# Upcoming Seminars & Events

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##### Dynamical relativistic liquid bodies

In this talk, I will discuss a new approach to establishing the well-posedness of the relativistic Euler equations for liquid bodies in vacuum. The approach is based on a wave formulation of the relativistic Euler equations that consists of a system of non-linear wave equations in divergence form together with a combination of acoustic and Dirichlet boundary conditions.

##### TBA - Amir Ali Ahmadi

##### Convergence of finite-range weakly asymmetric exclusion processes on a circle

We consider spatially periodic growth models built from weakly asymmetric exclusion processes with finite-range jumps and rates depending locally on configuration. We prove that at a large scale and after renormalization these processes converge to the Hopf-Cole solution of the KPZ equation driven by Gaussian space-time white noise. Since the driving noise of the discrete equation decorrelates slowly in time, the hydrodynamic behaviour of the system needs to be exploited.

##### TBA - Dmitry Batenkov

##### Min-max theory for constant mean curvature hypersurfaces

We describe the construction of closed constant mean curvature (CMC) hypersurfaces using min-max methods. In particular, our theory allows us to show the existence of closed CMC hypersurfaces of any prescribed mean curvature in any closed Riemannian manifold. This work is joint with Xin Zhou.

##### TBA - Ron Aharoni

##### TBA-Minh Binh Tran

##### TBA - Kyle Hayden

##### Kloosterman sums and Siegel zeros

Kloosterman sums arise naturally in the study of the distribution of various arithmetic objects in analytic number theory. The 'vertical' Sato-Tate law of Katz describes their distribution over a fixed field F_p, but the equivalent 'horizontal' distribution as the base field varies over primes remains open. We describe work showing cancellation in the sum over primes if there are exceptional Siegel-Landau zeros. This is joint work with Sary Drappeau, relying on a fun blend of ideas from algebraic geometry, the spectral theory of automorphic forms and sieve theory.

##### Some recent work on conformal biharmonic maps

Biharmonic maps are generalizations of harmonic maps and biharmonic functions. As solutions of a system of 4th order PDEs, examples and the general properties of biharmonic maps are hard to reveal. In this talk, we will talk about some recent work on the study of biharmonic maps among conformal maps. These include examples and classifications of biharmonic conformal immersions of surfaces, biharmonic conformal maps between manifolds of the same dimension, and the links between conformal biharmonicity and the notion of $f$-biharmonic maps and the equations of Yamabe type.

##### TBA - Yuval Peres

##### TBA - Yuval Peres

##### TBA-Lionel Levine

##### Compactification of the configuration space for constant curvature conical metrics

In this joint work with Rafe Mazzeo, we would like to understand the deformation theory of constant curvature metrics with prescribed conical singularities on a compact Riemann surface. We construct a resolution of the configuration space, and prove a new regularity result that the family of constant curvature conical metrics has a nice compactification as the cone points coalesce. This is one key ingredient to understand the full moduli space of such metrics with positive curvature and cone angles bigger than $2\pi$.

##### TBA - Hongbin Sun

##### TBA-Sam Punshon-Smith

##### Unlikely intersections for algebraic curves in positive characteristic

Please follow this link for the abstract: http://www.math.ias.edu/seminars/abstract?event=131079