10:30am SCGP: Mini Course by Paul Wiegmann Where: SCGP 313When: Mon, May 21 10:30am — 12:30pm Title: Selberg integrals and their applications to conformal field theory, quantum Hall effect and hydrodynamics.
Abstract: Seemingly different phenomena such as quantum Hall effect, superfluids, instabilities in hydrodynamics, models of unstable growth (such as Hele-Shaw problem) have common geometric properties. They could be studied on a unified platform based on Selberg integrals with large number of variables.
In the series of talks I will review recent advances in some of these fields emphasizing their common geometric aspects.
2:00pm SCGP: Physics Seminar: Luca Iliesiu When: Mon, May 21 2:00pm — 3:00pm Title: The conformal bootstrap at finite temperature
Abstract: I will explain how the conformal bootstrap, which has recently seen great success in understanding theories on R^d for d > 2, can be extended to analyzing theories at finite temperature. To do so, I will focus on thermal one and two-point functions of local operators on the plane (on R^{d−1} × S^1 ). By studying the analytic properties of thermal two-point functions, I will present a ”thermal inversion formula” whose output is the set of thermal one-point functions for all operators appearing in a given OPE. As an application of the inversion formula, I will show exact results for the large-N critical O(N)-vector model and will show estimates for the thermal one-point functions in the 3d Ising model.
Work in collaboration with M. Kologlu, R. Mahajan, E. Perlmutter, D. Simmons-Duffin.
Wednesday, May 23
10:00am Thesis Defense: Shaosai Huang - On the collapsing and convergence of Ricci flows and solitons Where: Math Tower 5-127When: Wed, May 23 10:00am — 11:30am Title: On the collapsing and convergence of Ricci flows and solitons Speaker: Shaosai Huang [Stony Brook University]
Abstract: Perelmans no local collapsing theorem asserts that at a positive-time slice of a given Ricci flow on a fixed closed manifold, the volume ratio has a uniform lower bound depending on the initial data, and thus, the blow-up model at a finite time singularity --- a gradient shrinking Ricci soliton --- is non-collapsing, depending on the initial data. This theorem, however, leaves one to wonder what happens for a family of Ricci flows whose initial data are themselves collapsing, and this is what my thesis explores. In this defense, we will present a theorem concerning the regularity of the collapsing limit of Ricci solitons. More specifically, we will present an epsilon-regularity theorem for four dimensional gradient shrinking Ricci solitons that are complete and non-compact, as well as a weak compactness result based on this theorem. This confirms a decade-long conjecture of Cheeger-Tian.
1:30pm SCGP: Physics Seminar: Guy Gur-Ari Where: SCGP 313When: Wed, May 23 1:30pm — 2:30pm Title: TBA
3:30pm Special Geometry/Topology Seminar: Ahmed Zeriahi - Plurisubharmonic envelopes and supersolutions Where: 5-127When: Wed, May 23 3:30pm — 4:30pm Title: Plurisubharmonic envelopes and supersolutions Speaker: Ahmed Zeriahi [Institut de Mathmeatiques de Toulouse]
Abstract: We will define (quasi-)plurisubharmonic envelopes (with obstacle) on compact Khler manifolds, as well as on domains of $C^n$.
We will extend and use an approximation process due to R. Berman to prove several results.
We show that the quasi-psh envelope of a viscosity super-solution is a
pluripotential super-solution for some complex Monge-Ampre equation.
We use these ideas to solve degenerate complex Monge-Ampre equations by
taking lower envelopes of super-solutions.
This is a joint work with Chinn H. Lu and Vincent Guedj. View Details
Thursday, May 24
1:00pm Topology and Symplectic Geometry / Math of Gauge Fields seminar: Andrew Hanlon - Categorical monodromy for mirrors of toric varieties Where: MAT 5-127When: Thu, May 24 1:00pm — 2:00pm Title: Categorical monodromy for mirrors of toric varieties Speaker: Andrew Hanlon [UC Berkeley]
Abstract: We will discuss a monodromy action on the Fukaya-Seidel category of a Laurent polynomial from varying the arguments of the polynomial's coefficients. We will see how this monodromy corresponds under homological mirror symmetry to tensoring by a line bundle naturally associated to the monomials whose coefficients are rotated. This will require a new interpretation of the Fukaya-Seidel category in this setting. View Details
Friday, May 25
10:30am SCGP: Mini Course by Paul Wiegmann Where: SCGP 313When: Fri, May 25 10:30am — 12:30pm Title: Selberg integrals and their applications to conformal field theory, quantum Hall effect and hydrodynamics.
Abstract: Seemingly different phenomena such as quantum Hall effect, superfluids, instabilities in hydrodynamics, models of unstable growth (such as Hele-Shaw problem) have common geometric properties. They could be studied on a unified platform based on Selberg integrals with large number of variables.
In the series of talks I will review recent advances in some of these fields emphasizing their common geometric aspects.
2:30pm Dynamical Systems Seminar: Alena Erchenko - Flexibility, negative curvature, and conformal classes Where: Math Tower P-131When: Fri, May 25 2:30pm — 3:30pm Title: Flexibility, negative curvature, and conformal classes Speaker: Alena Erchenko [Penn State University]
Abstract: Consider a closed orientable surface of negative Euler characteristic. In joint work with A. Katok, we showed the flexibility of metric and topological entropies of geodesic flow in the class of negatively curved metrics of fixed total area. In this talk, we will discuss the flexibility of entropies under the additional restriction that the metrics we consider are conformally equivalent to a fixed hyperbolic metric. It turns out that some restrictions arise. Also, we will point out connections with flexibility of some geometrical data (joint with T. Barthelm). View Details