10:30am **SCGP:** Mini Course by Paul Wiegmann

**Where:** SCGP 313**When:** 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.

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.

Work in collaboration with M. Kologlu, R. Mahajan, E. Perlmutter, D. Simmons-Duffin.

10:00am Thesis Defense: Shaosai Huang - On the collapsing and convergence of Ricci flows and solitons

**Where:** Math Tower 5-127**When:** 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.

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1:30pm **SCGP:** Physics Seminar: Guy Gur-Ari

**Where:** SCGP 313**When:** Wed, May 23 1:30pm — 2:30pm

**Title:** TBA

3:30pm Special Geometry/Topology Seminar: Ahmed Zeriahi - Plurisubharmonic envelopes and supersolutions

**Where:** 5-127**When:** 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.

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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.

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1:00pm Topology and Symplectic Geometry / Math of Gauge Fields seminar: Andrew Hanlon - Categorical monodromy for mirrors of toric varieties

**Where:** MAT 5-127**When:** 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.

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10:30am **SCGP:** Mini Course by Paul Wiegmann

**Where:** SCGP 313**When:** 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.

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-131**When:** 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).

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Memorial Day

**When:** Mon, May 28