Combinatorics and Arithmetic for Physics: special daysThe meeting’s focus is on questions of discrete mathematics and number theory with an emphasis on computability. Problems are drawn mainly from theoretical physics: renormalization, combinatorial physics, geometry, evolution equations (commutative and noncommutative), or related to its models, but not only. Computations, based on combinatorial structures (graphs, trees, words, automata, semirings, bases), or classical structures (operators, Hopf algebras, evolution equations, special functions, categories) are good candidates for computer-based implementation and experimentation.Organised by : Gérard H. E. DUCHAMP, Maxim KONTSEVICH, Gleb KOSHEVOY, Sergei NECHAEV, and Karol A. PENSON.Speakers:Cyril Banderier (CNRS, Univ. Paris Nord) Nicolas Behr (CNRS, Université Paris Cité, IRIF) Gérard H. E. Duchamp (LIPN, Université Paris Nord) Vladimir Fock (Strasbourg Univ.)Nihar Gargava (EPFL, Cambridge)Volker Genz (IBS CGP)Sasha Gorsky (IITP RAS) Darij Grinberg (Drexel University) Dimitry Gurevich (IITP, Moscou) Béa de Laporte (University of Cologne)Richard Kerner (LPTMC, Sorbonne Univ.) Maxim Kontsevich (IHES) Paul-André Melliès (CNRS, Université Paris Cité, IRIF) Frédéric Patras (CNRS, Univ. Côte d’Azur) Karol A. Penson (LPTMC, Sorbonne Univ.) Travis Scrimshaw (Hokkaido University) Thomas Simon (Laboratoire Paul Painlevé, Univ. Lille) Lauren Williams (Harvard University) Sergey Yurkevich (Univ. of Vienna & INRIA)Sponsors: IHESLPTMC (Univ. Paris 6)LIPN UMR CNRS-7030I.S.C.P. (UMI 2615 CNRS)

Homogeneous Dynamics and Geometry in Higher-Rank Lie Groups   The goal of the workshop is to explore links between homogeneous dynamics and recent developments on infinite-covolume discrete subgroups of Lie groups, including images of Anosov representations and generalizations. There will be three minicourses and a dozen research talks. This workshop is organized by Martin Bridgeman (Boston College), Richard Canary (University of Michigan), Fanny Kassel (CNRS & IHES), Hee Oh (Yale University), Maria Beatrice Pozzetti (Universität Heidelberg), and Jean-François Quint (CNRS & Université de Bordeaux).Minicourses: Jean-François Quint (CNRS & Université de Bordeaux) – “Dynamics on Higher-rank Lie Groups” [3h] Tengren Zhang (National University of Singapore) – “Anosov Representations” [3h]Andrés Sambarino (CNRS & IMJ-PRG) & Minju Lee (University of Chicago) – “Recent Developments” [2+2h]Research Talks:Pierre-Louis Blayac (University of Michigan) León Carvajales (Universidad de la Republica, Montevideo) Nguyen-Thi Dang (Université Paris-Saclay) Sam Edwards (Durham University) François Labourie (Université Côte d’Azur) Sara Maloni (University of Virginia) Giuseppe Martone (Yale University) Wenyu Pan (University of Toronto) Rafael Potrie (Universidad de la Republica, Montevideo) Pratyush Sarkar (UC San Diego) Andrew Zimmer (University of Wisconsin, Madison)      

Brylynski defined and studied the topological analogue of the Radon transform on Grassmannians over Complex numbers. Using techniques from the theory of D-modules he characterized the image of these Radon transforms in terms of their singular supports. In this talk, we shall discuss a characteristic p > 0 analogues of Brylynski’s work on the characterization of the image of the Radon transform and obtain a precise description in terms of Beilinson-Saito’s theory of singular support. This is joint work with Deepam Patel. 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. 

In characteristic $p neq 0$, it was observed by Katz that locally constant constructible (l.c.c.) étale sheaves of abelian p-groups can be alternatively described, using a mild extension of Artin-Schreier-Witt theory, in terms of $phi$-modules over the ring of Witt vectors. I will discuss the case of l.c.c. étale sheaves of possibly non-abelian $p$-groups, with applications to explicit description of Gabber-Katz extensions and to non-abelian analogs of local class field theory symbols. 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. 

In the study of resurgent structures underlying quantum invariants of knots, Garoufalidis-Gu-Marino conjectured that the state integrals of Andersen-Kashaev should give the Borel re-summation of some associated perturbative series. I will explain this conjecture and its extension to other examples relating to finite type invariants and closed 3-manifolds, along with relations to recently proposed q-series invariants.  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. 

The link between the hyperbolic geometry of 3-manifolds and the conformal metrics on their boundary has been explored extensively in the context of hyperbolic geometry and is also motivated by the AdS3/CFT2 correspondence. An elementary observation is that the group of Möbius transformations on the Riemann sphere coincides with the isometries of the hyperbolic 3-space H3. The Loewner energy is a Möbius-invariant quantity that measures the roundness of Jordan curves. It arises from large deviations of SLE0+ and is a Kähler potential on the universal Teichmüller space endowed with the Weil-Petersson metric. We show that the Loewner energy of a Jordan curve in the Riemann sphere equals the renormalized volume of a submanifold of H3 constructed using the Epstein surfaces associated with the hyperbolic metric on both sides of the curve. This is work in progress with Martin Bridgeman (Boston College), Ken Bromberg (Utah), and Franco Vargas-Pallete (Yale).

The fine curve graph is a Gromov hyperbolic graph on which the homeomorphism group of a surface acts. It allows to apply tools from geometric group theory and the theory of mapping class groups in this setting.In this talk, we will describe the first entries in a dictionary linking dynamical properties of homeomorphisms acting on the surface to the geometry of the action on the fine curve graph. Furthermore, we will discuss phenomena not encountered in the setting of « classical » curve graphs — namely, homeomorphisms acting as parabolic isometries. This is joint work with Jonathan Bowden, Katie Mann, Emmanuel Militon and Richard Webb.Time permitting, I will describe ongoing work with Jonathan Bowden and Richard Webb concerning the Gromov boundary of the fine curve graph.

Classical ramification theory deals with complete discrete valuation fields k((X)) with perfect residue fields k. Invariants such as the Swan conductor capture important information about extensions of these fields. Many fascinating complications arise when we allow non-discrete valuations and imperfect residue fields k. Particularly in positive residue characteristic, we encounter the mysterious phenomenon of the defect (or ramification deficiency). The occurrence of a non-trivial defect is one of the main obstacles to long-standing problems, such as obtaining resolution of singularities in positive characteristic. Degree p extensions of valuation fields are building blocks of the general case. In this talk, we will present a generalization of ramification invariants for such extensions and discuss how this leads to a better understanding of the defect. If time permits, we will briefly discuss their connection with some recent work (joint with K. Kato) on upper ramification groups. 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 give a definition of a certain category of « log quasicoherent » sheaves on a logarithmic variety which uses Falting’s « almost mathematics » and which has the property that log differential forms and log polyvector fields are the Hochshild homology (appropriately understood) and Hochschild cohomology, respectively, of this category. This implies a certain « noncommutative Hodge theory » associated to a log variety in mixed characteristic. I will also explain (if there is time left over) a relationship of the proof of the main results to mirror symmetry. 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. 

Séminaire Laurent Schwartz — EDP et applications 

Séminaire Laurent Schwartz — EDP et applications 

Séminaire Laurent Schwartz — EDP et applications