Du 13 au 15 septembre 2018
IRMA
The 102th Encounter between Mathematicians and Theoretical Physicists will take place at Institut de Recherche Mathématique Avancée (University of Strasbourg and CNRS) on September 13-15, 2018. The theme will be : Combinatorics, topology, and biology.
The Encounter is dedicated to Bob Penner for his work on the subject.
Organizer : Athanase Papadopoulos (IRMA Strasbourg)
The invited speakers include :
- Norbert A’Campo (Basel)
- Serguei Barannikov (Paris)
- Ara Basmajian (New York)
- George Daskalopoulos (Providence)
- Bertrand Eynard (CEA)
- Louis Funar (Grenoble)
- Soren Galatius (Copenhagen and Stanford)
- Basilis Gidas (Providence)
- Sachiko Hamano (Osaka)
- Yi Huang (Beijin)
- Nariya Kawazumi (Tokyo)
- Thomas Koberda (University of Virginia)
- Maxim Kontsevich (IHES)
- Yusuke Kuno (Tokyo)
- Yuri Manin (Bonn)
- Mahan Mj (Tata inst. Bombay)
- Nadya Morozova (IHES)
- Ken'ichi Ohshika (Osaka)
- Alexei Sossinsky (Moscou)
- Scott Wolpert (Maryland)
- Sumio Yamada (Tokyo)
- Mahmoud Zeinalian (New York)
Venue : Salle de conférences, IRMA building, University of Strasbourg.
The talks will be in english. A large part of them will be survey talks intended for a general audience.
Graduate students and young mathematicians are welcome.
Registration is free of charge but the potential participants are asked to register by sending an email to the organizer, Athanase Papadopoulos.
For more information, please contact the organizer.
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Jeudi 13 septembre 2018
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09:00
Athanase Papadopoulos, Strasbourg
A few words about Bob Penner
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09:15
Norbert A'campo, Basel
Local Ehresmann structures on Brieskorn manifolds
By a real blow-up of the Pham spine in the Milnor fiber one gets a
model for the nearby fiber of the singularity $f=z_0^{a_0}+ \cdots + z_n^{a_n}$. It follows that its boundary, the Brieskorn manifold $M^{2n-1}_{a_0a_1 \cdots a_n}$, admits an Ehresmann structure modelled on the space $(SO(n+1),T_1^*(S^n))$.
A locally homogeneous Riemannian metric on many exotic spheres appears. -
10:00
Coffee Break
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10:45
Soren Galatius, Copenhagen and Stanford
Moduli spaces of graphs and Riemann surfaces, and the Grothendieck-Teichmüller group
Abstract: I will explain the words in the title, and a new connection between them. In cohomology, we get a strong non-vanishing result: the (4g-6)th Betti number of the moduli space of genus g Riemann surfaces at least (1.324^g + constant). Joint work with Melody Chan and Sam Payne. -
11:30
Thomas Koberda, Univ. of Virginia
Right-angled Artin subgroups of mapping class groups
Abstract: I will give a survey of the theory of right-angled Artin subgroups of mapping class groups. I will give some applications to the study of diffeomorphism groups. Some of this work is joint with Sang-hyun Kim -
13:45
Scott Wolpert, Maryland
TBA
TBA -
14:30
Nariya Kawazumi, Tokyo
Johnson homomorphisms and the Morita-Penner cocycle --- a survey
Abstract: The extended first Johnson homomorphism, introduced by S. Morita, is a cornerstone of the cohomology algebra of the mapping class group. In this talk we survey the Morita-Penner cocycle, which represents the first extended Johnson homomorphism on the dual fatgraph complex, and its later developments. -
15:15
Coffee Break
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15:45
Ara Basmajian, CUNY
The type problem and geometric structures on hyperbolic surfaces
Abstract: As part of an ongoing project we describe new results involving the relationship between Fenchel-Nielsen coordinates and a version of the classical type problem (whether or not the Riemann surface carries a Green's function) on infinite type surfaces. Since non-existence of a Green's function is equivalent to ergodicity of the geodesic flow we provide geometric criteria on any infinite type surface to guarantee such behavior. This is joint work with Hrant Hakobyan and Dragomir Saric -
16:30
Ken'ichi Ohshika, Osaka
Maximality of mapping class group actions
Abstract : I shall show that the following two results which I obtained in collaboration with A. Papadopoulos: (1) The group of self-homeomorphisms of measured lamination space preserving the intersection form coincides with the extended mapping class group. (2) The group of self-homeomoprhism of geodesic lamination space with asymmetric Hausdorff distance coincides with the extended mapping class group. -
19:30
Conference Dinner At The Restaurant Le Petit Bois Vert - Everybody Is Invided.
