The informal seminar is open to all visitors at IHES and researchers and students in the Paris area. We aim at keeping the informality, which implies, many (friendly) interruptions, many (naive and basic, occasionally smart) questions, spontaneous (blackboard only, sometimes unfinished) talks, and a welcoming atmosphere. We expect the seminars to be in English only.
Organizers: Thierry Bodineau, Piet Lammers, Yilin Wang
If you want to be added to the mailing list, please write to Yilin (yilin@ihes.fr)
Past Sessions
Time and place:
IHES, Amphi Motchane, Fridays at 2 pm (unless indicated otherwise)
Up-coming sessions
Friday September 22
Nicolas Curien (Paris Saclay)
Ideal Poisson-Voronoi tiling
We study the limit in low intensity of Poisson--Voronoi tessellations in hyperbolic spaces.
In contrast to the Euclidean setting, a limiting non-trivial ideal tessellation appears as the intensity tends to 0. The tessellation obtained is a natural Möbius-invariant decomposition of the hyperbolic space into countably many infinite convex polytopes, each with a unique end. We study its basic properties, in particular the geometric features of its cells.
Based on joint works with Matteo d'Achille, Nathanel Enriquez, Russell Lyons and Meltem Unel.
Friday October 13
Max Fathi ( LJLL and LPSM)
Globally lipschitz transport maps
One way of proving probabilistic functional inequalities (concentration inequalities, logarithmic Sobolev inequalities...) is to use a change of variables, to transfer them from a simple reference measure (typically, Gaussian) to more general settings. One example of this is the Caffarelli contraction theorem, which states that uniformly log-concave measures can be realized as images of standard Gaussian measures by globally lipschitz maps, using the L2 optimal transport map. One open problem in this direction is to find an analogue of Caffarelli's theorem in the Riemannian setting.
In this talk, I will present a stochastic construction of non-optimal maps, due to Kim and Milman, and Lipschitz estimates in various settings, including certain measures on Riemannian manifolds. Joint work with Dan Mikulincer and Yair Shenfeld.
Friday November 3
Elton Hsu (Northwestern)
Friday November 10
Masha Gordina (University of Connecticut)
Friday November 17
Paul Melotti (Paris - Saclay)
Friday December 1
Nicolas Curien (Paris Saclay)
Ideal Poisson-Voronoi tiling
We study the limit in low intensity of Poisson--Voronoi tessellations in hyperbolic spaces.
In contrast to the Euclidean setting, a limiting non-trivial ideal tessellation appears as the intensity tends to 0. The tessellation obtained is a natural Möbius-invariant decomposition of the hyperbolic space into countably many infinite convex polytopes, each with a unique end. We study its basic properties, in particular the geometric features of its cells.
Based on joint works with Matteo d'Achille, Nathanel Enriquez, Russell Lyons and Meltem Unel.
Friday October 13
Max Fathi ( LJLL and LPSM)
Globally lipschitz transport maps
One way of proving probabilistic functional inequalities (concentration inequalities, logarithmic Sobolev inequalities...) is to use a change of variables, to transfer them from a simple reference measure (typically, Gaussian) to more general settings. One example of this is the Caffarelli contraction theorem, which states that uniformly log-concave measures can be realized as images of standard Gaussian measures by globally lipschitz maps, using the L2 optimal transport map. One open problem in this direction is to find an analogue of Caffarelli's theorem in the Riemannian setting.
In this talk, I will present a stochastic construction of non-optimal maps, due to Kim and Milman, and Lipschitz estimates in various settings, including certain measures on Riemannian manifolds. Joint work with Dan Mikulincer and Yair Shenfeld.
Friday November 3
Elton Hsu (Northwestern)
Friday November 10
Masha Gordina (University of Connecticut)
Friday November 17
Paul Melotti (Paris - Saclay)
Friday December 1
Past Seminars
Friday September 15
Marco Carfagnini (UC San Diego)
Spectral gaps via small deviations
In this talk we will discuss spectral gaps of second order differential operators and their connection to limit laws such as small deviations and Chung’s laws of the iterated logarithm. The main focus is on hypoelliptic diffusions such as the Kolmogorov diffusion and horizontal Brownian motions on Carnot groups. If time permits, we will discuss spectral properties and existence of spectral gaps on general Dirichlet metric measure spaces.This talk is based on joint works with Maria (Masha) Gordina and Alexander (Sasha) Teplyaev.
Marco Carfagnini (UC San Diego)
Spectral gaps via small deviations
In this talk we will discuss spectral gaps of second order differential operators and their connection to limit laws such as small deviations and Chung’s laws of the iterated logarithm. The main focus is on hypoelliptic diffusions such as the Kolmogorov diffusion and horizontal Brownian motions on Carnot groups. If time permits, we will discuss spectral properties and existence of spectral gaps on general Dirichlet metric measure spaces.This talk is based on joint works with Maria (Masha) Gordina and Alexander (Sasha) Teplyaev.
@ IHES, Bures-sur-Yvette, France
