VIASM Basic Notions Seminar

Thời gian: 14:15 đến 15:15 ngày 16/10/2018, 15:00 đến 16:00 ngày 13/11/2018, 14:00 đến 15:30 ngày 05/03/2019, 14:00 đến 15:30 ngày 10/04/2019, 14:00 đến 15:30 ngày 09/07/2019, 14:00 đến 15:30 ngày 16/07/2019, 14:00 đến 15:00 ngày 18/07/2019, 14:00 đến 15:30 ngày 23/07/2019, 14:00 đến 15:30 ngày 30/07/2019,

Địa điểm: B4-705, VIASM

Lấy ý tưởng từ chuỗi bài giảng cùng tên được tổ chức tại nhiều viện nghiên cứu và trường đại học trên thế giới, chuỗi bài giảng VIASM Basic Notions Seminar bao gồm các bài giảng riêng biệt, với mục đích giới thiệu ngắn gọn về một số khái niệm toán học cơ bản. Chuỗi bài giảng không nhằm mục đích làm cho người tham dự trở thành chuyên gia về nội dung được trình bày mà chỉ giúp người nghe nói chung đạt được những hiểu biết nhất định về các khái niệm được nêu ra, đặc biệt là đối với sinh viên và những nhà nghiên cứu không cùng chuyên ngành. Chuỗi bài giảng sẽ được tổ chức không định kỳ vào thứ Ba hoặc thứ Năm.
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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, 14:00-15:30

- 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.

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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.

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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.

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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: 

The purpose of this talk is to solve m-dimensional dynamical systems dYt = f(Yt)dXt driven by a d-dimensional control function X, which is not differentiable, being the main task how to define the integral against X. The natural assumption is that the control function Y has bounded p-variation for some p > 1. In the case 1 < p < 2, the equation can be formulated using Riemann-Stieltjes integrals and the theory of integration developed by Young. For β-H¨older-continuous drivers X with β > 1 2 (which corresponds to p < 2), Nualart and R˘a¸scanu applied the classical techniques of fractional calculus to formulate and solve rough dynamical systems. In this case, the integral can be expressed as a Lebesgue integral using fractional derivatives. In the case p ≥ 2, Young integration cannot be applied. Assuming 2 ≤ p < 3 (or 1/3 < β < 1/2), we can still use pathwise integration based on compensation of fractional derivatives. Another possibility is to use rough path analysis, in which the control function X is enhanced with a two-parameter function Xst that should be interpreted (in the smooth case) as the double integral R t s (Xs −Xr)⊗dXr. Then, the dynamical system can be extended to a rough differential equation and the main result of this theory is the continuity in the p-variation metric of the mapping (X, X) → (Y, Y). Finally we will also investigate the connections between rough path theory and fractional calculus.
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Talk5:

- Title: Information Geometry and its application

- Speakers:  Dr. Tat Dat Tran (Max Planck Institute for Mathematics in the Sciences, Germany)

- Time: Tuesday, 09.07.2019, 14:00-15:30

- Abstract: 

In this talk, I would like to give out an introductory overview to Information Geometry. Information geometry is a bridge connecting between non-Euclidean geometry and probability theory which reached maturity through the work of Amari in 1980s. The main idea is to find out the correspondence between structure of the families of distributions and that of manifolds. Formally, we can consider a distribution as a point, the score as a tangent vector, a family of distributions as a Riemannian manifold with the Riemannian metric is the Fisher information metric. The Fisher information metrics and dually affine connections are main objects in Information Geometry and they play important roles not only in statistical inference but also in wider areas of information sciences such as machine learning, signal processing, optimization, and neuroscience. The talk is designed in the language that can be accessible to undergraduate students.

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Talk4:

- Title: What is Operations Research?

- Speakers: Hà Minh Hoàng & Nguyễn Trung Thành

- Time: 10.4.2019

- Abstract: 

The aim of this talk is to provide a brief overview of Operations Research (or OR, for short), a distinct discipline explicitly devoted to aiding decision makers. In particular, we would like to give quick answers to the following fundamental questions: 
  • What is OR? 
  • Why is OR important?
  • What are OR approaches? 
  • What are real-world applications of OR?
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Talk3:

- Title: An elementary introduction to the Langlands Program

- Speaker: Đỗ Việt Cường

- Time: 5.3.2019

- 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, ..). The Wile's proof of the Fermat's last theorem is a very spectacular result which fall within the ambit of this program. In this talk, I would like to "introduce" this beautiful program in the language that can be accessible to undergraduate students. 

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Talk2:

- Title: Simple elementary but not necessarily solvable problems in plane geometry

- Speaker: Prof. Moshe Rosenfeld (University of Washington Tacoma, USA)

- Time: 13.11.2018

- Abstract: In this presentation I plan to expose simple problemd on points lines and segments in the plane that any highschool student can understand. One such problem witnessed a major progress in April 2018. For 68 years it was known that you can color the points of the plane by 7 colors so that points at distance 1 receive distinct colors. It was also know that at least 4 colors are needed. There is a $1000 USD prize for determining the exact number. 

In April 2018, Aubrey de Grey a British Gerontologist, proved that the lower bound is actually 5.

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Talk1:

- Title: Stanley-Reisner rings 

- Speaker: Nguyễn Đăng Hợp

- Time: 16.10.2018

- Abstract: A basic problem in discrete geometry is the following: For a polyhedron with n vertices in the three dimensional space (n is at least 4), what is the maximal possible number of facets it may have? More generally, for a convex polytope with n vertices of dimension d, and for 1<k<d, what is the maximal possible number of k-dimensional faces it may have? I will talk about this problem, and its connection with the algebraic theory of Stanley-Reisner rings.