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Vendredi 14 septembre 2018
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09:00
Scott Wolpert, Maryland
A few words about Bob Penner
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09:15
Mahmoud Zeinalian, CUNY
From 2D Hyperbolic Geometry to the Loday-Quillen-Tsygan Theorem
Sbstract: The space of hyperbolic structures on an oriented smooth surface has a rich geometry. The study of the Hamiltonian flow of various energy functions associated with a collection of closed curves has led to a host of algebraic structures: first, on the linear span of free homotopy classes of non trivial closed curves (Wolpert-Godman-Turaev Lie bi-algebra) and then, more generally, on the equivariant chains on the free loop spaces of higher dimensional manifolds under the umbrella of String Topology (Chas-Sullivan + Others).
While it is understood that the most natural way to organize the relevant algebraic data would be through topological field theories whereby chains on the moduli space of Riemann surfaces with input and output boundaries label operations, various aspects of these structures are poorly understood.
In this talk, I will provide some historical context and report on recent relevant joint work with Manuel Rivera on algebraically modeling the chains on the based and free loop spaces. One tangible result is that the long held simply-connected assumptions in various theorems, such as Adams’s 1956 cobar construction, can be safely removed once a derived version of chains is utilized. Towards the end of the talk I will report on a related ongoing joint work with Owen Gwilliam and Gregory Ginot based on the celebrated Loday-Quillen-Tsygan theorem which calculates the Lie algebra cohomology of the matrix algebras of very large size. -
10:00
Coffee Break
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10:30
Bertrand Eynard, IPHT-CEA-Saclay, & CRM Montreal CA
Topological recursion: a recursive way of counting surfaces
Sbstract: The space of hyperbolic structures on an oriented smooth surface has a rich geometry. The study of the Hamiltonian flow of various energy functions associated with a collection of closed curves has led to a host of algebraic structures: first, on the linear span of free homotopy classes of non trivial closed curves (Wolpert-Godman-Turaev Lie bi-algebra) and then, more generally, on the equivariant chains on the free loop spaces of higher dimensional manifolds under the umbrella of String Topology (Chas-Sullivan + Others).
While it is understood that the most natural way to organize the relevant algebraic data would be through topological field theories whereby chains on the moduli space of Riemann surfaces with input and output boundaries label operations, various aspects of these structures are poorly understood.
In this talk, I will provide some historical context and report on recent relevant joint work with Manuel Rivera on algebraically modeling the chains on the based and free loop spaces. One tangible result is that the long held simply-connected assumptions in various theorems, such as Adams’s 1956 cobar construction, can be safely removed once a derived version of chains is utilized. Towards the end of the talk I will report on a related ongoing joint work with Owen Gwilliam and Gregory Ginot based on the celebrated Loday-Quillen-Tsygan theorem which calculates the Lie algebra cohomology of the matrix algebras of very large size. -
11:15
Nadya Morozova, IHES
Geometry of Morphogenesis
Abstract: Translation of molecular information in cells into precise predetermined geometrical shape of an organism is one of the most intriguing unsolved problems. We propose a theory of a geometry of morphogenesis based on seven postulates. The mathematical import and biological significance of the postulates will be discussed. The Morphogenesis Software built on these postulates, and a set of computational experiments done by this Software will be presented as a proof-of-concept of the proposed theory. -
13:45
Louis Funar, Grenoble
Discrete groups related to mapping class groups of infinite type surfaces
We consider some subgroups of mapping class groups of closed orientable surfaces punctured along a Cantor set
consisting of mapping classes of homeomorphisms having controlled behavior at infinity.
They occur as smooth mapping class groups of these surfaces when the Cantor set is standard.
