报告题目：Foam evaluation and its applications

报告学者：Mikhail Khovanov

报告者单位：Columbia University

报告时间：2024年4月16日下午3：30---5：00

报告地点：学活十层报告厅

 

报告摘要： We explore a particular evaluation of combinatorial 2-dimensional CW-complexes in 3-space that relates to the Weyl character formula for SL(3), link homology and the 4-color theorem.

 

报告者简介：Mikhail Khovanov is a recognized leader of the “categorification” program, which plays an important role in modern mathematics and physics.  

Khovanov earned his Ph.D. in 1997 under the supervision of Professor Igor Frenkel at Yale University. Shortly thereafter he came up with his famous idea of categorifying the Kauffman bracket, which is a version of the celebrated Jones polynomial of links in a 3-sphere. This was the first example of the categorification which interprets polynomial invariants as Poincare polynomials of new homology theories. The construction of Khovanov homology was amazingly fruitful and very unexpected.

A further categorification of the HOMFLY-PT polynomial of links and a categorification of quantum groups are other major achievments of Khovanov which have now important implications in low-dimensional topology, algebraic and symplectic geometry, geometric representation theory and string theory.