- Title:  Some applications of p-adic numbers

- Speaker:  Nguyễn Xuân Thọ  (Đại học Bách khoa Hà Nội)

- Time: 10:00 - 11:00 (Wednesday, July 7).

- Abstract:  In this talk, we give some applications of p-adic numbers to Diophantine equations. We present a technique to prove the nonexistence of positive rational points on curves and surfaces.  One of our earlier results in this direction is to show that equation (x+y+z+w)(1/x+1/y+1/z+1/w)=n does not have solutions in positive integers if n=4m^2 or n=4m^2+4, where 4 does not divide m-2. We will show how to apply the Hilbert symbol to study the problem of sum of positive rationals with given products and to give counter examples to the Hasse principle. This extends some earlier works by Garaev, Swinnerton-Dyer. 

- Title:  Random polynomials: an invitation

- Speaker:  Assoc. Prof. Đỗ Quang Yên (University of Virginia, USA)

- Time: 10:00 - 12:00 (Wednesday, June 16).

- Abstract:  It is well known that solving polynomial equations of high degrees is a highly challenging talk, even numerically. Understanding the location and estimating the number of real roots for a generic polynomial equation are central topics in many studies. In this talk, I would like to introduce some basic concepts and some basic questions related to these themes, and a brief survey of recent progresses.

- Homepage: https://profile.virginia.edu/yqd3p

- Đăng ký tham dự tại đây

- Title:  Some questions on Fekete polynomials

- Speaker:  PGS. Nguyễn Duy Tân (Đại học Bách khoa Hà Nội)

- Time: 14:00 - 15:30 (Tuesday, May 25).

- Abstract:  Fekete polynomials were known in the nineteenth-century  in connection with Dirichlet L-functions. However, their arithmetic  properties are not well-studied. In this talk, we discuss some quite surprising properties of these polynomials. This is based on joint work with Jan Minac and Nguyen Tho Tung.

- Title:  On the expected number of zeros of random polynomials: real and p-adic cases

- Speaker:  TS. Phạm Việt Hùng (Viện Toán học)

- Time: 9:30 - 10:30 (Wednesday, May 12).

- Abstract:  In this talk, we review some results on the expected number of zeros of random polynomials in two cases: real and p-adic. For the real case, we present the Kac-Rice formula and its geometric meaning through Integral Geometry. To extend these ideas to the p-adic case, we discuss the works of Evans; Kulkarni and Lerario.

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Talk 13:

- Title: INTERSECTION GRAPHS OF GENERAL LINEAR GROUPS

- Speaker:  Do Hoang Viet (A JOINT WORK WITH MAI HOANG BIEN).

- Time: 14:30 - 15:30 (Thursday, June 11).

- 

Talk 11 & 12 - Postponed:

- Title: p-adic integration and p-adic zeta functions

- Speaker:  Dr. Le Quy Thuong.

- Time: 14:00 - 15:30 (Wednesday, March 11 & March 18).

Talk10:

- Title: Rings of Prime Characteristic

- Speaker:  Assoc. Prof. Pham Hung Quy (FPT University).

- Time: 09:30 - 11:30 (Thursday, March 05).

- Abstract:

Study of rings of prime characteristic is a vast and active area in Commutative Algebra. In this talk we introduce some basic notions in this topic: F-singularities, tight closure, Hilbert-Kunz multiplicity, ...

Talk9:

- Title: Inertial manifolds and master-slave synchronization

- Speakers:  Prof. Dr. Bj¨orn Schmalfuß (Friedrich-Schiller-Universit¨at Jena, Germany)

- Time: Tuesday, 30.07.2019, 16:00-17:30

- Abstract:

We consider dynamical systems and random dynamical systems. We present objects describing the long time behavior of these systems. Particular objects are attractors and inertial manifolds. Both objects allow to introduce the concept of small/ finite dimensionality of high/infinite dynamical systems. We will consider inertial manifolds in more details. Two techniques allowing to state these manifolds are the Lyapunov Perron transform and the graph transform. We will consider the dynamics on these manifolds by the inertial form. Attractors and inertial manifolds can be used to describe synchronization of two or more parallel systems. We will describe the main issues of this topic. All these things will be applied to random and non random reaction diffusion equations.

Talk8:

- Title: Stability theory for stochastic systems

- Speakers:  Dr. Luu Hoang Duc (Hanoi Institute of Mathematics, Vietnam Academy of Science and Technology & Max Planck Institute for Mathematics in the Sciences, Germany)

- Time: Tuesday, 23.07.2019, 14:00-15:30

- Abstract: 

Control theory and asymptotic dynamics is deeply concerned with problem of stability, which studies how trajectories of a dynamical system behave in the long run under small perturbations of initial conditions. The problem dates back to the Russian mathematician A. M. Lyapunov with his pioneer work (also his PhD thesis) on ”The general problem of stability motion” in 1892, in which he introduced two different methods to study stability, now well-known under his name: Lypapunov exponents and Lyapunov functions. This talk presents how the classical ideas since Lyapunov are extended to study stability for systems under the influence of random and stochastic noises, for instance stochastic differential equations driven by Brownian motions. Various notions of stability based on types of convergence are discussed, as well as many stability criteria. There is also a fundamental difference in analytic techniques for investigating stochastic systems using either Ito calculus or rough path theory. The talk is illustrated by many real life applications.

Talk7:

- Title: Restriction problem for spheres and its application to the Erd˝os-Falconer distance conjecture over finite fields

- Speakers:  Doowon KOH (Chungbuk National University)-Thang Pham (University of Rochester New York)

- Time: Thursday, 18.07.2019, 14:00-15:00

- Abstract: 

 In this talk we study both the Erd˝os-Falconer distance problem and the restriction problem for spheres in vector spaces over finite fields. The purpose of this talk is to present how to deduce a result on the Erd˝os-Falconer distance problem from the finite field restriction theorems for spheres. In fact, we will see that the L 2 restriction estimates play a crucial role in deriving results on the Erd˝os-Falconer distance problem.

Keywords: Extension/Restriction theorems, Distances, Harmonic analysis over finite fields.

Talk6:

- Title: Fractional calculus and rough paths

- Speakers:  Prof. Dr. Maria J. Garrido-Atienza (University of Sevilla, Spain)

- Time: Tuesday, 16.07.2019, 14:00-15:30

- Abstract: 

Talk4:

- Title: What is Operations Research?

- Speakers: Hà Minh Hoàng & Nguyễn Trung Thành

- Time: 10.4.2019

- Abstract: 

• What is OR? 
• Why is OR important?
• What are OR approaches? 
• What are real-world applications of OR?