Monday, February 14, 2022
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All day |
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4:00pm |
02/14/2022 - 4:00pm Let $\Gamma$ be a Gromov-hyperbolic group and $S$ a finite symmetric generating set. The choice of $S$ determines a metric on $\Gamma$ (namely the graph metric on the associated Cayley graph). Given a representation $\rho: \Gamma \to GL_d(\mathbb R)$, we are interested in obtaining results analogous to random matrix products theory (RMPT) but for the deterministic sequence of spherical averages (with respect to $S$-metric). We will discuss a general law of large numbers and more refined limit theorems such as central limit theorem and large deviations. If time allows, we will also see boundary limit theorems and convergence of interpolated matrix norms along geodesic rays to the standard Brownian motion. The connections with (and results in) the classical RMPT, a result of Lubotzky–Mozes–Raghunathan and a question of Kaimanovich–Kapovich–Schupp will be discussed. Joint work with S. Cantrell. Location:
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02/14/2022 - 4:30pm Abstract: A compact hyper-Kähler manifold is a higher dimensional generalization of a K3 surface. An elliptic fibration of a K3 surface correspondingly generalizes to the so-called Lagrangian fibration of a compact hyper-Kähler manifold. It is known that an elliptic fibration of a K3 surface is always "self-dual" in a certain sense. This turns out to be not the case for higher-dimensional Lagrangian fibrations. In this talk, I will propose a construction for the dual Lagrangian fibration of all currently known examples of compact hyper-Kähler manifolds, and try to justify this construction. Location:
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