Because of this, one cannot ``plug into'' Brion's formula at such points.
We shall present a ``degenerate'' extension of Brion's formula for which one can still ``plug in'' at such troublesome points. Like Brion's formula it will be made up of terms each of which only depends on some local geometry of $P$. Our formula is particularly useful for understanding how the Fourier-Laplace transform varies over a family of polytopes with the same normal fan. In the generic case our formula reduces to the original Brion's formula, and in the maximally degenerate case ($\xi = 0$) it reduces to the volume of the polytope (resp. the Ehrhart quasi-polynomial).
14:45-15:45: Jacinta Torres (Jagiellonian University)
Title: A new branching model in terms of flagged hives
Abstract: We prove a bijection between the branching models of Sundaram and Kwon. Along the way, we obtain a new branching model In terms of flagged hives polytopes. This is joint work with Sathish Kumar.
16:00-17:00: Evrydiki Nestoridi (Stony Brook University)
Title: Shuffling via transpositions
Abstract: In their seminal work, Diaconis and Shahshahani proved that shuffling a deck of $n$ cards sufficiently well via random transpositions takes $1/2 n log n$ steps. Their argument was algebraic and relied on the combinatorics of the symmetric group. In this talk, I will focus on two other shuffles, generalizing random transpositions and I will discuss the underlying combinatorics for understanding their mixing behavior and indeed proving cutoff. The talk will be based on joint works with A. Yan and S. Arfaee.
Meeting
The meeting will take place on Wednesday, January 22 at the Institut de Mathématiques de Jussieu, Sorbonne Université, Paris in Room 1516-4-11.
Also through zoom using the link:
https://cnrs.zoom.us/j/92318027540?pwd=rduObmTSjxvPWPue3i7aKr3hyUranh.1
Meeting ID: 923 1802 7540
Passcode: RjHzF6
Scedule
11:30-12:30: Danylo Radchenko (University of Lille)
Title: Polylogarithms and the Steinberg module
Abstract: I will talk about a surprising connection between the Steinberg module of rationals and a certain space of multiple polylogarithms on tori. I will expain how this idea leads to several important implications for Goncharov's program on structure of multiple polylogarithms, and if time permits I will also discuss how it relates to the Church-Putman-Farb conjecture for the cohomology of GL_n(Z). The talk is based on a joint work in progress with Steven Charlton and Daniil Rudenko.
14:45-15:45: Olga Trapeznikova (ISTA)
Title: Intersection cohomology of moduli spaces of semistable bundles on curves
Abstract: The study of the intersection cohomology of moduli spaces of semistable bundles on Riemann surfaces began in the 80's with the works of Frances Kirwan. Motivated by the work of Mozgovoy and Reineke, in joint work with Camilla Felisetti and Andras Szenes, we give a complete description of these structures via a detailed analysis of the Decomposition Theorem applied to a certain map. We also give a new formula for the intersection Betti numbers of these moduli spaces, which has a clear geometric meaning. In this talk, I will describe our results.
16:05-17:05: Claire Burrin (University of Zurich)
Title: Rational points on spheres
Abstract: A sequence of point-sets is considered optimally distributed with respect to covering it its covering exponent is 1. I will discuss some new results on the covering exponent for sequences of rational points on spheres. This is joint work with Matthias Gröbner.
Meeting
The meeting will take place on Wednesday, September 25 at the Institut de Mathématiques de Jussieu, Sorbonne Université, Paris in Room 1516-2-01.
Also through zoom using the link:
https://cnrs.zoom.us/j/92318027540?pwd=rduObmTSjxvPWPue3i7aKr3hyUranh.1
Meeting ID: 923 1802 7540
Passcode: RjHzF6
Scedule
10:00-11:00: Gavin Brown( University of Warwick)
Title: Noncommutative singularity theory
Abstract: I describe a noncommutative version of Arnold's classification of function germs and its application to the classification of simple 3-fold flops. The connection is the noncommutative deformation theory of a crepant rational curve on a 3-fold, which in turn exposes an ADE classification on noncommutative Jacobian algebras. This is joint work with Michael Wemyss (Glasgow).
