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In this talk, the dispersive revival and fractalization phenomena for bidirectional dispersive equations on a bounded interval subject to periodic boundary conditions and discontinuous initial profile...
In this talk, we report several very recent asymptotic results on certain classical geometric quantities viewed as random variables on the moduli space of Riemann surfaces for large genus (and many cu...
We single out a notion of staticity which applies to any domain in hyperbolic space whose boundary is a non-compact totally umbilical hypersurface. For (time-symmetric) initial data sets modeled at in...
In this talk, I will introduce our recent result on Heintze Karcher type inequalities for capillary hypersurfaces supported on different types of umbilical hypersurfaces in hyperbolic space. I will in...
I will present the joint work with Jialun Li and Pratyush Sarkar in the talk. As a final work to establish that the frame flows for geometrically finite hyperbolic manifolds of arbitrary dimensions ar...
I will present the joint work with Jialun Li and Pratyush Sarkar in the talk. As a final work to establish that the frame flows for geometrically finite hyperbolic manifolds of arbitrary dimensions ar...
In this talk, we discuss Y. Wei, B. Yang and T. Zhou’s preprint arXiv:2210.06035, in which they consider volume preserving curvature flows of smooth, closed and convex hypersurfaces in hyperbolic spac...
We show that for arbitrary fixed conjugacy classes C1, . . . , Cl, l ≥ 3, of loxodromic isometries of the two-dimensional complex or quaternionic hyperbolic space there exist isometries g1, . . . , gl...
THE SYMPLECTIC GEOMETRY OF POLYGONS IN HYPERBOLIC 3-SPACE.
We extend a one-dimensional central-scheme first introduced by Liu and Tadmor, to the rather general framework of two-dimensional systems of conservation laws. This scheme is based on a two-dimensiona...
We establish stable ergodicity of diffeomorphisms with partially hyperbolic attractors whose Lyapunov exponents along the central direction are all negative with respect to invariant SRBmeasur...
Mathematical theory of billiards is a fascinating subject providing a fertile source of new problems as well as conjecture testing in dynamics, geometry, mathematical physics and spectral theory. Th...
One of the major discoveries of the 20th century mathematics is the possibility of random behavior of deterministic systems. There is a hierarchy of chaotic properties for a dynamical systems but on...
We study compact group extensions of hyperbolic diffeomorphisms. We relate mixing properties of such extensions with accessibility properties of their stable and unstable laminations. We show that g...
We show that a smooth compact Riemannian manifold of dimension  2 admits a Bernoulli di eomorphism with nonzero Lyapunov exponents.

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