Geometry Seminar

Seminar information archive ~03/28Next seminarFuture seminars 03/29~


2010/10/06

14:45-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Kei Irie (Kyoto Univ.) 14:45-16:15
Handle attaching in wrapped Floer homology and brake orbits in classical Hamiltonian systems (JAPANESE)
[ Abstract ]
In this talk, the term "classical Hamiltonian systems" means special types of Hamiltonian systems, which describe solutions of classical equations of motion. The study of periodic solutions of Hamiltonian systems is an interesting problem, and for classical Hamiltonian systems, the following result is known : for any compact and regular energy surface $S$, there exists a brake orbit (a particular type of periodic solutions) on $S$. This result is first proved by S.V.Bolotin in 1978, and it is a special case of the Arnold chord conjecture. In this talk, I will explain that calculations of wrapped Floer homology (which is a variant of Lagrangian Floer homology) give a new proof of the above result.
Atsushi Takahashi (Osaka Univ.) 16:30-18:00
Mirror Symmetry for Weighted Homogeneous Polynomials (JAPANESE)
[ Abstract ]
First we give an overview of the algebraic and the geometric aspects of the mirror symmetry conjecture for weighted homogeneous polynomials. Then we concentrate on polynomials in three variables, and show the existence of full (strongly) exceptional collection of categories of maximally graded matrix factorizations for invertible weighted homogeneous polynomials. We will also explain how the mirror symmetry naturally explains and generalizes the Arnold's strange duality between the 14 exceptional unimodal singularities.