11:30-12:30: Alexander Esterov (LIMS)
Title: Solvable systems of equations, Galois groups in enumerative geometry, and small lattice polytopes
Abstract: The general polynomial of a degree higher than 4 cannot be solved by radicals. This classical theorem has a multidimensional version: solvable general systems of polynomial equations are in (almost) one-to-one correspondence with lattice polytopes of volume 4, and the latters admit a finite classification. In the narrow sense, I will talk about this xix-century-style result. In a broader sense, we shall look at the Galois groups of problems of enumerative geometry (such as Schubert calculus), and how their study leads to seemingly distant topics such as polyhedral geometry and braid groups.
l15:00-16:00: Joni Teräväinen (University of Turku)
Title: Uniformity of the primes in short intervals
Abstract: Gowers norms are a measure of the pseudorandomness properties of a set. Green, Tao and Ziegler showed in 2012 that the set of prime numbers is Gowers uniform, in the sense that a suitably normalised version of it has small Gowers norms. We show that the primes are Gowers uniform also when restricted to short intervals [x,x+x^c] for suitable c. Morover, the admissible value of c is smaller if we look at primes in almost all short intervals. I will also discuss an application of such results to an averaged version of the Hardy--Littlewood conjecture. This is based on joint works with Kaisa Matomäki, Maksym Radziwiłł, Xuancheng Shao and Terence Tao.
16:30-17:30: Sean Eberhard (Queen's University)
Title: Diameter bounds for finite classical groups generated by transvections
Abstract: The diameter of a group G with respect to a symmetric generating set X is the smallest integer d such that every element of G is the product of at most d elements of X. A well-known conjecture of Babai predicts that every nonabelian finite simple group G has diameter (log |G|)^O(1) with respect to any generating set. This is known to be true for bounded-rank groups of Lie type (Helfgott; Pyber--Szabo; Breuillard--Green--Tao), but the conjecture is wide open for high-rank groups. There has bee a good deal of progress recently for generating sets containing either special elements or random elements. In this talk I will outline the proof that the conjecture holds for the classical groups SL_n(q), Sp_{2n}(q), SU_n(q) and any generating set containing a transvection. The proof is based essentially on (a) the positive resolution of Babai's conjecture in bounded rank and (b) a result of Kantor classifying finite irreducible linear groups generated by transvections.
Meeting
The meeting will take place on Wednesday, July 17th at the Institut de Mathématiques de Jussieu, Sorbonne Université, Paris in Room 1516-1-01.
Also through zoom using the link:
https://cnrs.zoom.us/j/92318027540?pwd=rduObmTSjxvPWPue3i7aKr3hyUranh.1
Meeting ID: 923 1802 7540
Passcode: RjHzF6
Scedule
13:30-14:30: Sergey Avvakumov (Weizmann)
Title: Boxing inequality
Abstract: Recall the definition of the $m$th Hausdorff content of a metric space $X$: it is the infimum of $\sum d_i^m$, where
the infimum is taken over all coverings of $X$ by a finite collection of open metric balls, and $d_i$ denote the diameters of these balls.
A subset $X$ of a Banach space (of finite or infinite dimension) can always be contracted, or "filled", via a homotopy to an $(m-1)$-dimensional subpolyhedron. The boxing inequality states that the $m$th Hausdorff content of the homotopy can be bounded in terms of the $m$th Hausdorff content of $X$. Note, that this differs from the classical isoperimetric inequality where the $(m+1)$th volume of the filling is bounded.
I will discuss the proof of this result and its connections to the notions of Gromov's filling radius, Urysohn width, systole, relations between these notions, and corresponding geometric inequalities.
15:00-16:30: Dawid Kielak (University of Oxford)
Title: One-relator groups
Abstract: I will survey the history of the subject, and present new developments.
Meeting
The meeting will take place on Friday, June 14th at the Institut de Mathématiques de Jussieu, Sorbonne Université, Paris in Room 1516-1-01 for the talks from 11:00 to 14:00 and in Room 1626-1-13 for the rest of the talks.
