Institute of Mathematics, VAST

Institute's Colloquium 2010

( Auditorium 301, Building A5 )

 

January 5, 2010:

Speaker: Prof. Ariun K. Gupta, Bowling Green State University, Ohio, USA
Title: Modeling skewness with applications in epidemiology and finance
Venue: Auditorium Room 201, Building A5
Time: 14:00-16:00


 

 

March 10, 2010:

Speaker: Prof. Neal Koblitz, Washington University
Title: OVERVIEW OF THE ROLE OF MATHEMATICS IN CRYPTOGRAPHY
Venue: Auditorium Room 301, Building A5
Time: 10:00-11:00

Abstract:  I will outline some of the different ways that mathematics is used in cryptography. I will illustrate some of the subtleties by discussing isogenies between elliptic curves. The study of isogenies has led to our questioning some "conventional wisdom" about random choice of parameters.

 (Đây là báo cáo nhân dịp Lễ trao tặng bằng Tiến sĩ danh dự của Viện Khoa học và Công nghệ Việt Nam cho GS Koblitz.)

 

March 12, 2010:

Venue: Auditorium Room 301, Building A5
Time: 14:00


Speaker: Prof. Dr. Karl-Heinz Hoffmann, Technical University of Munich
Title: Convection-Diffusion-Equations With Absorption-Boundary-Conditions: Modelling a Biosensor
Abstract: 

We consider a problem which appears when developing sensors which serve for detecting of certain proteins in solutions. An important part of such a sensor is a wet cell, say a cube, filled with a liquid into which a solution containing the protein to be detected is injected. Special molecules called aptameres are immobilized on the bottom of the wet cell. The aptameres can selectively bind the desired protein from the solution. The change of the surface mass loading can be analyzed using acoustic waves propagating along the aptamere-layer. Thus, the concentration of the protein in the solution will be estimated.

In this presentation, a model that describes the propagation of the protein in the wet cell and its adhering to the aptameres is proposed. It is assumed for simplicity that the propagation of the injected protein in the wet cell is governed by a diffusion equation. A special boundary condition on the bottom provides the monotone grows of the deposited layer with saturation which means the exhaustion of free aptamere-molecules.

 

Speaker: Prof. Dr. Willi Jäger, University of Heidelberg
Title: Mathematical Modelling and Simulation of Complex, Nonlinear Systems in Biosciences
Abstract: 

Modelling and simulations of biological structures and functions are challenges to Mathematics and Computational Sciences. Due to the rapid increase of information about processes and structures on the molecular and cellular level, it is necessary to couple model equations for macroscopic state variables to the equations describing the processes on the micro-scale. In this lecture two examples will be discussed to illustrate the challenges and the potential for analysis and numerical mathematics in investigating bio systems:

(1) Coupling reactive flow and biomechanics in tissues and membranes In joint research with M. Neuss-Radu and A. Mikelic, we derived effective equations for processes in tissues and membranes, using multi-scale techniques to determine the limit with respect to a characteristic scale. The resulting model equations are generalization of model equations known as Biot-laws in case of porous media.

(2) Interaction of biomechanics and biochemistry of cell walls Models for the mechanics of cell walls lead to flows involving mean and Gaussian curvatures. In case of interactions with internal fiber networks or under the influence of chemical reactions on the cell wall, the dynamical equations have to be adjusted. Here the penetration of virus through a cell wall and the dynamics of blood cell will be discussed. Results obtained in PhD thesis of D. Hartmann und in a running project jointly with M. Mercker will be presented.

 

 

August 6, 2010:

Speaker: Prof. Benedict H. Gross (VEF Lecturer, DH Havard, My)
Title: Selmer groups and stable orbits
Venue: Auditorium Room 301, Building A5
Time: 9:30

Abstract:  The talk will begin with an overview of the recent work of Manjul Bhargava on the average ranks of elliptic curves over the rational numbers. Bhargava determines the average order of the 2-Selmer group by counting stable orbits in the representation of SL_2(Z) on the lattice of integral binary quartic forms. I will describe this orbit problem in slightly greater generality, using only elementary linear algebra, and will show how the 2-Selmer groups of hyperelliptic curves appear in its solution.

