Seminars & Events for 2017-2018

September 12, 2017
3:00pm - 4:00pm
The Tutte embedding of the mated-CRT map converges to Liouville quantum gravity

We discuss the proof that the Tutte embeddings (a.k.a. harmonic or barycentric embeddings) of certain random planar maps converge to $\gamma$-Liouville quantum gravity ($\gamma$-LQG). Specifically, we treat mated-CRT maps, which are discretized matings of correlated continuum random trees, and $\gamma$ ranges from $0$ to $2$ as one varies the correlation parameter.

Speaker: Ewain Gwynne , MIT
Location:
Fine Hall 110
September 13, 2017
3:00pm - 4:00pm
A conformally invariant gap theorem in Yang-Mills theory

We show a sharp conformally invariant gap theorem for Yang-Mills connections in dimension 4 by exploiting an associated Yamabe-type problem. This is joint work with Jeffrey Streets (UC Irvine) and Matthew Gursky (University of Notre Dame).

Speaker: Casey Kelleher, Princeton University
Location:
Fine Hall 314
September 14, 2017
12:30pm - 1:30pm
Unknotting 2-dimensional spheres in S^4

In this talk, we discuss an interesting link between topology in dimensions 3 and 4. Scharlemann (1985) proved that a 2-sphere embedded in S^4 with 4 critical heights (an analog of bridge number from knot theory in S^3) is the boundary of a smooth 3-ball.

Speaker: Maggie Miller, Princeton University
Location:
Fine Hall 110
September 14, 2017
4:30pm - 5:30pm
2^∞-Selmer groups, 2^∞-class groups, and Goldfeld's conjecture

Take E/Q to be an elliptic curve with full rational 2-torsion (satisfying some extra technical assumptions). In this talk, we will show that 100% of the quadratic twists of E have rank less than two, thus proving that the BSD conjecture implies Goldfeld's conjecture in these families.

Speaker: Alex Smith , Harvard University
Location:
IAS Room S-101
September 18, 2017
3:00pm - 4:30pm
Regularity and blow up in models of fluid mechanics

I will discuss a family of modified SQG equations that varies between 2D Euler and SQG with patch-like initial data defined on half-plane. The family is modulated by a parameter that sets the degree of the kernel in the Biot-Savart law. The main result I would like to describe is the phase transition in the behavior of solutions that happens right beyond the 2D Euler case.

Speaker: Alexander Kiselev, Duke University
Location:
Fine Hall 314
September 18, 2017
4:00pm - 5:00pm
Walking within growing domains: recurrence versus transience

When is simple random walk on growing in time d-dimensional domains recurrent? For domain growth which is independent of the walk, we review recent progress and related universality conjectures about a sharp recurrence versus transience criterion in terms of the growth rate.

Speaker: Amir Dembo, Stanford University
Location:
Fine Hall 214
September 19, 2017
2:30pm - 3:30pm
Towards de-mystification of deep learning: function space analysis of the representation layers

PLEASE NOTE DIFFERENT DAY (TUESDAY).  We propose a function space approach to Representation Learning [1] and the analysis of the representation layers in deep learning architectures. We show how to compute a `weak-type'  Besov smoothness index that quantifies the geometry of the clustering in the feature space.

Speaker: Shai Dekel, Tel Aviv University
Location:
Fine Hall 224
September 19, 2017
4:30pm - 5:30pm
A variety with non-finitely generated automorphism group

If X is a projective variety, then Aut(X)/Aut^0(X) is a countable group, but little is known about what groups can occur. I will construct a projective variety for which this group is not finitely generated, and discuss how the construction can adapted to give an example of a complex projective variety with infinitely many non-isomorphic real forms.

Speaker: John Lesieutre , Penn State
Location:
Fine Hall 322
September 20, 2017
3:00pm - 4:00pm
Local Universality of Random Functions

In this talk, we discuss local universality results for a general class of random functions that includes random trigonometric polynomials and random orthogonal polynomials. We then apply these results to obtain estimates for the number of real roots and prove, in some cases, that this number satisfies the Central Limit Theorem. This is joint work with Van Vu.

Speaker: Oanh Nguyen, Princeton University
Location:
Fine Hall 214
September 20, 2017
3:00pm - 4:00pm
Almost Rigidity of the Positive Mass Theorem

The Positive Mass Theorem states that an asymptotically flat Riemannian manifold, $M^3$, with nonegative Scalar curvature has nonnegative ADM mass, $m_{ADM}(M)\ge 0$, and if the ADM mass is 0 then we have rigidity: the manifold is isometric to Euclidean space.  It has long been known that if one has a sequence of such manifolds $M^3_j$ with $m_{ADM}(M_j) \to 0$ then $M_j$ need not converge smoo

Speaker: Christina Sormani , CUNY
Location:
Fine Hall 314
September 21, 2017
3:00pm - 4:30pm
Stability results in graphs of given circumference

In this talk we will discuss some Turan-type results on graphs with a given circumference. Let W_{n,k,c} be the graph obtained from a clique K_{c-k+1} by adding n-(c-k+1) isolated vertices each joined to the same k vertices of the clique, and let f(n,k,c)=e(W_{n,k,c}).

Speaker: Jie Ma , University of Science and Technology of China
Location:
Fine Hall 224
September 21, 2017
4:30pm - 5:30pm
Global well-posedness for the 2D Muskat problem

The Muskat problem was originally introduced by Muskat in order to model the interface between water and oil in tar sands. In general, it describes the interface between two incompressible, immiscible fluids of different constant densities in a porous media.

Speaker: Stephen Cameron, University of Chicago
Location:
Fine Hall 322
September 21, 2017
4:30pm - 5:30pm
Bordered Heegaard Floer homology with torus boundary via immersed curves

I will describe a geometric interpretation of bordered Heegaard Floer invariants in the case of a manifold M with torus boundary. In particular these invariants, originally defined as homotopy classes of modules over a particular algebra, can be described as collections of decorated immersed curves in the boundary of M.

Speaker: Jonathan Hanselman, Princeton University
Location:
Fine Hall 314
September 21, 2017
4:30pm - 5:30pm
Cohomology of p-adic Stein spaces

I will discuss a comparison theorem that allows us to recover p-adic (pro-)etale cohomology of p-adic Stein spaces with semistable reduction over local rings of mixed characteristic from complexes of differential forms. To illustrate possible applications, I will show how it allows us to compute cohomology of Drinfeld half-space in any dimension and  of its coverings in dimension one.

Speaker: Wieslawa Niziol , ENS Lyon
Location:
Fine Hall 214
September 25, 2017
3:00pm - 4:00pm
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.

Speaker: Todd Oliynyk , Monash University
Location:
Fine Hall 314
September 25, 2017
4:00pm - 5:00pm
TBA - Amir Ali Ahmadi
Speaker: Amir Ali Ahmadi, Princeton University
Location:
Fine Hall 214
September 26, 2017
3:00pm - 4:00pm
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.

Speaker: Konstantin Matetski , University of Toronto
Location:
Fine Hall 110
September 27, 2017
2:30pm - 3:30pm
TBA - Dmitry Batenkov
Speaker: Dmitry Batenkov, MIT
Location:
Fine Hall 224
September 27, 2017
3:00pm - 4:00pm
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.

Speaker: Jonathan Zhu, Harvard University
Location:
Fine Hall 314
September 28, 2017
3:00pm - 4:30pm
TBA - Ron Aharoni
Speaker: Ron Aharoni , Haifa University
Location:
Fine Hall 224

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