Archive for the 'seminars' Category

At 2pm on Tuesday, 24th May, 2011

Prof. Daomin Cao

from the Chinese Academy of Science

will speak in MC206 (Building C26)

on a

System of Elliptic Equations.

Abstract:

In this talk the speaker will consider a system of elliptic equations arising from physics. Previous results on the existence of solutions will be presented. The speaker
will also introduce the results on the existence of ground state in his joint work with I.L.Chern and J.C.Wei.

On Tuesday, 17th May, 2011

JORGE GARCIA-MELIAN
Universidad de La Laguna

will speak on

BOUNDARY BLOW UP ELLIPTIC PROBLEMS WITH SIGN-CHANGING WEIGHTS: EXISTENCE AND MULTIPLICITY OF POSITIVE SOLUTIONS

at 2pm in MC206.

Abstract. We consider an elliptic boundary blow-up problem in a bounded smooth domain of R^N, and show that as a parameter in the equation varies, the solution set form a smooth curve in a suitable function space, and the curve has a turning point at a critical value of the parameter. The proofs are mainly based on continuation methods.

18th November 2010, 1100 MC206

Emeritus Professor Dmitri Alekseevski

from

University of Edinburgh

will speak on

Quantizable Kähler Geometry, Sasakian Geometry, Conical Kähler Geometry and Locally Conformal Kähler Geometry

We discuss relations between these four types of geometries. In particular, we associate with a quantizable Kähler manifold M a principal bundle S → M with the structure group A=S¹ or R and a contact form, θ, which, together with the complex structure, J, of M, defines a Sasakian structure on S. The Riemannian cone C(S) over S has a canonical Kähler conical structure and its quotient carries a Vaisman locally conformal Kähler structure. We will discuss under which conditions this construction can be inverted. We consider also the homogeneous case and indicate some applications. This is joint work with V. Cortes, H. Hasegawa and Y. Kamishima

13th April 2010, 1500 MC206

Professor Gary Lieberman

from

Iowa State University

will speak on

Elliptic equations with singular lower order terms

The classical theory of elliptic equations assumes that the lower order terms are all bounded (or are in some L^p space with p sufficiently large). In this talk, we examine equations with singular lower order terms. Although some elements of the classical theory can be carried over to this case, several interesting new phenomena occur. In some cases, the equation has only one bounded solution in a given bounded domain. In other cases, there are solutions for arbitrary Dirichlet data but only one smooth solution.

2nd March 2010, 1500 MC206

Professor Le Hai Khoi

from

NTU Singapore

will speak on

Representation of Functions in A^−∞ by Dirichlet Series and Applications

Consider a space A^−∞(Ω) of holomorphic functions in a bounded convex domain Ω of Cⁿ, with the so-called polynomial growth near the boundary ∂Ω. Introducing a space A^∞_Ω of entire functions with certain growth condition, we establish the mutual duality of A^−∞(Ω) and A^−∞. As one of applications of the obtained duality, a possibility of Ω representation of functions from both spaces A^−∞(Ω) and A^−∞_Ω in a form of Dirichlet series is given. These results are due to Abanin A.V. and myself.

24nd February 2010, 1500 MC206

Dr. Béatrice Bleile

from

UNE

will speak on

Poincaré Duality Complexes

Poincaré duality complexes are homotopy generalisations of manifolds. This talk will provide a brief introduction and an overview of results and open questions concerning Poincaré duality complexes in low dimensions.

22nd February 2010, 1400 MC206

Professor Cornelia Schiebold

from

Mid Sweden University

will speak on

Integrable systems: noncommutative versus commutative

After a general introduction to integrable systems, we will explain an approach to their solution theory, which is based on Banach space theory. The main point is first to shift attention to noncommutative integrable systems and then to extract information about the original setting via projection techniques. The resulting solution formulas turn out to be particularly well-suited for the qualitative study of certain solution classes. We will show how one can obtain a complete assymptotic description of the so called multiple pole solutions, a problem that was only treated for special cases before.

19th February 2010, 1500 MC206

Professor Egmont Porten

from

Mid Sweden University

will speak on

Holomorphic and meromorphic extension on complex spaces

The famous Hartogs extension theorem belongs to the first important results in the beginning of several complex variables. After early attempts to prove the theorem by geometrical methods, most of the known generalizations were obtained by ∂ techniques. In this talk I will explain how to give a complete proof by Morse theoretic methods and how this argument can be adapted to derive the theorem in the before open case of (n-1)-complete normal complex spaces. The result was obtained in joint work with Joel Merker.

3rd February 2010, 1400 MC206

Professor Yihong Du

from

UNE

will speak on

Spreading Speed Revisited: A Free Boundary Model

In this talk, I will report recent joint work with my visitors on the spreading of new or invasive species. Traditionally the mathematical investigation of this problem is based on the “travelling wave solution” approach, built on the pioneering works of Fisher and Kolmogorov et al in the 1930s. Our research introduces a new approach, where we use the dynamics of a free boundary to describe the evolution of the spreading front of a new or invasive species.

The talk will start by recalling the background and empirical evidence, with a brief review of the advantages and short-comings of the traditional approach. Then the new approach will be presented with minimal mathematical technicalities. The talk will end with some comparisons of the new and traditional approaches and a brief discussion of possible new directions of research.