Upcoming Seminars & Events
Please note special day (Tuesday).
Given a projective variety X over a field of characteristic 0, and a positive integer r, we study the rth secant variety of Veronese re-embeddings of X. In particular, I'll explain recent work which shows that the degrees of the minimal equations (and more generally, syzygies) defining these secant varieties can be bounded in terms of X and r independent of the Veronese embedding. This is based on arXiv:1510.04904 and arXiv:1608.01722.
The study of the Poisson geometry of the Teichmuller space and the moduli space of local systems gave rise to the discovery of the Goldman bracket of curves on a surface which in turn led Chas and Sullivan to discover string topology operations on chains on the free loop space of an oriented manifold. Their string topology operations also generalized the Turaev cobracket which did not come from a Poisson geometric origin, and the search for the geometric meaning of all string topology operations continues. I will discuss some Poisson geometry aspects of the moduli stack of Chen connections and how in the large N limit an additional relevant structure appears. This is part of a joint work in progress with Gregory Ginot and Owen Gwilliam.
This is a joint Algebraic Topology / Topology seminar.
This is a joint Topology / Algebraic Topology seminar.
Please note different day and location (Monday, Fine 110.)