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DynamIC Seminars (Complete List)

Name Title Date Time Room
Yi Shi (Peking University)Spectral rigidity and joint integrability for Anosov diffeomorphisms on tori (Zoom talk) Abstract: In this talk, we address the strong rigidity properties from joint integrability in the setting of Anosov diffeomorphisms on tori. More specifically, for an irreducible Anosov diffeomorphism with split stable bundle, the joint integrability of the strong stable and full unstable subbundles implies the existence of fine dominated splitting along the weak stable subbundle as well as Lyapunov exponents rigidity. This builds an equivalence bridge between the geometric rigidity (joint integrability) and dynamical spectral rigidity (Lyapunov exponents rigidity) for Anosov diffeomorphisms on tori. This talk is based on a joint work with A. Gogolev. Tuesday, 29 November 2022 13:00 Huxley 410
Timothée Benard (University of Cambridge)Local limit theorem on nilpotent Lie groupsAbstract: We prove the local limit theorem for biased random walks on a simply connected nilpotent Lie group G. The result allows to approximate at scale 1 the n-step distribution of a walk by the time n of a smooth diffusion process for a new group structure on G. We also show this approximation is robust under deviation. The proof uses a Gaussian replacement scheme, combining Fourier analysis and a swapping argument inspired by the work of Diaconis-Hough. As a consequence, we obtain a probabilistic version of Ratner's theorem: Ad-unipotent random walks on finite-volume homogeneous spaces equidistribute toward algebraic measures. Joint work with Emmanuel Breuillard. Tuesday, 6 December 2022 13:00 Huxley 410
Alexandre Rodrigues (University of Porto)Stability of heteroclinic cycles: a new approachAbstract: In this informal talk, I discuss the stability of cycles within a heteroclinic network formed by different cycles, for a one-parameter model developed in the context of game theory. I describe an asymptotic technique to decide which cycle (within the network) is visible in numerics. The technique consists of reducing the relevant dynamics to a suitable one-dimensional map -- the projective map. Stability of the fixed points of the projective map determines the stability of the associated cycles. All concepts will be gently introduced and the talk will be accessible to non-specialists. This is a joint work with Telmo Peixe (ISEG, CEMAPRE). Tuesday, 13 December 2022 13:00 Huxley 642

DynamIC Workshops and Mini-Courses (Complete List)

Title Date Venue
Mini-Workshop on Heterodimensional DynamicsWednesday, 2 November 2022Imperial College London
Online Workshop on Critical Transitions in Complex SystemsWednesday, 29 July 2020 – Friday, 31 July 2020online

Short-term DynamIC Visitors (Complete List)

Yi Shi Peking University Tuesday, 29 November 2022 Tuesday, 29 November 2022
Timothée Benard University of Cambridge Tuesday, 6 December 2022 Tuesday, 6 December 2022
Alexandre Rodrigues University of Porto Tuesday, 13 December 2022 Tuesday, 13 December 2022