Title: The geometry and topology of lower bounds on scalar curvatureAbstract: In this talk, I will discuss some recent results about controlling the geometry and topology of manifolds from a (positive) lower bound on their scalar curvature.
Title: Curves on Varieties and the Degree of Irrationality.Abstract: Inspired by the Noether-Lefschetz theorem, it has been conjectured that the degree of any curve on a (very) general complete intersection variety is divisible by the degree of the variety itself. In this talk, we present a weaker version of this conjecture. Using this result, we confirm a […]
Title: Unipotent Representations of Real Reductive Groups and Mixed Hodge Modules Abstract: Let Pi(G) denote the set of irreducible unitary representations of a semisimple Lie group G. A fundamental problem in representation theory is to describe the structure of this set. In previous joint work with Losev and Matvieievskyi, we have defined a class of […]
Title: A Khovanov-like Categorification of the Four Color TheoremAbstract: The four color theorem states that each bridgeless trivalent planar graph has a proper 4-face coloring. It can be generalized to certain types of CW complexes of any closed surface for any number of colors, i.e., one looks for a coloring of the 2-cells (faces) of […]
Langlands functoriality and stable transfer. (Continued.)