# Upcoming Seminars & Events

## Primary tabs

##### Effective Ratner Theorem for ASL(2,R) and gaps in n^(1/2) modulo 1

Let G=SL(2, R) \ltimes R^2 and \Gamma= SL(2, Z) ltimes Z^2. We prove a rate of equidistribution for the orbits of a certain 1-dimensional unipotent flow of \Gamma \quot G, which projects to a closed horocycle in the unit tangent bundle to the modular surface.

##### Slices of co-operations for KGL

The classic structure of the co-operations KU(KU) of topological K-theory as a Hopf algeboid is due to Adams. In joint work with Pelaez, we determine the analogous structure for algebraic K-theory KGL, regarded as a motivic spectrum. Applying the motivic slice filtration, we solve a problem of Voevodsky.

##### Non-simple genus minimizers in lens spaces

When does a knot in a 3-manifold have the smallest genus amongst all knots homologous to it? This is a basic but largely unexplored problem, and addressing it for lens spaces is closely connected with the Berge conjecture, which posits when surgery along a knot in the three-sphere can produce a lens space.

##### Unique Ergodicity and Mixing for the Degenerately forced Boussinesq Equations and related systems

We establish the existence, uniqueness and attraction properties of an ergodic invariant measure for the Boussinesq Equations in the presence of a degenerate stochastic forcing acting only in the temperature equation and only at the largest spatial scales. The central challenge is to establish time asymptotic smoothing properties of the Markovian dynamics corresponding to this system.

##### Epipelagic representations and rigid local systems

Reeder and Yu have constructed in a uniform way certain supercuspidal representations of p-adic groups called "epipelagic representations", using invariant theory studied by Vinberg et al.

##### Berger decomposition, Weitzenbock formula and canonical metrics on four-manifolds

In this talk we will first provide an alternative proof of the Weitzenbock formula using Berger curvature decomposition, as applications we will discuss rigidity of Einstein four-manifolds under some positive curvature

conditions. At the end we will discuss the Weitzenbock formula for generalized quasi-Einstein metrics on four-manifolds.

##### Bounds on the Bondi mass in perturbations of the Schwarzschild exteriors

**Please note special time (4:15). **We consider vacuum perturbations of the Schwarzschild black hole exteriors and derive bounds on the Bondi mass and energy at past null infinity in terms of the area of certain carefully chosen sections of the apparent horizon. The method relies on a perturbation argument; in particular it only requires a slab of space-time around a smooth nul

##### TBA - Okounkov

##### Recent progress on the Landis conjecture

PLEASE CLICK ON SEMINAR TITLE FOR COMPLETE ABSTRACT. In the late 60's, E.M. Landis conjectured that if $\Delta u+Vu=0$ in $\mathbb{R}^n$ with $\|V\|_{L^{\infty}(\mathbb{R}^n)}\le 1$ and $\|u\|_{L^{\infty}(\mathbb{R}^n)}\le C_0$ satisfying $|u(x)|\le C\exp(-C|x|^{1+})$, then $u\equiv 0$.

##### A transition formula for mean values of Dirichlet polynomials

**Please note special day (Monday) and location.**

##### Curvature suppresses the Rayleigh-Taylor instability

PLEASE CLICK ON COLLOQUIUM TITLE FOR EACH COMPLETE ABSTRACT. Naima Hammoud's abstract: Thin films on curved surfaces are widely observed in coating and painting processes and wetting problems.

Haoshu Tian's abstract: The default of one bank can cause other banks to default through two channels: financial contagion in the inter-bank liability network and fire sale in the asset selling market. When the defaulted bank cannot fully pay its debt, the loss is transmitted to other banks.

##### Birational geometry of moduli of stable rational curves

I will report on joint work with Castravet on birational geometry of moduli of stable rational curves with n punctures. In particular, we show that it is not a Mori Dream Space when n is at least 134, answering a question of Hu and Keel.

##### TBA - Li

##### TBA - Avdeeva

##### TBA - Bendersky

##### TBA - Boxer

##### On active scalar equations with nonlocal velocity.

The problem of finite-time singularity versus global regularity for active scalar equations with nonlocal velocities has attracted much attention in recent years. In this talk, I will discuss some recent results in this direction.

##### Structure of measures in Lipschitz differentiability spaces

This talk will present results showing the equivalence of two very different ways of generalising Rademacher's theorem to metric measure spaces. The first was introduced by Cheeger and is based upon