Meeting on Arithmetic groups, Topology and Automorphic forms
Arithmetic lattices are central to the theory of automorphic forms, whose main objects of study are functions with invariance properties with respect to arithmetic groups. The cohomology of these groups is thus a particular instance which is relatively easily accessible and has been the focus of much study over the past years. It also relates to their deformation theory.
More recently it has been realised that mapping class groups of surfaces admit many representations to certain arithmetic groups. These representations originally come from so-called TQFTs but are realised very concretely by matrix generators. Despite being well-studied the remain quite mysterious, in particular their rigidity properties are still not well-understood.
The aim of this short meeting is to bring together, on a mostly local scale, people interested in these two fields and see what interactions this may bring to light through expository talks on both topics and discussion sessions.
The meeting will take place at the Institut des hautes études scientifiques. Financial and admnistrative support is provided by the IHES, université Aix--Marseille and ANR through the AGDE grant.
Contact : Amina Abdurrahman (amina@ihes.fr), Léo Bénard (leo.BENARD@univ-amu.fr), Jean Raimbault (jean.raimbault@univ-amu.fr).
More recently it has been realised that mapping class groups of surfaces admit many representations to certain arithmetic groups. These representations originally come from so-called TQFTs but are realised very concretely by matrix generators. Despite being well-studied the remain quite mysterious, in particular their rigidity properties are still not well-understood.
The aim of this short meeting is to bring together, on a mostly local scale, people interested in these two fields and see what interactions this may bring to light through expository talks on both topics and discussion sessions.
The meeting will take place at the Institut des hautes études scientifiques. Financial and admnistrative support is provided by the IHES, université Aix--Marseille and ANR through the AGDE grant.
Contact : Amina Abdurrahman (amina@ihes.fr), Léo Bénard (leo.BENARD@univ-amu.fr), Jean Raimbault (jean.raimbault@univ-amu.fr).
Participants
- Amina Abdurrahman
- Léo Bénard
- Pierre Charollois
- Lilou Domingues
- Sami Douba
- Pierre Godfard
- Katia Hadj Said
- Veronica Fantini
- Julien Marché
- Arnaud Maret
- Gregor Masbaum
- Joan Porti
- Jean Raimbault
- Ramanujan Santharoubane
- Franco Vargas Pallete
Schedule
| Lundi | Mardi | Mercredi | |
|---|---|---|---|
| 9h30-10h30 | Franco Vargas Pallete | Sami Douba | |
| 11h-12h | Pierre Charollois | Joan Porti | |
| 14h-15h | Gregor Masbaum | ||
| 15h30-16h30 | Arnaud Maret | Ramanujan Santharoubane | |
| 17h-18h | Veronica Fantini | Julien Marché (TBC) |
Abstracts
Pierre Charollois
TBA: TBA
Sami Douba
Negative curvature, unipotents, and rational entries: We discuss various questions surrounding the relationship between negative/nonpositive curvature of finitely generated groups and the availability of faithful linear representations containing no nontrivial unipotents and consisting entirely of rational matrices.
Veronica Fantini
Resurgence and summability for perturbative invariants of knots: Motivated by complex Chern-Simons theory, a perturbative approach to quantum invariants of knots and 3-manifolds has been extensively studied. In a nutshell, new invariants have been defined in the form of divergent power series (e.g. Dimofte–Garoufalidis perturbative invariant of hyperbolic knots, the Ohtsuki series of homology 3-spheres, etc.), which should agree with the all-order asymptotics of the non-perturbative invariants (e.g. the Kashaev invariant, the Andersen–Kashaev state integral, the Witten–Reshetikhin–Turaev invariant, the Gukov–Pei–Putrov–Vafa invariant, etc.). In this talk, I will discuss the approach of resurgence and Borel-Laplace summability to the study of perturbative invariants of knots. These techniques are commonly used to study divergent power series and allow us to understand the relationship between perturbative and non-perturbative invariants.
Julien Marché
TBA: TBA
Arnaud Maret
TBA: TBA
Gregor Masbaum
TBA: TBA
Joan Porti
Character varieties in characteristic p: The variety of SL2(C) characters of a finitely generated group is defined by polynomials with rational coefficients. In fact they are dyadic, eg lie in Z[1/2], so for a prime p>2 we may consider the reduction mod p of the variety of characters, and this yields the variety of characters in SL2(Fp) for an algebraically closed field Fp of characteristic p. The goal of the talk is to provide examples of ramifications, and I have more questions than results.
Ramanujan Santharoubane
TBA: TBA
Franco Vargas Pallete
TBA: TBA
