Public Lectures

The talk will be devoted to explaining two relatively recent mathematical developments involving what physicists know as topological gravity in two dimensions.   These results have not yet become well-known.

Among physicists, Maryam Mirzakhani, in her PhD work of roughly a decade ago, discovered a beautiful new proof of the Virasoro and KdV formulas for intersection theory on the moduli space of Riemann surfaces – formulas that reflect the relation of this intersection theory with matrix models of two-dimensional gravity.  Much more recently, Pandharipande, Solomon, and Tessler (with later work by Buryak and Tessler) defined a version of intersection theory on the moduli space of Riemann surfaces with boundary and found a generalization of the Virasoro and KdV equations.  Their results fit naturally in an extension of the matrix models to include vector degrees of freedom, as shown recently by Dijkgraaf and the speaker.