Abstracts

Sanjay Ramassamy (ENS de Lyon)
Title: Miquel dynamics for circle patterns
Abstract: Circle patterns are one of the ways to uniformize graphs on surfaces, by embedding them insuch a way that every face admits a circumcircle. In this talk I will describe a discrete-time dynamicalsystem on circle patterns with the combinatorics of the square grid. This dynamics, based on theclassical six-circles theorem of Miquel, is called Miquel dynamics. It was introduced by Richard Kenyon
as an attempt to find a connection between circle patterns and a model from statistical mechanics
called the dimer model. I will present some properties of this dynamics which suggest its integrability.
Partly joint work with Alexey Glutsyuk (ENS de Lyon/Higher School of Economics)
Denis Serre (ENS de Lyon)
Title: Divergence-free positive tensors ; applications to gas dynamics.
Abstract: For positive tensors T that satisfy Div T = 0, the determinant enjoys a curious integrability
property. One may relax the constraint by asking that Div T be a bounded measure. These results
contain, as a particular case, the isoperimetric inequality. An important application concerns gas
dynamics, where the conservation of mass and momentum can be written as Div T = 0. We obtain a
new fundamental estimate, in terms of a space-time integral. This can be done either for dense gases(Euler equations) or rarefied gases (Boltzmann equation).
Takahito Kashiwabara (The University of Tokyo)
Title: Semigroup approach and maximal-regularity theory for the primitive equations
Abstract: Analytic semigroup and maximal regularity are powerful tools to study nonlinear parabolicequations. In this talk, we apply these theories to study the primitive equations, which describe
large-scale motion of ocean or atmosphere and are obtained by assuming the hydrostatic balance in thevertical direction of the 3D Navier-Stokes equations. We establish existence and uniqueness of a
global-in-time strong solution to the primitive equations within the Lp -framework, either by analytic
semigroup approach or by maximal regularity. We will also discuss our recent results corresponding to
the end-point case p = ∞, whose proof essentially requires both of the two theories mentioned above.
Shigeki Aida (The University of Tokyo)
Title: Asymptotics of spectral gaps on infinite dimensional spaces
Abstract: Let E be a smooth function on RN and consider theR normalized probability measureµλ (dx) = Zλ−1 e−λE dx on RN and a Dirichlet form Eλ (f, f ) = RN |Df (x)|2 dµλ (x) on L2 (RN , µλ ). The
asymptotic behavior of the spectral gap of the generator of Eλ as λ → ∞ and related asymptotic
problems of the spectrum of Schrödinger operators −∆ + λ2 U on L2 (RN , dx) have been studied bymany researchers and many important results are obtained. In this talk, we discuss infinite dimensionalversion of this problem e.g. in the cases of loop spaces and spatially cut-off P (φ)2 -Hamiltonians.

1Marco Mazzucchelli (ENS de Lyon)
Title: Periodic orbits of Tonelli Hamiltonian systems on surfaces
Abstract: This talk is about the existence of periodic obits of classical Hamiltonian systems, often
called Tonelli or optical Hamiltonian systems, in the cotangent bundle of closed surfaces. This setting
encompasses several celebrated dynamical systems, such as the Riemannian and Finsler geodesic flows,
and the so called magnetic geodesic flows. After recalling the background, I will summarize some open
conjectures in the field, and present a few recent results, including the existence of remarkable action
minimizing periodic orbits and of infinitely many periodic orbits on almost all low energy levels.
Hideko Sekiguchi (The University of Tokyo)
Title: Representations of semisimple Lie groups and Penrose transform
Abstract: The classical Penrose transform is generalized to an intertwining operator on Dolbeault
cohomologies of complex homogeneous spaces X of (real) semisimple Lie groups. I plan to discuss adetailed analysis when X is an indefinite Grassmann manifold. To be more precise, we determine theimage of the Penrose transform, from the Dolbeault cohomology group on the indefinite Grassmann
manifold consisting of maximally positive k-planes in Cp,q (1 ≤ k ≤ min(p, q)) to the space ofholomorphic functions over the bounded symmetric domain. Furthermore, we prove that there is aduality between Dolbeault cohomology groups in two indefinite Grassmann manifolds, namely, that ofpositive k-planes and that of negative k-planes.
Valentin Seigneur (ENS de Lyon)
Title: Extending Morse functions from a neighborhood of the sphere to the ball
Abstract: Consider a smooth function defined in a neighborhood of the unit sphere in some euclidean
space. Assume this function has no critical point and that its restriction to the sphere is Morse. Can
one extend it to a function defined in the unit ball without critical points? We will discuss this question
when the dimension of the sphere is at least 6.
Oleksii Leontiev (The University of Tokyo)
Title: Symmetry breaking operators for the restriction of representations of indefinite orthogonal groups
O(p, q)Abstract: For the pair (G, G0 ) = (O(p + 1, q + 1), O(p, q + 1)), we construct and give a complete
classification of intertwining operators (symmetry breaking operators) between most degenerate
spherical principal series representations of G and those of the subgroup G0 , extending the work
initiated by Kobayashi and Speh [Mem. Amer. Math. Soc. 2015] in the real rank one case where q = 0.
Functional identities and residue formulae of the regular symmetry breaking operators are also providedexplicitly. This is a joint work with T. Kobayashi.

2Takeshi Tsuji (The University of Tokyo)
Title: Recent progress in integral p-adic Hodge theory
Abstract: A few years ago, Bhatt, Morrow, and Scholze introduced a new cohomology theory, which
gives us a way to compare integral p-adic cohomologies (p-adic etale, crystalline, and de Rham) ofdegree higher than p for varieties with good reduction over a p-adic field. After briefly reviewing resultsin p-adic Hodge theory known before their work, I will survey the new theory and some developments
afterward (on p-adic vanishing cycles, semi-stable reduction case, cohomologies with coefficientsc).
Laurent Berger (ENS de Lyon)
Title: The Nottingham group
Abstract: Abstract: The Nottingham group is a group of power series with coefficients in a finite field,
the group operation being composition of power series. It is an object of interest to number theorists
and (more recently) group theorists. I will discuss some features of this group, and of the arithmetic ofthese power series.

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