Classical mapping class groups, i.e. for surfaces of finite type, are well-studied but they are not particularly interesting from the point of view of topological groups as they are discrete.When we turn our attention to surfaces of infinite type, the situation changes drastically: In particular, the mapping class groups are now « big » (here: uncountable) and we can define an interesting (here: non-discrete) topology on them. In particular, big mapping class groups are Polish groups and we can ask many new questions such as on automatic continuity or their (large-scale) geometry.In this talk, I will give an introduction to surfaces of infinite type and big mapping class groups and then focus on the question of topological behaviour of conjugacy classes. The second part is based on joint work with Jesús Hernández Hernández, Michael Hrušák, Israel Morales, Manuel Sedano, and Ferrán Valdez, and will feature tools from model theory in the proofs.

Probability and analysis informal seminarThe goal of this informal lecture series is to explain the analysis/PDE point of view of some problems which arise in statistical physics and probability. I will try to argue that the language of elliptic/parabolic homogenization brings a new perspective to a wide range of problems, and that the quantitative « coarse-graining » methods are surprisingly useful and adaptable. We will try to cover the first part of the recent monograph co-written with Tuomo Kuusi (available here: https://arxiv.org/abs/2210.06488), and then proceed based on the interests of the audience.  ========Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

Probability and analysis informal seminarThe goal of this informal lecture series is to explain the analysis/PDE point of view of some problems which arise in statistical physics and probability. I will try to argue that the language of elliptic/parabolic homogenization brings a new perspective to a wide range of problems, and that the quantitative « coarse-graining » methods are surprisingly useful and adaptable. We will try to cover the first part of the recent monograph co-written with Tuomo Kuusi (available here: https://arxiv.org/abs/2210.06488), and then proceed based on the interests of the audience.  ========Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

Probability and analysis informal seminarThe goal of this informal lecture series is to explain the analysis/PDE point of view of some problems which arise in statistical physics and probability. I will try to argue that the language of elliptic/parabolic homogenization brings a new perspective to a wide range of problems, and that the quantitative « coarse-graining » methods are surprisingly useful and adaptable. We will try to cover the first part of the recent monograph co-written with Tuomo Kuusi (available here: https://arxiv.org/abs/2210.06488), and then proceed based on the interests of the audience.  ========Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

Probability and analysis informal seminarThe main goal of this talk is to discuss a series of works (Kenyon’11, Dubédat’14, Basok-Ch.’18, Bai-Wan’21) on the convergence of double-dimer loop ensembles in Temperleyan domains to the nested CLE(4). Contrary to the convergence results available for several other lattice models in 2D (LERW/UST, critical Ising and percolation), this approach does not rely upon martingale observables for single interfaces and uses a probabilistic interpretation of a certain SL(2)-isomonodromic tau-function instead.The plan is to start with a crash introduction on what is known/predicted for the scaling limits of loop O(N) models in 2D – even though this is not directly related to the main subject of the talk – so as to keep a bigger picture in mind and to have more room for informal questions/discussions. ========Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

I will start with discussing time-like axially symmetric zero-mean-curvature hypersurfaces in ${mathbb R}^{1,3}$.  Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide. 

(joint work with O. Brinon and N. Mazzari) Let K be a complete valued field extension of ${mathbb Q}_p$ with perfect residue field. We consider p-adic representations of a finite product $G_{K,Delta} = G_K^{Delta}$ of the absolute Galois group $G_K$ of K. This product appears as the fundamental group of a product of diamonds. We develop the corresponding p-adic Hodge theory by constructing analogues of the classical period rings ${mathbb B}_{rm dR}$ and ${mathbb B}_{rm HT}$, and multivariable Sen theory. In particular, we associate to any p-adic representation V of $G_{K,Delta}$ an integrable p-adic differential system in several variables ${mathbb D}_{rm dif} (V)$. We prove that this system is trivial if and only if the representation V is de Rham. Finally, we relate this differential system to the multivariable overconvergent $(varphi,Gamma)$-module of V  constructed by Pal and Zabradi along classical Berger’s construction.  Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide. 

A convex real projective surface is one obtained as the quotient of a properly convex open set in the projective plane by a discrete subgroup of SL(3,R), called the holonomy group, that preserves this convex set. The most basic examples are hyperbolic surfaces, for which the convex set is an ellipse, and the holonomy group is conjugate into SO(2,1). In this case, the eigenvalues of elements of the holonomy group are symmetric. More generally, the asymmetry of the eigenvalues of the holonomy group is a natural measure of how far a convex real projective surface is from being hyperbolic. We study the problem of determining which elements (and more generally geodesic currents) may have maximal eigenvalue asymmetry. We will present some limited initial results that we hope may be suggestive of a bigger picture. Joint work with Florian Stecker.

Following C.T.C. Wall, we say that a group G is of type Fn if it admits a classifying space which is a CW complex with finite n-skeleton. For n = 2, one recovers the notion of being finitely presented. We prove that in a cocompact complex hyperbolic arithmetic lattice with positive first Betti number, deep enough finite index subgroups admit plenty of homomorphisms to Z with kernel of type Fm-1 but not of type Fm. This provides many non-hyperbolic finitely presented subgroups of hyperbolic groups and answers an old question of Brady. This is based on a joint work with C. Llosa Isenrich.

We discuss Agol’s construction of real hyperbolic lattices with arbitrarily small systole. Agol proposed his strategy in dimension 4, where the problem had theretofore been open, but Belolipetsky–Thomson and Bergeron–Haglund–Wise independently showed that this strategy goes through in all dimensions. As a byproduct, one obtains nonarithmetic real hyperbolic lattices in each dimension, and genuinely different examples from those of Gromov and Piatetski-Shapiro. Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide. 

  Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_physique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

How can mathematical results be represented visually in such a way that much information can instantly be read off the images in minimal time and easily?   How can visualization problems contribute to our understanding and progress in the theory from which these tasks arose?   Built of wedges, like « V » or « Lambda », Kontsevich’s directed graphs are a pictorial realization of non-commutative associative star-products: every such directed graph encodes an expression which is differential-polynomial with respect to the coefficients of Poisson brackets (that are placed in the internal vertices) and which is a bi-differential operator with respect to the content of the graph sinks. More general Formality graphs can contain tridents or higher out-degree vertices; Kontsevich’s Formality theorem itself suggests how, by the defition of their weights using integral formulas, the graphs in star-products want to be drawn in the upper half-plane with hyperbolic metric.   The visualization problem which we solve is how the graphs in star-product theory can be drawn — nicely! — in large quantities by using the LaTeX {picture} environment, i.e. the most economical way to draw pictures in scientific texts. In a joint work with S.Kerkhove (Utrecht) we design and implement an algorithm which, given a graph encoding, offers its several drawings in the LaTeX picture environment.   For graphs which do show up in star-products, we obtain the drawings up to order 4 in the deformation parameter. For similar graphs which never show up in the star-product (such as the vacuum diagrams) we explore their visual representations and properties.   Finally, we examine how neural networks can be deployed in two classes of problems about Kontsevich’s graphs and their weights in star-products.      We shall discuss what the Mathematics of « beauty » is in graph visualization: `nice’ is informative, `nice’ is simple, `nice’ is balanced, `nice’ is flexible, `nice’ is whole, `nice’ is unexpected. Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.