• Speaker: Boris Shapiro, Stockholm University
• Title: Around Waring problem for homogeneous polynomials
• Date: 11/07/2018
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall

Waring problem for homogeneous polynomials (forms) asks to represent a given form of degree k*d as a sum of d-th powers of forms of degree k. The main objective is to find a presentation with a small number of summands. The classical case going back to J.J. Sylvester deals with k=1 and binary forms. We will survey some of the results in this area and pose some elementary looking open problems. No preliminary knowledge of the topic is required

• Speaker: Vincent Bouchard , University of Alberta
• Title: W-algebra constraints and higher Airy structures
• Date: 11/13/2018
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall

Virasoro constraints are omnipresent in enumerative geometry. Recently, Kontsevich and Soibelman introduced a generalization of Virasoro constraints in the form of Airy structures. It can also be understood as an abstract framework underlying the topological recursion of Chekhov, Eynard and Orantin. In this talk I will explain how the triumvirate of Virasoro constraints, Airy structures and topological recursion can be generalized to W-algebra constraints, higher Airy structures and higher topological recursion. The resulting formalism includes as a special case the W-algebra constraints satisfied by generating functions for intersection numbers on the moduli space of r-spin curves, but is much more general. This is joint work with Gaetan Borot, Nitin Chidambaram and Dmitry Noschenko.