Wednesday, December 15, 2021
Time | Items |
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All day |
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2pm |
12/15/2021 - 2:30pm Abstract: In this talk, I will describe a new class of methods for estimating a low-rank matrix from a noisy observed matrix, where the error is measured by a type of weighted loss function. Such loss functions arise naturally in problems such as submatrix denoising, heteroscedastic noise filtering, and estimation with missing data. I will introduce a family of spectral denoisers, which preserve the left and right singular subspaces of the observed matrix. I will also show how denoising with weighted loss yields a new approach to unweighted denoising that is asymptotically at least as good as singular value shrinkage, and can perform better when the matrix is heterogeneous. I will demonstrate the behavior of the method through numerical simulations. Location:
https://yale.zoom.us/j/97458245891
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4pm |
12/15/2021 - 4:15pm Abstract: L-functions of number fields, elliptic curves, and other objects of diophantine geometry, are ubiquitous in number theory, but their study almost always relies on the Langlands correspondence, which predicts that they encode “eigenfrequencies” of arithmetic manifolds, and realizes them as “period integrals” of automorphic forms on such manifolds (e.g., of modular forms). After introducing these notions, I will explain how the idea of quantization of symplectic manifolds can provide a symmetric interpretation of the duality between L-functions and periods (based on ongoing joint work with D. Ben-Zvi and A. Venkatesh), and will present evidence for its relevance to the Langlands functoriality conjecture (“different arithmetic drums share the same eigenfrequencies”), based on recent work of mine on the rank-1 case. Location: |