Du 7 au 9 juin 2018
IRMA
The 101th Encounter between Mathematicians and Theoretical Physicists will take place at Institut de Recherche Mathématique Avancée (University of Strasbourg and CNRS) on June 7-9, 2018. The theme will be : Geometry, topology of manifolds, and physics.
The Encounter is dedicated to Vladimir Turaev for his work on the subject.
Organizer : Athanase Papadopoulos (IRMA Strasbourg)
The invited speakers include :
- Norbert A'Campo (Basel)
- Jørgen Ellegaard Andersen (Aarhus)
- Gourab Bhattacharya (IHES)
- Qingtao Chen (Zurich)
- François Costantino (Toulouse)
- Dale Husemoller (MIP Bonn)
- Rinat Kashaev (Genève)
- Toshikate Kohno (Tokyo)
- Gwenael Massuyeau (Dijon)
- Nadya Morozova (IHES)
- Hugo Parlier (Luxembourg)
- Robert C. Penner (IHES)
- Arkady Plotnitsky (Purdue)
- Valentin Poenaru (IHES)
- Vladimir Turaev (Bloomington)
- Muhammed Uludag (Istanbul)
- Oleg Viro (Stony Brook)
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 7 juin 2018
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09:00
Norbert A'campo, Basel
Combinatorics of special mapping classes
A tête-à-tête graph on a compact surface with boundary defines a mapping class with support in a regular neighborhood of the graph. This construction was used and extended by Christian Graf, Pablo Portilla Cuadrada, Javier Fernandez de Bodabilla, Maria Pe Pereira, Baldur Sigurdsson in order to obtain new insight for the study of special mapping classes, such as being of finite order, being a root of a Dehn twist, or being the local geometric monodromy of curve singularity on a singular complex surface. -
10:00
Coffee Break
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10:30
Oleg Viro, Stony Brook
A tribute to Vladimir Turaev, I
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10:45
Vladimir Turaev, Indiana
Brackets and double brackets in topology of manifolds
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11:45
Hugo Parlier, Luxembourg
Hyperbolic surfaces, simple closed geodesics and moduli spaces
Abstract: This talk will be about various properties of simple closed geodesics on hyperbolic surfaces and how this relates to underlying moduli spaces. A particular focus will be given to quantifications of a result of Birman and Series which states that simple closed geodesics are nowhere dense on a given closed hyperbolic surface. -
14:30
Gourab Bhattacharya, IHES
Stability Structures on Varieties, and String Theory
Abstract: I shall discuss the evolution and role of "Bad Group Actions" on varieties and how String theory manages and gives inputs to understand various Quotient Structures and their Moduli Spaces. If time permits, the future directions and various links to other branches of Mathematics may be described, namely with Resurgence, Higher Teichmüller Theory of Fock-Goncharev, and Gaiotto-Moore-Nietzke's Spectral Networks. -
15:30
Coffee Break
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16:00
Francesco Costantino, Toulouse
Modified traces and non semi-simple TQFTs
Abstract: After recalling how link invariants are obtained from ribbon categories, we will discuss how the introduction of modified traces allows to extend these constructions. Then we will review how to build three manifold invariants out of the link invariants associated to modular categories. We will in particular recall the example issued from the representation theory of U_q(sl_2) at roots of unity. Then we will outline the construction of the non semi-simple TQFTs based on the modified link invariants in the case of U_q(sl_2). -
17:00
Arkady Plotnitsky, Purdue
Heisenberg's purely algebraic method: geometry, algebra, and probability in quantum theory
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19:30
Conference dinner at the restaurant Le Petit Bois Vert - everybody is invited.
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Vendredi 8 juin 2018
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09:00
Toshikate Kohno, The university of Tokyo
Higher category extensions of KZ connections and representations of braid cobordisms
We explain a method to construct higher category extensions of
holonomy representations of homotopy path groupoids
by means of Chen's formal homology connections.
As an application, using a 2-functor from the path
2-groupoid of configuration spaces, we construct
representations of the 2-category of braid cobordisms.
