Probabilistic sum-product estimates via entropy method

讲座名称：Probabilistic sum-product estimates via entropy method

讲座人：薛博卿 副教授

讲座时间：4月3日10:00-11:00

讲座地点：长安校区网安大楼A-1236

讲座人介绍：

薛博卿，2013年于上海交通大学获得博士学位，现为上海科技大学数学科学研究所副教授。研究方向以加性组合与解析数论为主，也涉及一点算术几何、算子代数、动力系统、理论物理等其它数学分支，在国内外重要数学期刊发表论文多篇。

讲座内容：

In this talk, we will discuss entropy sum-product phenomena related to additive combinatorics and geometric measure theory. After a brief overview of the area, we introduce a hierarchy of new Frostman-type conditions for possibly dependent bivariate random variables (X,Y), together with a framework based on discretized entropy H_n(.). Using these tools, we prove nontrivial entropy growth for max{H_n(X+Y),  H_n(f(X,Y))}, where f(x,y) belongs to a broad class of polynomial forms of arbitrary degree. As an application, we obtain innovative discretized sum-product-type estimates along dense graphs. The talk will also describe some of the main ingredients of the proof, including Falconer distance results, Shmerkin-Wang framework, discretized Balog-Szemerédi-Gowers mechanism, and Ruzsa-type entropy inequalities. This is a joint work with Alex Iosevich, Thang Pham, Nguyen Dac Quan, and Steven Senger.

主办单位：信息交叉学部