1,188 Works

Geometric recursion

Jorgen Ellegaard Andersen
Geometric Recursion is a very general machinery for constructing mapping class group invariants objects associated to two dimensional surfaces. After presenting the general abstract definition we shall see how a number of constructions in low dimensional geometry and topology fits into this setting. These will include the Mirzakhani-McShane identies, mapping class group invariant closed forms on Teichmüller space (including the Weil-Petterson symplectic form) and the Goldman symplectic form.

Was the Russian theory of cycles a mathematical theory?

Irina Konovalova-Peaucelle
Cournot Centre session devoted to the transformations that took place in mathematical economics during the interwar period.

Steady states and long range correlations in driven systems - Lecture 1

David Mukamel
In these three lectures steady states and dynamical properties of nonequilibrium systems will be discussed. Systems driven out of thermal equilibrium often reach a steady state which under generic conditions exhibits long-range correlations. This is very different from systems in thermal equilibrium where long-range correlations develop only at phase transition points. In some cases these correlations even lead to long-range order in d=1 dimension, of the type occurring in traffic jams. Simple examples of such...

Entropy and entanglement bounds for reduced density matrices of fermionic states

Elliott H. Lieb
One of the important aspects of many-body quantum mechanics of electrons is the analysis of two-body density matrices. While the characterization of one-body density matrices is well known and simple to state, that of two-body matrices is far from simple – indeed, it is not fully known. In this talk I will present joint work with Eric Carlen in which we study the possible entropy of such matrices. We find, inter alia, that minimum entropy...

Combination therapies and drug resistance in heterogeneous tumoral populations

Marcello Delitala
How combination therapies can reduce the emergence of cancer resistance? Can we exploit intra-tumoral competition to modify the effectiveness of anti-cancer treatments? Bearing these questions in mind, we present a mathematical model of cancer-immune competition under therapies. The model consists of a system of differential equations for the dynamics of two cancer clones and T-cells. Comparisons with experimental data and clinical protocols for non-small cell lung cancer have been performed. In silico experiments confirm that...

On the Hall-MHD equations

Dongho Chae
In this talk we present recent results on the Hall-MHD system. We consider the incompressible MHD-Hall equations in $\mathbb{R}^3$. $\partial_tu +u \cdot u + \nabla u+\nabla p = \left ( \nabla \times B \right )\times B +\nu \nabla u,$ $\nabla \cdot u =0, \nabla \cdot B =0, $ $\partial_tB - \nabla \times \left (u \times B\right ) + \nabla \times \left (\left (\nabla \times B\right )\times B \right ) = \mu \nabla B,$ $u\left (x,0...

Using Harris’s theorem to show convergence to equilibrium for kinetic equations

Josephine Evans
I will discuss a joint work with Jose Canizo, Cao Chuqi and Havva Yolda. I will introduce Harris’s theorem which is a classical theorem from the study of Markov Processes. Then I will discuss how to use this to show convergence to equilibrium for some spatially inhomogeneous kinetic equations involving jumps including jump processes which approximate diffusion or fractional diffusion in velocity. This is the situation in which the tools of ’Hypocoercivity’ are used. I...

The congruence $f(x) + g(y) + c = 0$ $(mod$ $xy)$

Andrzej Schinzel
The assertions made by L. J. Mordell in his paper in Acta Mathematica 44(1952) are discussed. Mordell had been to a certain extent anticipated by E. Jacobsthal (1939). backward induction - congruence - equation - non-zero coefficients - polynomials

Liouville's inequality for transcendental points on projective varieties

Carlo Gasbarri
Liouville inequality is a lower bound of the norm of an integral section of a line bundle on an algebraic point of a variety. It is an important tool in may proofs in diophantine geometry and in transcendence. On transcendental points an inequality as good as Liouville inequality cannot hold. We will describe similar inequalities which hold for "many" transcendental points and some applications

Théorie de la dynamique adaptative: l'évolution en équation

Mathias Gauduchon
dynamique adaptative - évolution

A computational approach to Milnor fiber cohomology

Alexandru Dimca
In this talk we consider the Milnor fiber F associated to a reduced projective plane curve $C$. A computational approach for the determination of the characteristic polynomial of the monodromy action on the first cohomology group of $F$, also known as the Alexander polynomial of the curve $C$, is presented. This leads to an effective algorithm to detect all the roots of the Alexander polynomial and, in many cases, explicit bases for the monodromy eigenspaces...

Multiple ergodic theorems: old and new - Lecture 3

Bryna Kra
The classic mean ergodic theorem has been extended in numerous ways: multiple averages, polynomial iterates, weighted averages, along with combinations of these extensions. I will give an overview of these advances and the different techniques that have been used, focusing on convergence results and what can be said about the limits.

Low temperature interfaces and level lines in the critical prewetting regime

Dmitry Ioffe
Complete wetting in the context of the low temperature two-dimensional Ising model is characterized by creation of a mesoscopic size layer of the "-" phase above an active substrate. Adding a small positive magnetic field h makes "-"-phase unstable, and the layer becomes only microscopically thick. Critical prewetting corresponds to a continuous divergence of this layer as h tends to zero. There is a conjectured 1/3 (diffusive) scaling leading to Ferrari-Spohn diffusions. Rigorous results were...