 

 

September 17, 2010:

Speaker: PGS.TSKH Nguyễn Minh Trí (Viện Toán học)
Title: SEMILINEAR DEGENERATE ELLIPTIC EQUATIONS
Venue: Auditorium Room 301, Building A5
Time: 9:30

Abstract:  Boundary value problems and smoothness of solutions to nonlinear elliptic equations and linear nonelliptic equations have been investigated for more than a century. However, the study of semilinear degenerate elliptic differential equations, i. e., nonlinear equations the principle parts of which are linear and degenerate elliptic, is not enough taken up. In this talk we give a survey of recent results on those problems for a fairly large class of semilinear degenerate elliptic differential equations. Here we will discuss the critical exponents phenomenon for boundary value problems and interior regularity of solutions of the equations.

 

 


October 7, 2010:

Speaker: PROF. VOLKER MEHRMANN (TECHNISCHE UNIVERSITäT BERLIN)
Title: SEMILINEAR DEGENERATE ELLIPTIC EQUATIONS
Venue: Auditorium Room 301, Building A5
Time: 9:30

Abstract:  A classical research topicin approximation theory discusses the question whether we can approximate a signal or an image that is represented by a linear combination of n basis functions in a different way using much fewer (say log(n) basis functions, i.e. whether there is a sparse approximation of the function. Due to recent work of Candes, Daubechies, Tao and many others this topic has received a lot of attention under the name of compressed sensing. One of the key results in this field is that under some (rather strong) conditions the sparse solution can be computed via minimization in 1-norm, i.e. via linear programming.We will briefly review some of the work and then discuss how this idea can be used for the adaptive grid refinement in the solution of elliptic partial differential equations.

 

(Đây là sinh hoạt học thuật bắt buộc của Viện, đề nghị các cán bộ nghiên cứu của Viện tham gia đầy đủ.)  

 

 

November 26, 2010:

Speaker: Prof. Dr. Rolf Jeltsch, ETH Zurich, Switzerland
Title: From Numerics to Computational Science and Engineering
Venue: Auditorium Room 301, Building A5
Time: 9:30

Abstract:  The birth of the discipline numerics is due to the invention of modern computers in the forties of the last century. The main task was to learn to live with the deficiencies of computers, which are the limited memory space, that only a finite number of arithmetical operations can be carried out and that these can not be performed accurately. We briefly touch on the development of numerics and computers which made that it is now possible to solve large problems of very high complexity. This development gave rise to a new field and new curricula: Computational Science and Engineering, CSE. We then describe CSE. Classically one tried to understand phenomena by developing mathematical theories based on observations and experiments. The need to use simulations to understand phenomena is exemplified. After a brief introduction to ordinary differential equations we concentrate on models based on such equations. In particular we focus on the control of robots used in industry and in the space shuttle. As examples where a very large number of equations have to be solved simulations of particle beams in accelerators, transonic flow around disk and three dimensional combustion are given. To show the importance of mathematical modeling we look at transport problems in particular the shallow water equations which governs weather and climate models, tsunamis but also debris flow.  

 

 

 
 

 

 

December 22, 2010:

Speaker: PROF. IMRE KÁTAI
Title: RESEARCH PROBLEMS IN NUMBER THEORY
Venue: Auditorium Room 301, Building A5
Time: 9:30

Abstract:  In this talk, I will describe a variety of results and problems from arithmetical functions on some subsets of integers. Continuous homomorphisms as arithmetical functions, and sets of uniqueness are also treated. The topics of my talk are:

  1. Sets of uniqueness,
  2. Characterization of log as an additive function,
  3. Characterization of ns as a multiplicative function,
  4. Additive functions (mod 1),
  5. Characterization of continuous homomorphisms.
( Đây là sinh hoạt học thuật bắt buộc của Viện, đề nghị các cán bộ nghiên cứu của Viện tham gia đầy đủ.)