We also discuss categorification of KZ connections. -
10:00
Coffee break
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10:30
Valentin Poenaru, Orsay
On geometric group theory
This will be a talk for large audience. After showing the connections of finitely presented groups with algebraic topology, mathematical logic and metric geometry, we will talk about the old classical notion of simple connectivity at infinity, for groups. A bit of history will be presented too.We will then introduce the modern ,revamped version of this asymptotic property, the QSF of Brick, Mihalik and Stallings and briefly present Po's recent result on the topic. -
10:30
Athanase Papadopoulos, Strasbourg
A tribute to Vladimir Turaev, II
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11:30
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. -
14:30
Muhammed Uludag, Galatasaray University, Istanbul
Mapping Class Groupoids, Thompson's groups and outer automorphism groups of free groups
Abstract : We concoct a uniform treatment of mapping class groupoids and Thompson's groups thereby introducing their hybrid groupoids. As a by-product we obtain a description of the outer automorphism group of free groups as the isotropy group of a groupoid, which extends the mapping class groupoid of Mosher and Penner. We illustrate some arithmetic aspects of these groupoids at the end of our talk -
15:30
Coffee break
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16:00
Gwenael Massuyeau, Dijon
Intersection and self-intersection operations on surfaces
Abstract: Turaev introduced in 1978 two operations on the fundamental group of a surface with boundary. The first operation measures the "homotopy" intersection of two loops on a surface; nowadays, it is known to control the Atiyah-Bott Poisson structures on representation spaces of surface groups, and to have generalizations for higher-dimensional manifolds. As for the second operation, it measures the "homotopy" self-intersection of a single loop, and it appears to be more mysterious than the first one. In this talk, we will survey these loop operations before addressing the problem of their formal descriptions. -
17:00
Bob Penner, IHES et UCLA
The Lie algebra of homeomorphisms of the circle (revisited)
The space of tesselations of the the Poincaré disk with a distinguished oriented edge can be identified with the space of orientation-preserving homeomorphims of the circle, and by analogy with decorated Teichmüller theory, much structure results. Specifically, there are global coordinates together with a mapping class group-like action and an invariant two-form. Infinitesimally on the quotient by the Möbius group, one finds a natural tangent space at the identity which plays the role of the Lie algebra for the topological group. Work starting 25 years ago on this universal Teichmüller space has been re-invigorated by certain recent developments, and we shall report on various aspects of this long-term project. -
18:30
Reception by the mayor of Strasbourg at the City Hall (place Broglie)
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Samedi 9 juin 2018
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09:00
Rinat Kashaev, Genève
Symmetric matrices associated with oriented link diagrams
Abstract: Motivated by metaplectic invariants of Goldschmidt–Jones, generalizing the cyclotomic invariants of Kobayashi–Murakami–Murakami, I will explain a construction which associates to each oriented link diagram a symmetric matrix with elements being quadratic polynomials in one indeterminate with integer coefficients. Based on a slightly modified S-equivalence of Trotter and Murasugi in the space of symmetric matrices, the construction gives rise to an invariant of oriented links. In particular, the signature of the matrix is conjecturally related to the Tristram–Levine signature function
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10:00
Coffee break
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10:30
Norbert A'campo, Basel
A tribute to Vladimir Turaev, III
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10:45
Qingtao Chen, Zurich
Recent progress of various Volume Conjectures for links as well as 3-manifolds
Abstract:
The original Volume Conjecture of Kashaev-Murakami-Murakami predicts a precise relation between the asymptotics of the colored Jones polynomials of a knot in S^3 and the hyperbolic volume of its complement. I will discuss two different directions that lead to generalizations of this conjecture.
The first direction concerns different quantum invariants of knots, arising from the colored SU(n) (with the colored Jones polynomial corresponding to the case n= 2). I will first display subtle relations between congruence relations, cyclotomic expansions and the original Volume Conjecture for colored Jones polynomials of knots. I will then generalize this point of view to the colored SU(n) invariant of knots. Certain congruence relations for colored SU(n) invariants, discovered in joint work with K. Liu, P. Peng and S. Zhu, lead us to formulate cyclotomic expansions and a Volume Conjecture for these colored SU(n) invariants. If time permits, I will briefly discuss similar ideas for the superpolynomials that arise in HOMFLY-PT homology.
Another direction for generalization involves the Witten-Reshetikhin-Turaev and (modified) Turaev-Viro quantum invariants of 3-manifolds. In a joint work with T. Yang, we formulated a new Volume Conjecture for the asymptotics of these 3-manifolds invariants evaluated at certain roots of unit, and numerically checked it for many examples. Interestingly, this conjecture uses roots of unity that are different from the one usually considered in literature. This may indicate that the understanding of this new phenomenon requires new physical and geometric interpretations that go beyond the usual quantum Chern-Simons theory. I will also introduce the current status of different group of people studying these new Volume Conjectures which include a work on Krillov-Reshetikhin quantum 6j-symbols did by J. Murakami & myself.
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11:45
Jørgen Ellegaard Andersen, Aarhus
Geometric Recursion
Abstract:
Geometric Recursion is a very general machinery for constructing mapping class group invariants objects associated to two dimensional surfaces. After presenting the general abstract setup 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 and Zeta-functions based on the simpel closed geodesic length spectrum. We shall see how Geometric Recursion provides us with a kind of categorification of Topological Recursion, namely any application of Topological Recursion can be lifted to a Geometric Recursion setting involving continuous functions on Teichmüller space, where the connection back to Topological Recursion is obtained by integration over the moduli space of curve. We will end the talk by applying the machinery to obtain interesting results on expectation values of various statistics of length of simple closed geodesic over moduli spaces of hyperbolic surfaces. The work presented is joint with G. Borot and N. Orantin.