# Seminars & Events for 2014-2015

##### Outer billiards and the plaid model

Outer billiards is a billiards-like dynamical system which is defined on the outside of a convex shape in the plane. Even for simple shapes, like kites (bilaterally symmetric quadrilaterals), the orbits have an intricate fractal-like structure. I'll explain a combinatorial model, which I call the plaid model, which gives a precise picture of that the outer billiards orbits look like on kites.

##### Moduli space actions and cyclic operads

**Please note different location. **I will describe a combinatorial dg model for the homology of the open moduli spaces of punctured Riemann spheres.

##### Reductions of Galois representations of small slopes.

We investigate the shape of the reduction of certain crystalline Galois representations of integral slope 1 and of fractional slopes in (1,2).

##### Is Dispersion a Stabilizing or Destabilizing Mechanism?

In this talk I will present a unified approach for the effect of fast rotation and dispersion as an averaging mechanism for, on the one hand, regularizing and stabilizing certain evolution equations, such as the Navier-Stokes and Burgers equations.

##### q-Combinatorics: A new view

**Please note special day (Friday). **The idea of q-analogues can be traced back to Euler in the 1700's who was studying q-series, especially specializations of theta functions. Recall a q-analogue is a method to numerate a set of objects by keeping track of its mathematical structure.

##### Variational stability of Kähler Ricci Solitons

I will explain the solution of the varational stability problem for compact Kähler Ricci Solitons.

##### Geometry of minimal surfaces in homogeneous spaces

**Please note special time. ** We will discuss global geometric properties of minimal surfaces and non compact constant mean curvatures surfaces in hyperbolic spaces H(3), H(2)xR and Heisenberg Riemannian space.

##### On a polynomial Carleson operator along the paraboloid

Since Carleson’s original work, the study of the Carleson operator has been taken in many directions, including new methods of proof, higher dimensions, and versions called polynomial Carleson operators with polynomial rather than linear phase.

##### Polynomial Bounds for the Grid-Minor Theorem

**THIS IS A SPECIAL PACM COLLOQUIUM. **One of the key results in Robertson and Seymour's seminal work on graph minors is the Grid-Minor Theorem (also called the Excluded Grid Theorem). The theorem states that for every fixed-size grid H, every graph whose treewidth is large enough, contains H as a minor. This theorem has found many applications in graph theory and algorithms.

##### Boundary layer separation for stationary Prandtl

**This is a joint Analysis of Fluids & Related Topics and Analysis seminar. **We give a rigorous proof of the speed at which Boundary layer separation occurs in Prandtl system. In particular this justifies a heuristic rate proposed by Landau and formal asymptotic expansions proposed by Goldstein and Stewartson.

##### Boundary layer separation for stationary Prandtl

**This is a joint Analysis of Fluids & Related Topics and Analysis seminar. **We give a rigorous proof of the speed at which Boundary layer separation occurs in Prandtl system. In particular this justifies a heuristic rate proposed by Landau and formal asymptotic expansions proposed by Goldstein and Stewartson.

##### A borderline Sobolev inequality on the hyperbolic spaces

About a decade ago, Bourgain, Brezis and van Schaftingen established some borderline Sobolev embeddings on $\mathbb{R}^n$, which lent themselves to the proof of some Gagliardo-Nirenberg inequalities for differential forms on $\mathbb{R}^n$ (see e.g. work of Lanzani and Stein).

##### On the scattering operators for Kahler-Einstein manifolds with strictly pseudoconvex CR-infinity

I will talk about the positivity of scattering operators for Kahler-Einstein manifolds with strictly pseudoconvex CR-infinity which has positive Webster scalar curvature. The result is parallel to Guillarmou-Qing's positivity result for scattering operators for Poincare-Einstein manifolds. I will also give an energy identity between the boundary and the interior.

##### Women and Mathematics - Princeton Day

The mathematics department will host the Princeton day of this year's Women and Mathematics program on Monday, May 18. Since 1994 the Princeton mathematics department and the Institute for Advanced Study have hosted the Women and Mathematics program. The program brings graduate and undergraduate women together with leading researchers for an 11-day intensive mentoring program.

##### On the convergence of Kahler-Ricci flow on minimal models of general type

I will show that the Kahler-Ricci flow on a three dimensional minimal model of general type converges in the Gromov-Hausdorff topology to the unique singular Kahler-Einstein metric. The proof depends on an integral version of Cheeger-Colding-Tian theory and a diameter bound estimate to the singular Kahler-Einstein metric by Song. It is a joint work with Tian.

##### Alumni Open House

Please join the Mathematics Department for our annual Alumni Open House, Friday, May 29 from 2-3:30 pm in the Fine Hall common room (3rd floor). Connect with old friends and hear about some of the current research being done by Math faculty and students.

*There will be informal tea refreshments for the speakers and participants throughout the open house.*

##### Princeton Low-Dimensional Topology Workshop 2015

The workshop will focus on recent developments in low-dimensional topology, with a particular emphasis on modern homological invariants such as Heegaard Floer homology. The workshop is open to anyone; if you wish to register and be included in the mailing list for workshop related updates, please see the conference website at: https://web.math.princeton.edu/~sucharit/TopologyWorkshop15