Also through zoom using the link:
https://cnrs.zoom.us/j/92318027540?pwd=rduObmTSjxvPWPue3i7aKr3hyUranh.1
Meeting ID: 923 1802 7540
Passcode: RjHzF6
Scedule
Join Zoom Meeting
11:00-12:00: Alessandra Sarti (Université de Poitiers)
Title: Automorphisms of irreducible holomorphic symplectic manifolds, Enriques manifolds and the cone conjecture.
Abstract: Irreducible holomorphic symplectic (IHS) manifolds can be seen as higher dimensional generalisations of K3 surfaces. Enriques manifolds are non simply connected manifolds whose universal cover isan irreducible holomorphic symplectic manifold and as such they are natural generalizations of Enriques surfaces. In the first part of the talk I will recall basic facts about IHS manifolds and their automorphisms group, I will then introduce Enriques manifolds and their properties. As an application I will discuss the famous Morrison--Kawamanta cone conjecture for Enriques manifolds. The results are contained in several papers with Boissière, Nieper-Wisskirchen, Pacienza.
14:00-15:00: Elad Tzalik (Weizmann Istitute of Science)
Title: The Geometry and Algebra of q-Complexes
Abstract: q-complexes are the q-analog of simplicial complexes. While a simplicial complex is a downword closed collection of sets, a q-complex is a downward closed collection of linear spaces over F_q. In the talk we will discuss some differences and similarities of complexes and their q-analogs and present a few conjectures on their geometric structure. Based on joint work with Ran Tessler.
15:30-16:30: Ryoshun Oba (University of Tokyo )
Title: Multigraded strong Lefschetz property for a-balanced simplicial spheres.
Abstract: For a simplicial sphere (a triangulation of a sphere), count the number of i-dimensional faces for each i. The sequence obtained is the f-vector. The complete characterization of the f-vector of a simplicial sphere was a long standing open problem, which was recently settled by Adiprasito and is now known as the g-theorem. Among the g-theorem, generalized lower bound inequality (GLBI) asserts that the h-vector, a certain invertible linear transformation of the f-vector, of a simplicial (d-1)-sphere is unimodal. Balanced GLBI by Juhnke-Kubitzke and Murai asserts that the stronger inequality holds if additionally the graph is d-colorable. To bridge between them, we consider an (a_1,...,a_m)-balanced simplicial sphere, a simplicial sphere whose vertices can be colored into m colors so that every facet contains a_i vertices of the i-th color. We prove inequalities among the flag h-numbers of an (a_1,...,a_m)-balanced simplicial sphere that implies both GLBI and balanced GLBI. The proof is done by adapting the anisotropy technique of Papadakis and Petrotou to a certain l.s.o.p. and proving a multigraded analogue of strong Lefschetz property for the Stanley-Reisner ring.
Meeting
The meeting will take place on Wednesday, April 17th at the Institut de Mathématiques de Jussieu, Sorbonne Université, Paris in Room 1516-1-01.
Also through zoom using the link:
https://cnrs.zoom.us/j/92201731119?pwd=L2VLN1VBRVl3emIveGJQa1gzY1JFZz09
Schedule
11:00-12:00: Louis Funar (Institut Fourier, France)
Title: Mapping class groups and Kahler manifolds
Abstract: We explore the relation between mapping class groups representations and Kahler geometry.
13:30-14:30: Anna Erschler (Ecole Normale Superieure, France)
Title: Bounded harmonic functions, isoperimetry and distinct subset sums in groups.
Abstract: I will discuss cube independence property of elements for group actions and its relation to growth and asymptotic geometry of groups, studied in joint works with Laurent Bartholdi and Tianyi Zheng.
A particular case is when G acts on itself and the elements commute, in this case the cube independence property states that the elements have distinct subset sums. I will speak about the results, joint with Josh Frisch and Marc Rychnovsky, about the Liouville property (the absence of non-constant bounded harmonic functions) for linear groups. I will explain the role of commuting cube independent elements for solvable groups for the violation of the Liouville property and Isoperimetric problem for these groups. For solvable linear groups the existence elements of linear length and with distinct subset sums is related to a divisibility question of polynomials in several variables over ℤ.
15:00-16:00: Yuri Bilu (Université de Bordeaux, France)
Title: Skolem meets Schanuel
Abstract: For the abstract please use the following link: