From Industrial Software to Artificial Intelligence: Intelligent Engines of Scientific Breakthroughs and Technological Innovations

Abstract: Industrial software is the weakest component in the entire Chinese industrial system. Its research and application in China lag far behind those in developed Western countries, with over 80% of key industrial software reliant on imports. It is currently a critical technology that has challenged scientific breakthroughs and technological innovations in this country, particularly with t...

报告人：Zhangxing Chen

Instance-dependent Sample Complexity for Bilinear Saddle Point Optimization with Noisy Feedback: An LP-Based Approach

Abstract: In this work, we study the sample complexity of finding a Nash Equilibrium (NE) of two-player zero-sum matrix games with noisy feedback. We propose a novel algorithm based on resolving linear programs (LP), achieving an $\veps$-approximate NE with sample complexity $O(\min\{\frac{m_1m_2}{\epsilon^2}\log\frac{m_1m_2}{\epsilon}, \frac{m_1m_2}{\epsilon\delta^2}\log(\frac{m_1m_2}{\epsilon...

报告人：Jiashuo Jiang(Hong Kong University of Science and Technology)

Derived representation schemes and derived Schur algebras

摘要：For an associative algebra, its n-dimensional representations are represented by an affine scheme, called the representation scheme. About 15 years ago, Berest-Khachatryan-Ramadoss showed that the representation func tor has a derived functor, and the n-dimensional derived representations of a DG algebra are represented by the so-called derived representation scheme. In particular, they s...

报告人：Farkhod Eshmatov （New Uzbekistan University）

Coefficientwise Hankel-total positivity in enumerative combinatorics

Abstract: A matrix $M$ of real numbers is called {\em totally positive}\/ if every minor of $M$ is nonnegative. Gantmakher and Krein showed in 1937 that a Hankel matrix $H = (a_{i+j})_{i,j \ge 0}$ of real numbers is totally positive if and only if the underlying sequence $(a_n)_{n \ge 0}$ is a Stieltjes moment sequence, i.e.~the moments of a positive measure on $[0,\infty)$. Moreover, this...

报告人：ALAN DAVID SOKAL (Professor of mathematics at University College London, Professor Emeritus of physics, New York University)

Hodge-Riemann多项式

时间：6月20日 14:00-15:00报告人：郑维喆（中科院数学研究所）题目：Hodge-Riemann多项式地点：双清综合楼B627摘要：复代数簇上丰沛线丛的Hodge-Riemann关系是Hodge理论的重要推论。本报告将介绍丰沛向量丛Hodge-Riemann关系的新进展。我们将引入Hodge-Riemann多项式的概念，探讨其与Lorentz多项式的联系，并展示关于Schur多项式导数序列的组合学应用

报告人：郑维喆（中科院数学研究所）