报告学者：Mikhail Khovanov

报告者单位：Johns Hopkins University

报告时间：2025年3月6日下午4：30---5：30

报告地点：机械楼105

报告摘要： A Tait coloring of a trivalent graph labels edges by 1, 2, 3 so that at each vertex the three labels are distinct. Tait colorings of planar trivalent graphs are closely related to the 4-Color Theorem.

I'll explain an extension of this story one dimension up, where we build a state sum model that includes a count of surfaces in a 2-dimensional foam for each Tait coloring of the foam. This is based on a joint work with Louis-Hadrien Robert from several years ago.

 

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.