REPRESENTATION
THEORY AND RELATED TOPICS SEMINAR
ABSTRACT: A
conjecture of Ronald Read predicts that the coefficients of the chromatic
polynomial of a graph form a log-concave sequence for any graph. A
related conjecture of Dominic Welsh predicts that the number of linearly
independent subsets of varying sizes form a log-concave sequence for
any configuration of vectors in a vector space. In this talk, I will
argue that two main results of Hodge theory, the Hard Lefschetz theorem
and the Hodge-Riemann relations, continue to hold in a realm that goes
beyond that of Kahler geometry. This implies the above mentioned
conjectures and their generalization to arbitrary matroids. Joint work
with Karim Adiprasito and Eric Katz.
For further information visit http://www.northeastern.edu/martsinkovsky/p/rtrt.html or contact Alex Martsinkovsky alexmart >at< neu >dot< edu