Monday, October 24, 2022
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All day |
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3pm |
10/24/2022 - 3:00pm Abstract: We describe remarkable nonlinear analytic approximation tools in the classical setting of Hardy spaces in the upper half plane, and show how to transfer them to the higher dimensional real setting of harmonic functions in upper half spaces. It is known [6] that all harmonic functions in higher dimensions are combinations of holomorphic functions on 2 dimensional planes, extended as, constant in normal directions. We derive representation theorems, with corresponding isometries, opening the door for applications in higher dimensions, to the processing of highly oscillatory multidimensional signals. Authors: Ronald R. Coifman, Jacques Peyrière, Guido Weiss Location:
AKW 200
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4pm |
10/24/2022 - 4:00pm Let $\mathcal{S}$ be a complete hyperbolic surface and consider the horocycle flow on its unit tangent bundle $T^1\mathcal{S}$. Whenever $\mathcal{S}$ is geometrically finite, it is well known that all horocycle orbits are either closed or dense in $\mathcal{E} \subseteq T^1\mathcal{S}$, the non-wandering set for the horocycle flow. We consider $\mathbb{Z}$-covers of compact surfaces, arguably the simplest examples of geometrically infinite surfaces, and study the possible horocycle orbit closures that they carry. We show that the structure of the orbit closures in such covers is delicately dependant on the particular geometry of the covered compact surface and allow for wide variability. We present a construction of a family of surfaces for which a complete explicit orbit closure classification is given. Based on joint work in progress with James Farre and Yair Minsky. Location: 10/24/2022 - 4:30pm I will present recent results about Homological mirror symmetry (HMS) of algebraic symplectic varieties coming from representation theory. The first is about HMS of the universal centralizer of a complex reductive group G. The second, which is a joint work with Yun, is about HMS of a moduli space of Higgs bundles on P^1 with certain automorphic data. The latter variety is closely related to the first one as it is a symplectic compactification of the former. No prior knowledge about HMS is required. Location:
LOM214
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