1. Dr. Đỗ Việt Cường - VNU Hanoi University of Science
Title: On the Langlands program
Abstract:
One of the most fascinating and important developments in mathematics in the last 50 years is the Langlands program. Roughly speaking, the Langlands program is a collection of ideas (conjectures) that provide a unification of many areas of mathematics (such as: number theory, harmonic analysis, representation theory, ...). Wiles' proof of Fermat's last theorem is a very spectacular result which falls within the ambit of this program. This talk will give a “survey” on this beautiful program.

2. Dr. Nguyễn Hải Đăng - University of Alabama
Title: Stochastic Kolmogorov systems from a dynamical system point of view
Abstract:
In recent years there has been a growing interest in the study of the dynamics of stochastic populations. A key question in population biology is to understand the conditions under which populations coexist or go extinct. Theoretical and empirical studies have shown that coexistence can be facilitated or negated by both biotic interactions and environmental fluctuations. We study the dynamics of n populations that live in a stochastic environment and which can interact nonlinearly. Our models are described by n-dimensional Kolmogorov systems with random noise. This talk discusses the long-term properties of stochastic Kolmogorov systems from a dynamical system point of view and gives sharp conditions for extinction and coexistence.

3. Assoc. Prof. Nguyễn Tiến Dũng - VNU Hanoi University of Science
Title: Fisher information and the central limit theorem
Abstract: In this talk, we introduce a general method to study the Fisher information distance in the central limit theorem for nonlinear statistics.

4. Dr. Đậu Sơn Hoàng - RMIT University
Title: On a Polynomial Interpolation Problem and Its Applications
Abstract:
In the classical problem of polynomial interpolation, given a (finite) field F, in order to recover (interpolate) a polynomial f(x) ∈ F[x] of degree less than k, the values/evaluations of f at k different points f(α1), . . . , f(αk) are required. Here α1, . . . , αk are distinct elements in F. The question that we are interested in is the following: if we want to recover only one evaluation f(α∗) of f at some point α∗ ∈ F, can we reduce the amount of information required? The answer turns out to be Yes if we relax the problem by allowing extraction of partial information from more than k evaluations of f. For example, when F = F28 , while each value f(αi) is represented by 8 bits, we may need to extract just one bit. Interestingly, this simple variant of the polynomial interpolation problem has a very practical application in distributed storage systems employed by industry leaders such as Google, Facebook, or Baidu, which is the focus of this talk. It is also related to the problem of local leakage-resilient secret sharing schemes in cryptography.

2. Dr. Nguyễn Đức Mạnh - Bordeaux University
Title: Variation of Hodge structure and enumerating tilings of surfaces by triangles and squares
Abstract:
A translation surface can be defined as a Riemann surface equipped with a holomorphic Abelian differential. The set of translation surfaces having the same genus, the same number of zeros (of the Abelian differential) and their orders is called a stratum. An easy way to construct translation surfaces is to glue some copies of the unit square together (for instance one can construct a torus from a single unit square). Translation surfaces constructed from unit squares are called square tiled surfaces.
Since the work of Eskin-Okounkov in 2001, it has been known that in any stratum, the number of square-tiled surfaces constructed from at most m squares is asymptotic to c·π2g·md, where d is the (complex) dimension of the stratum, g is the genus of the surfaces, and c is a rational number. Similar phenomena also occur in strata of quadratic differentials. Counting square-tiled surfaces in a given stratum is more or less the same as counting quadrangulations of a topological surface, with some constraints on the singularities and on the holonomy of the associated flat metric. In this talk, we will explain how the asymptotics above are related to the volume of some moduli spaces. Moreover, in some situations they can be computed from the self-intersection number of a divisor in some complex projective varieties. This implies in particular that the constant α belongs actually to either Q·πd or Q·(3π)d in those cases. This is joint work with Vincent Koziarz (University of Bordeaux).