Department of Mathematics 數學系
The Institute of Mathematical Sciences
數學科學研究所The Chinese University of Hong Kong
香港中文大學Phone: (852) 3943 7988 / 3943 7989 • Fax: (852) 2603 5154 • Email: dept@math.cuhk.edu.hk Phone: (852) 3943 8036 / 3943 8038 • Fax: (852) 2603 7636 • Email: ims@ims.cuhk.edu.hk Rm. 220, Lady Shaw Building, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong Unit 601, Academic Building No. 1, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong
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Homological Mirror Functor via Counting Polygons
by
Professor Cheol-Hyun Cho Seoul National University
at
10:00am - 11:00am
Abstract: We propose a new method to define mirror potential W from immersed Lagrangian in a space X, called generalized Strominger-Yau-Zaslow method. In this setting, we define a canonical functor from the Fukaya category of X to the matrix factorization category of W via counting J-holomorphic polygons, which explains geometric origin of homological mirror symmetry.
When X is an orbifold sphere with three orbifold points of Z/a, Z/b, Z/c, we get a mirror Landau-Ginzburg potential W with leading order terms xa+yb+zc – σ xyz, and we prove that the corresponding canonical functor gives an equivalence when 1/a+1/b+1/c ≦1, proving homological mirror symmetry. This is a joint work with Hansol Hong and Siu-Cheong Lau.
Cubics, Squares and Lines
by
Professor Sergey Galkin
National Research University Higher School of Economics
at
11:20am - 12:20pm
Abstract: There is a universal linear relation between a cubic hypersurface and two auxiliary varieties, parametrising lines and pairs of points on it. It holds in the Grothendieck ring of varieties, and by various specializations one easily derives corollaries. Some are classical, such as 27 lines on a cubic surface or Hodge structures of the variety of lines, some are new.
This is a joint work with Evgeny Shinder.
*There will be a tea break at 11:00-11:20a.m. and lunch at 12:20 – 2:20p.m.
