Forthcoming Mathematics Seminars

[math]

M A T H E M A T I C S   S E M I N A R S   2010

Tuesday, 27 July, at 14:00

Dr. Huagui Duan
(School of Mathematics, Nankai University, P.R. China)

"The Morse index and multiplicity of closed geodesics"

Abstract:
The problem of closed geodesics is a traditional and
important topic in dynamical systems and differential geometry.
There is a longstanding conjecture that there exist infinitely many
distinct closed geodesics on every compact Riemannian manifold. The
current interest on this problem is on compact simply connected
manifolds, specially spheres. So far not much is known on the
multiplicity of closed geodesics on such manifolds when their
dimensions are at least 3. Recently, Professor Yiming Long and
myself have proved the following

Theorem: There exist at least two distinct closed geodesics on
every compact simply connected Riemannian (or Finsler) manifold
whose dimension is at least 2.

In this talk, I shall give a survey on the study of the problem of
closed geodesics and explain some main ideas in the proof of the
above theorem.

VENUE: Luigi Stasi Seminar Room
(ICTP Leonardo da Vinci Building, first floor)

* * * * *

Tuesday, 3 August, at 14:00

Dr. Naqing Xie
(Fudan University, Shanghai, P.R. China)

"Some geometric problems related to quasi-local mass in general relativity"

VENUE: Luigi Stasi Seminar Room
(ICTP Leonardo da Vinci Building, first floor)