Monday, October 10, 2022
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All day |
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3pm |
10/10/2022 - 3:00pm Abstract: Suppose you observe very few entries from a large matrix. Can we predict the missing entries, say assuming the matrix is (approximately) low rank? We describe a very simple method to solve this matrix completion problem. We show our method is able to recover matrices from very few entries and/or with ill conditioned matrices, where many other popular methods fail. Furthermore, due to its simplicity, it is easy to extend our method to incorporate additional knowledge on the underlying matrix, for example to solve the inductive matrix completion problem. On the theoretical front, we prove that our method enjoys some of the strongest available theoretical recovery guarantees. Finally, for inductive matrix completion, we prove that under suitable conditions the problem has a benign optimization landscape with no bad local minima. Joint work with Pini Zilber. Bio: Boaz Nadler received his Ph.D. at Tel Aviv University. After 3 years as a Gibbs instructor/assistant professor at Yale University, he joined the faculty at the department of computer science and applied mathematics at the Weizmann Institute of Science. His research interests span mathematical statistics, machine learning, applied mathematics, and various applications, including optics and signal processing. Location:
AKW 200
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4pm |
10/10/2022 - 4:30pm Let X and Y be compact hyper-Kahler manifolds deformation equivalent to the Hilbert scheme of n points on a K3 surface. A cohomology class in their product XxY is an analytic correspondence, if it belongs to the subalgebra generated by Chern classes of coherent analytic sheaves. Let f be a Hodge isometry of the second rational cohomologies of X and Y with respect to the Beauville-Bogomolov-Fujiki pairings. We prove that f is induced by an analytic correspondence. We furthermore lift f to an analytic correspondence F between their total rational cohomologies, which is a Hodge isometry with respect to the Mukai pairings, and which preserves the gradings up to sign. When X and Y are projective the correspondences f and F are algebraic. The case n=1 (when X and Y are K3 surfaces) was known as the Shafarevich conjecture and was solved by Nikolay Buskin in 2015 using work of Mukai. The higher dimensional case is based on recent results on equivalences of derived categories of hyperkahler varieties due to Taelman. We will also comment on the analogous result for hyperkahler manifolds of generalized Kummer deformation type (work in progress). Location:
LOM214
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