Upcoming Seminars & Events

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September 19, 2017
2:30pm - 3:30pm
Towards de-mystification of deep learning: function space analysis of the representation layers
PACM IDeAS

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. This approach was already applied successfully to improve the performance of machine learning algorithms such as the Random Forest [2] and tree-based Gradient Boosting [3].

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
Algebraic Geometry Seminar

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
Almost Rigidity of the Positive Mass Theorem
Differential Geometry & Geometric Analysis Seminar

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 smoothly to Euclidean space.  To avoid bubbling, one forbids the sequence of manifolds to have closed interior minimal surfaces, but allows the manifolds to have minimal boundaries.  Dan Lee and I conject

Speaker: Christina Sormani , CUNY
Location:
Fine Hall 314
September 20, 2017
3:00pm - 4:00pm
Local Universality of Random Functions
Probability Seminar

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 21, 2017
3:00pm - 4:30pm
Stability results in graphs of given circumference
Discrete Mathematics Seminar

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}). Improving the Erdos-Gallai theorem, Kopylov proved in 1977 that for c<n, any 2-connected graph G on n vertices with circumference c has at most max (f(n,2,c),f(n,[c/2],c)) edges, with equality if and only if G equals W_{n,2,c} or W_{n,[c/2],c}. Recently, Furedi et al. obtained a stability version of Kopylov's theorem.

Speaker: Jie Ma , University of Science and Technology of China
Location:
Fine Hall 224
September 21, 2017
4:30pm - 5:30pm
TBA - Jonathan Hanselman
Topology Seminar
Speaker: Jonathan Hanselman, Princeton University
Location:
Fine Hall 314
September 21, 2017
4:30pm - 5:30pm
Princeton University/IAS Number Theory Seminar

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. This is a joint work with Pierre Colmez and Gabriel Dospinescu.

Speaker: Wieslawa Niziol , ENS Lyon
Location:
Fine Hall 214
September 21, 2017
4:30pm - 5:30pm
Global well-posedness for the 2D Muskat problem
Analysis of Fluids and Related Topics

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. In this talk I will prove the existence of global, smooth solutions to the 2D Muskat problem in the stable regime whenever the initial data is monotonic or has slope strictly less than 1. The curvature of these solutions solutions decays to 0 as $t$ goes to infinity, and they are unique when the initial data is $C^{1,\epsilon}$.

Speaker: Stephen Cameron, University of Chicago
Location:
Fine Hall 322
September 25, 2017
4:00pm - 5:00pm
PACM/Applied Mathematics Colloquium
Speaker: Amir Ali Ahmadi, Princeton University
Location:
Fine Hall 214
September 27, 2017
2:30pm - 3:30pm
TBA - Dmitry Batenkov
PACM IDeAS
Speaker: Dmitry Batenkov, MIT
Location:
Fine Hall 224
September 27, 2017
3:00pm - 4:00pm
Min-max theory for constant mean curvature hypersurfaces
Differential Geometry & Geometric Analysis Seminar

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
Discrete Mathematics Seminar
Speaker: Ron Aharoni , Haifa University
Location:
Fine Hall 224
September 28, 2017
4:30pm - 5:30pm
TBA - Kyle Hayden
Topology Seminar
Speaker: Kyle Hayden , Boston College
Location:
Fine Hall 314
September 28, 2017
4:30pm - 5:30pm
Kloosterman sums and Siegel zeros
Princeton University/IAS Number Theory Seminar

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.

Speaker: James Maynard , University of Oxford, England
Location:
Fine Hall 214
October 2, 2017
4:00pm - 5:00pm
TBA - Yuval Peres
PACM/Applied Mathematics Colloquium
Speaker: Yuval Peres , Microsoft Research
Location:
Fine Hall 214
October 3, 2017
4:30pm - 6:00pm
TBA - Yuval Peres
Mathematical Physics Seminar
Speaker: Yuval Peres , Microsoft Research
Location:
October 4, 2017
3:00pm - 4:00pm
TBA-Lionel Levine
Probability Seminar
Speaker: Lionel Levine, Cornell University
Location:
Fine Hall 214
October 4, 2017
3:00pm - 4:00pm
Compactification of the configuration space for constant curvature conical metrics
Differential Geometry & Geometric Analysis Seminar

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 $2\pi$.

Speaker: Xuwen Zhu, Stanford University
Location:
Fine Hall 314
October 4, 2017
4:30pm - 5:45pm
Speaker: ,
Location:
TBD
October 5, 2017
4:30pm - 5:30pm