Venue: Lecture Hall, 2nd Floor, Building A6.

This Colloquium aims to present recent developments in the mathematical research of some research groups at
the Beijing International Center for Mathematical Research, Peking University and the Institute of Mathematics, Vietnam Academy of Science and Technology.

All interested colleagues are cordially invited.

Program: (each talk: 45 minutes)

Morning: 9:00-12:00

1. Ruochuan Liu, Title: p-adic Riemann-Hilbert correspondence, de Rham comparison and periods on Shimura varieties
2. Zaiwen Wen, Title:Second-Order Type Optimization Methods For Data Analysis
3. Doan Thai Son, Title: Some new aspects of stochastic bifurcation theory

Afternoon: 14:00-16:00

1. Zhiyu Tian, Title: Asymptotic of space of rational curves
2. Ngo Viet Trung, Title: Membership criteria and containments of powers of monomial ideals

Detailed information

Speaker: Prof. Ruochuan Liu

Title: p-adic Riemann-Hilbert correspondence, de Rham comparison and periods on Shimura varieties
Abstract: In the previous work with Xinwen Zhu we construct a p-adic analogue of the classical Riemann-Hilbert correspondence. As a by-product the de Rham periods of a general Shimura variety are obtained. In a recent joint work with Hansheng Diao, Kai-Wen Lan and Xinwen Zhu, we further establish a logarithmic version of the correspondence which enables us to establish the de Rham comparison theorem with coefficients for quasi-projective varieties and compare the de Rham periods and complex periods for a general Shimura variety.

Speaker：Prof. Zaiwen Wen

Title: Second-Order Type Optimization Methods For Data Analysis
Abstract: Optimization models are ubiquitous in data analysis. In this talk, we will review Gauss-Newton methods for phase retrieval, semi-smooth Newton methods for composite convex programs and its application to large-scale semi-definite program problems, sub-sampled semismooth Newton method for nonsmooth composite minimization problems from large-scale machine learning, as well as an adaptive regularized Newton method for Riemannian Optimization.


Speaker: Prof. Zhiyu Tian

Title: Asymptotic of space of rational curves
Abstract: In this talk I will discuss two conjectures describing the asymptotic behavior of the space of rational curves on a Fano/rationally connected variety, one topological (Segal's conjecture), one arithmetic (Manin's conjecture). The striking similarity and compatibility between the two conjectures also suggest that everything should be motivic in a suitable sense.

Speaker: Prof. Doan Thai Son

Title: Some new aspects of stochastic bifurcation theory
Abstract: Despite its importance for applications, relatively little progress has been made towards the development of a bifurcation theory for random dynamical systems. In this talk, we first give a brief overview of the random bifurcation theory. Next, we present our recent contributions on this theory which includes the Pitchfork and Hopf bifurcation with additive noise and a topological classification of random circle maps.

Prof. Ngo Viet Trung

Title: Membership criteria and containments of powers of monomial ideals
Abstract: We present relationships between optimal solutions in combinatorial optimization and membership criteria for powers of monomial ideals. This relationship leads to several new results and problems on containments between ordinary powers, symbolic powers and their integral closures.