We present some of their properties: they are finitely presented, closely related to Thompson groups,
pairwise non-isomorphic, not residually finite and dense inside the mapping class group. -
14:30
Yusuke Kuno, Tokyo
Formality of the Goldman-Turaev Lie bialgebra and the Kashiwara-Vergne problem
Abstract: For an oriented surface, the linear span of the free homotopy classes of loops in the surface has an interesting Lie bialgebra structure, called the Goldman-Turaev Lie bialgebra. I will talk about a formality question about this Lie bialgebra, which asks whether the structure is isomorphic to the naturally defined, associated graded version of it. I will explain that this question is closely related to the Kashiwara-Vergne problem, which originally came from Lie theory. -
15:15
Coffee Break
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15:45
Sachiko Hamano, Osaka
Variational formulas for hydrodynamic differentials and its applications
Abstract: A planar open Riemann surface admits the Schiffer span. Shiba showed that an open Riemann surface $R$ of genus one admits the hyperbolic span $\sigma(R)$, which gives a generalization of the Schiffer span and the size of ideal boundary of $R$. In this talk, we establish the variational formulas of hydrodynamic differentials (i.e., $L_s$-canonical semiexact differentials; $(-1< s \le 1)$) for the deformed open Riemann surfaces $R(t)$ of genus one with complex parameter $t$. As an application, we show the rigidity of $\sigma(R(t))$ under pseudoconvexity. -
16:30
Yi Huang, Beijing
A McShane identity for finite-area convex projective surfaces
The Teichmueller space T(S) for an orientable surface S is equivalent to the character variety of discrete faithful PSL(2,R) representations of the fundamental group of S. This approach to Teichmueller theory leads to a natural family of generalized Teichmueller spaces by increasing the rank of PSL(2,R) to PSL(n,R). For n=3, there is a geometric interpretation of this higher (rank) Teichmueller theory as the theory of strictly convex real projective structures on S. We show that there is a generalization of McShane's identity to this context: an infinite-series of an analytic expression involving geometric invariants of S, so that the series sums to 1. This is collaborative work with Zhe SUN, University of Luxembourg. -
17:30
Reception By The Mayor Of Strasbourg At The City Hall (place Broglie)
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Samedi 15 septembre 2018
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09:15
Sumio Yamada, Tokyo
The Einstein equation according to Hermann Weyl
Abstract: In 1917, H. Weyl had solved the Einstein equation with an axial symmetry by converting it to a Dirichlet problem over the upper half plane. One hundred years later, we solve the Einstein equation in 5 dimension by finding a harmonic map from the upper half plane to the symmetric space SL(3, R)/SO(3), under a certain axial symmetry condition. The new consequences in the century-old approach is that we can construct 5 dimensional spacetimes with various non-spherical 3-dimensional event horizons as well as various asymptotic ends -
10:00
Coffee Break
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10:30
Serguei Barannikov, IMJ-PRG Paris, NRU HSE Moscow
Summations over generalized ribbon graphs and all genus categorical Gromov-Witten invariants
The construction, starting form a derivation of cyclic associative/A_oo -algebra, whose square is nonzero in general, and defining cohomology classes of compactified moduli spaces of curves via summations over generalized ribbon graphs, was described in the works of the speaker about 10 years ago. The construction defines cohomological field theory. Conjecturally this construction produces categorical all-genus Gromov Witten invariants of mirror manifolds. Two simple byproducts will be also presented. One is a counterexample to a theorem of Kontsevich. Second is the formula for cohomology valued generating function for all products of psi classes of compactified moduli spaces of curves, which was the first nontrivial computation of categorical Gromov-Witten invariants of higher genus. -
11:15
Mahan Mj, Mumbai
Stable Random Fields, Bowen-Margulis measures and Extremal Cocycle Growth
Abstract: We establish a connection between extreme values of stable random fields arising in probability and groups G acting geometrically on CAT(-1) spaces X. The connection is mediated by the action of the group on its limit set equipped with the Patterson-Sullivan measure. Based on motivation from extreme value theory, we introduce an invariant of the action called extremal cocycle growth and show that its non-vanishing is equivalent to finiteness of the Bowen-Margulis measure for the associated unit tangent bundle U(X/G) provided X is not a tree whose edges are (up to scale) integers. We also establish an analogous statement for normal subgroups of free groups.