GAUGE-TOPOLOGY-SYMPLECTIC
January 31, 2020 3:30 pmSymplectic embedding problems are at the core of symplectic topology. Many results have been found involving balls, ellipsoids and polydisks. More recently, there has been progress on problems involving lagrangian...
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MATHEMATICAL PICTURE LANGUAGE
January 7, 2020 3:30 pmIn the search for finite temperature quantum memory, people have found an exotic 3D topological model, called the fracton model. A large class of them are known to have foliation...
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GAUGE-TOPOLOGY-SYMPLECTIC
December 6, 2019 3:30 pmThe Donaldson-Uhlenbeck-Yau theorem relates the existence of Hermitian-Yang-Mills connections over a compact Kahler manifold with algebraic stability of a holomorphic vector bundle. This has been extended by Bando-Siu in 1994 to a class...
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DIFFERENTIAL GEOMETRY
November 26, 2019 4:15 pmIn the last 35 years, geometric flows have proven to be a powerful tool in geometry and topology. The Mean Curvature Flow is, in many ways, the most natural flow...
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RANDOM MATRIX
November 20, 2019 3:15 pmLet $s_n(M_n)$ denote the smallest singular value of an $n\times n$ random matrix $M_n$. We will discuss a novel combinatorial approach (in particular, not using either inverse Littlewood--Offord theory or...
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NUMBER THEORY
November 20, 2019 3:00 pmIn a recent joint work with Kisin and Shin, we compared the Grothendieck-Lefschetz trace formula for abelian-type Shimura varieties with the stable Arthur-Selberg trace formulas. In this talk I will...
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OPEN NEIGHBORHOOD
November 13, 2019 4:30 pmConsider these basic questions: What can we say about finite sums of powers of consecutive whole numbers? What can we say about whole number solutions to polynomial equations? What about...
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DIFFERENTIAL GEOMETRY
November 12, 2019 4:15 pmThe Strominger-Yau-Zaslow conjecture predicts the existence of special Lagrangians fibration in Calabi-Yau manifolds near large complex structure limit. The SYZ conjecture has been an important guiding principle for mirror symmetry...
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