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Flops of any length, Gopakumar-Vafa invariants and 5d Higgs Branches

Geometry and Physics Seminar
Recent theoretical advances in non convex optimization

Abstract In this report, we give an overview of recent theoretical results on global performance guarantees of optimization algorithm for non convex optimization about deep neural network and data
探索神经网络解微分方程的理论与应用

Abstract 在这个报告中，我将讨论我们组在神经网络方法解微分方程这个领域的探索。内容包括1）从频率角度理解神经网络方法的特点，并提出多尺度网络结构；2）算子学习的特点以及在反问题的应用；3）解高维刚性常...
High-order bound-preserving numerical methods for chemically reacting flows

Abstract Chemically reacting flows have many applications in combustion. There are several difficulties in constructing high-order numerical methods: (1) Due to the rapid reaction rate, the system
Generalized complexity and Mukai’s type conjecture.

Abstract We discuss some variants of Mukai’s conjecture for the characterization of projective spaces. We discuss the relation of the complexity of generalized pairs and such kind conjectures. I w...
A Type of Robust Bound-preserving MUSCL-Hancock Schemes

Abstract The MUSCL-Hancock upwind scheme, as a variation of the MUSCL scheme, only do the initial data reconstruction once in every cell and solve the Riemann problem once at every cell interface i...
Abstract Consider the action of GL_d(Z) on the d-dimensional torus R^d/Z^d. Given a probability

Abstract Chemically reacting flows have many applications in combustion. There are several difficulties in constructing high-order numerical methods: (1) Due to the rapid reaction rate, the system
On the statistics of irreducible subrepresentations in large tensor powers of finite dimensional

Abstract I will explain the solution to the following problem. Given a finite dimensional irreducible representation of a simple Lie algebra, consider its N-th tensor power. It has a decomposition ...
Quantitative equidistribution of linear random walk on the torus

Abstract Consider the action of GL_d(Z) on the d-dimensional torus R^d/Z^d. Given a probability measure on GL_d(Z) and a point on the torus, a random walk is defined. In this talk, I will report so...
On a generalized Kashiwara-Kawai theorem for tame harmonic bundles

Abstract In the 1980s, there was significant progress in the $L^2$-theory of polarized variations of Hodge structure on higher dimensional varieties. In particular, according to the celebrated

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