Resonant two-soliton interaction for the one dimensional half wave equation

Patrick Gérard
The one dimensional half wave equation is an interesting example of a nonlinear wave equation with vanishing dispersion, displaying arbitrarily small mass solitons. I will discuss how, in some resonant regime, the interaction of two such solitons leads to long time transition to high frequencies. This talk is issued from a jointwork with Enno Lenzmann, Oana Pocovnicu and Pierre Raphael.

Preprojective algebras and Cluster categories

Osamu Iyama
The preprojective algebra $P$ of a quiver $Q$ has a family of ideals $I_w$ parametrized by elements $w$ in the Coxeter group $W$. For the factor algebra $P_w = P/I_w$, I will discuss tilting and cluster tilting theory for Cohen-Macaulay $P_w$-modules following works by Buan-I-Reiten-Scott, Amiot-Reiten-Todorov and Yuta Kimura.

Chemins à grands pas dans le quadrant

Mireille Bousquet-Mélou
L'énumération des chemins du quadrant formés de petits pas (c'est-à-dire de pas aux 8 plus proches voisins) est maintenant bien comprise. En particulier, leur série génératrice est différentiellement finie (solution d'une ED linéaire à coefficients polynomiaux) si et seulement si un certain groupe de transformations rationnelles, associé à l'ensemble des pas autorisés (encore appelé modèle), est fini. Il n'est pas du tout évident d'étendre à des marches à pas plus grands les méthodes qui ont...

Subtle Stiefel-Whitney classes and the J-invariant of quadrics

Alexander Vishik
I will discuss the new ?subtle? version of Stiefel-Whitney classes introduced by Alexander Smirnov and me. In contrast to the classical classes of Delzant and Milnor, our classes see the powers of the fundamental ideal, as well as the Arason invariant and its higher analogues, and permit to describe the motives of the torsor and the highest Grassmannian associated to a quadratic form. I will consider in more details the relation of these classes to...

Interview au CIRM : Pascal Hubert

Pascal Hubert
Pascal Hubert est mathématicien, professeur au sein d'Aix-Marseille Université et directeur de la FRUMAM. Il parle ici de son grand-père, qui lui a donné le goût des mathématiques, de ses recherches, de la richesse mathématique marseillaise, de sa collaboration avec Artur Avila (Médaille Fields 2014), etc. Artur Avila que nous avons pu contacter avant l'interview de Pascal Hubert, et qui nous a demandé de lui parler de Jean-Christophe Yoccoz...

Geometric control and dynamics

Ludovic Rifford
The geometric control theory is concerned with the study of control systems in finite dimension, that is dynamical systems on which one can act by a control. After a brief introduction to controllability properties of control systems, we will see how basic techniques from control theory can be used to obtain for example generic properties in Hamiltonians dynamics.

Localization of eigenfunctions via an effective potential

David Jerison
We discuss joint work with Doug Arnold, Guy David, Marcel Filoche and Svitlana Mayboroda. Consider the Neumann boundary value problem for the operator $L = divA\nabla + V$ on a Lipschitz domain $\Omega$ and, more generally, on manifolds with and without boundary. The eigenfunctions of $L$ are often localized, as a result of disorder of the potential $V$, the matrix of coefficients $A$, irregularities of the boundary, or all of the above. In earlier work,...

​On Hitchin’s hyperkähler metric on moduli spaces of Higgs bundles

Andrew Neitzke
I will review a conjecture (joint work with Davide Gaiotto and Greg Moore) which gives a description of the hyperkähler metric on the moduli space of Higgs bundles, and recent joint work with David Dumas which has given evidence that the conjecture is true in the case of $SL(2)$-Higgs bundles.

Rank 3 rigid representations of projective fundamental groups

Carlos Simpson
This is joint with Adrian Langer. Let $X$ be a smooth complex projective variety. We show that every rigid integral irreducible representation $ \pi_1(X,x) \to SL(3,\mathbb{C})$ is of geometric origin, i.e. it comes from a family of smooth projective varieties. The underlying theorem is a classification of VHS of type $(1,1,1)$ using some ideas from birational geometry.

Forward and backward simulation of Euler scheme

Emmanuel Gobet
We analyse how reverting Random Number Generator can be efficiently used to save memory in solving dynamic programming equation. For SDEs, it takes the form of forward and backward Euler scheme. Surprisingly the error induced by time reversion is of order 1.

Bandits in auctions (& more)

Vianney Perchet
In this talk, I will introduce the classical theory of multi-armed bandits, a field at the junction of statistics, optimization, game theory and machine learning, discuss the possible applications, and highlights the new perspectives and open questions that they propose We consider competitive capacity investment for a duopoly of two distinct producers. The producers are exposed to stochastically fluctuating costs and interact through aggregate supply. Capacity expansion is irreversible and modeled in terms of timing...

Privacy and statistical minimax: quantitative tradeoffs

Martin Wainwright
privacy mechanism#local differential privacy#discolure risk#Laplacian mechanism#statistical minimax with privacy#location estimation#total variation contraction#non-parametric density estimation#Sobolev smoothness class#nonparametric deconvolution#metric entropy#mutual information and Fano's inequality#mutual information contraction

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