Out-of-city admitted students can check into the hotel on 07/15 afternoon, and check-out date is 07/28. Please see the logistics page.
All courses and lectures are in 理教106 (Natural Science Teaching Bldg). We have also reserved 理教318 for discussion. The building "理教" (Natural Science Teaching Bldg.) is marked on the map in the summer school information booklet.
First week (July 16-20)
| Mon |
Tue |
Wed |
Thu |
Fri |
| Opening session (8:30-9:30) |
AG(8:30-10:30) |
HA(8:30-10:30) |
AG(8:30-10:30) |
AG(8:30-10:30) |
| FC (9:30-11:30) |
|
Lecture(Cho,11:00-12:00) |
|
|
| SG(1:15-3:15) |
FC(1:15-3:15) |
FC(1:15-3:15) |
HA(1:15-3:15) |
HA(1:15-3:15) |
| OD(3:30-5:30) |
SG(3:30-5:30) |
OD(3:30-5:30) |
SG(3:30-5:30) |
OD(3:30-5:30) |
Second week (July 23-27)
| Mon |
Tue |
Wed |
Thu |
Fri |
| HA(8:30-10:30) |
AG(8:30-10:30) |
OD(8:30-10:30) |
AG(8:30-10:30) |
AG(8:30-10:30) |
| Lecture(Kohno,11:00-12:00) |
OD(10:40-12:40) |
Lecture(Koert,11:00-12:00) |
Lecture(Nikonov,11:00-12:00) |
Lecture(Fedor,11:00-12:00) |
| SG(1:15-3:15) |
FC(1:15-3:15) |
FC(1:15-3:15) |
HA(1:15-3:15) |
FC(1:15-3:15) |
| OD(3:30-5:30) |
SG(3:30-5:30) |
HA(3:30-5:30) |
SG(3:30-5:30) |
Lecture(Sharygin,3:30-4:30) |
Note: FC=Fiber bundle & characteristic classes; SG=Symplectic geometry; AG=Basic algebraic geometry; HA=Harmonic analysis; OD=Algebra, Geometry and Analysis of Commuting Ordinary Differential Operators
Prof. Bo Dai will be the instructor of Symplectic Geometry for the first week; Prof. Tian-Jun Li will be the instructor of Symplectic Geometry for the second week.
Download course syllabi
Titles and abstracts for lectures
Cheol-Hyun Cho (Seoul National University): Introduction to A-infinity category
We introduce a notion of an A-infinity category, which is a
generalization of a category, relaxing strict associativity condition.
Given a surface, curves on this surface form an A-infinity category,
which is called Fukaya category of the surface.
Such a structure is essential in mirror symmetry conjecture, which we
will explain if time permits.
Otto van Koert (Seoul National University): Smooth and symplectic topology of hypersurface singularities
Singular points on varieties can often be recognized by looking at their links. These are boundaries of small balls enclosing a singular point. In the case of surface singularities, such links are links in the sense of knot theory. In higher dimensions links provide a wide class of interesting manifolds, including exotic spheres. In this talk, we will describe both the smooth topology of links and some of their symplectic topology which captures finer detail.
Toshitake Kohno (The University of Tokyo): Introduction to representation theory of braid groups Slides
The notion of braid groups was investigated by E. Artin in the 1920's. Especially after the discovery of the Jones polynomial in the middle of the 1980's braid groups have appeared in various areas of mathematics such as quantum groups, conformal field theory and hypergeometric integrals. In this talk I will focus on recent developments concerning various aspects of representation theory of braid groups.
Igor Nikonov (Moscow State University): On some combinatorial aspect of knot theory
Initially, a knot is defined as an embedding of the circle into the three-dimensional space considered up to isotopies. But it is often convenient to look at them more combinatorially. From a combinatorial point of view, knots are determined by graphs of special type (called knot diagrams, they can be thought of as projections of knots on a plane), which can be turned into each other by series of special transformations (called Reidemeister moves). In the talk we concern the question what hidden information can be contained in a knot diagram (namely, in the vertices of the diagram), and the theory of parity originated by this question.
Georgy Sharygin (Moscow State University): Deformation quantization and index theorem
For any symplectic manifold one can define a formal noncommutative product on the algebra of functions on it, such that the commutator of two functions will coincide with the Poisson bracket up to the second degree of the deformation parameter. In my talk I shall describe the Fedosov's construction of this product, and if time permits, I shall also briefly describe the applications of this construction in index theory.