Seminars & Events for 2014-2015

September 25, 2014
3:00pm - 4:00pm
Excluding topological minors and well-quasi-ordering

Robertson and Seymour proved that graphs are well-quasi-ordered by the minor relation and the weak immersion relation. In other words, given infinitely many graphs, one graph contains another as a minor (or a weak immersion, respectively). Unlike the relation of minor and weak immersion, the topological minor relation does not well-quasi-order graphs in general.

Speaker: Chun-Hung Liu , Princeton University
Location:
Fine Hall 224
September 25, 2014
4:30pm - 6:30pm
Some results on singular transport equations arising in fluid mechanics

We will discuss a few recent results in the study of fluid equations which stem from studying the dynamics of transport equations with non-local forcing. These are equations of the form: $f_t +u\cdot\nabla f =R(f)$ where $R$ is a singular integral operator and $u$ is a divergence-free vector field possibly depending upon $f$. These types of equations arise in a variety of physical scenarios.

Speaker: Tarek Elgindi , Princeton University
Location:
Fine Hall 322
September 26, 2014
3:00pm - 4:00pm
Umbilicity and characterization of Pansu spheres in the Heisenberg group

For n≥2 we define a notion of umbilicity for hypersurfaces in the Heisenberg group H_{n}. We classify umbilic hypersurfaces in some cases, and prove that Pansu spheres are the only umbilic spheres with positive constant p(or horizontal)-mean curvature in H_{n} up to Heisenberg translations. This is joint work with Hung-Lin Chiu, Jenn-Fang Hwang, and Paul Yang. 

Speaker: Jih-Hsin Cheng , Academia Sinica, Taiwan
Location:
Fine Hall 314
September 29, 2014
3:15pm - 4:30pm
Focal points and sup-norms of eigenfunctions

Please note special location.  If (M,g) is a compact real analytic Riemannian manifold, we give a necessary and sufficient condition for there to be a sequence of quasimodes saturating sup-norm estimates.

Speaker: Christopher Sogge, Johns Hopkins University
Location:
Fine Hall 110
September 29, 2014
4:30pm - 5:30pm
A geometric approach for sharp Local well-posedness of quasilinear wave equations

Please note special location and time.   The commuting vector fields approach, devised for Strichartz estimates by Klainerman, was employed for proving the local well-posedness  in the Sobolev spaces $H^s$ with $s>2+\frac{2-\sqrt{3}}{2}$ for general quasi-linear wave equation in ${\mathbb R}^{1+3}$ by him and Rodnianski.

Speaker: Qian Wang , University of Oxford, England
Location:
Fine Hall 110
September 29, 2014
4:30pm - 5:30pm
Applications of diffusion maps in dynamical systems

There is great current interest in the use of diffusion maps for dimension reduction. We discuss some examples of diffusion methods applied to understanding dynamical data, in particular combining spectral approaches with delay coordinates. In addition, we extend the usual diffusion map construction by introducing local kernels, a generalization of the standard isotropic kernel.

Speaker: Tim Sauer , George Mason University
Location:
Fine Hall 214
September 30, 2014
2:00pm - 3:30pm
TBA - Nori
Speaker: Madhav Nori , University of Chicago
Location:
IAS Room S-101
September 30, 2014
3:30pm - 4:30pm
TBA - Huh
Speaker: June Huh , Princeton University and IAS
Location:
IAS Room S-101
October 1, 2014
11:15am - 12:15pm
The topology of proper toric maps

Please note special day and time.  I will discuss some of the topology of the fibers of proper toric maps and a combinatorial invariant that comes out of this picture.  Joint with Luca Migliorini and Mircea Mustata.

Speaker: Mark de Cataldo , Stony Brook University
Location:
IAS Room S-101
October 1, 2014
2:00pm - 3:00pm
Increasing subsequences on the plane and the Slow Bond Conjecture

For a Poisson process in R^2 with intensity 1, the distribution of the maximum number of points on an oriented path from (0,0) to (N,N) has been studied in detail, culminating in Baik-Deift-Johansson's celebrated Tracy-Widom fluctuation result.

Speaker: Allan Sly , UC Berkeley
Location:
Fine Hall 322
October 1, 2014
4:30pm - 5:30pm
The 15-theorem & the 290-theorem

The citation for Manjul Bhargava's recent Fields Medal mentions his improvement of my proof (partly with Will Schneeberger) of the 15- theorem, and his proof (with John Hanke) of the 290-theorem. I shall talk about the history of universal quadratic forms, which was started in 1770 by Lagrange's four squares theorem, and culminated about 20 years ago in these two theorems.

Speaker: John Conway, Princeton University
Location:
Fine Hall 314
October 2, 2014
12:30pm - 1:30pm
Uniform strong primeness in matrix rings

A ring $R$ is uniformly strongly prime if some finite $S \subseteq R$ is such that for $a,b \in R$, $aSb = \{0\}$ implies $a$ or $b$ is zero, in which case the bound of uniform strong primeness of $R$ is the smallest possible size of such an $S$. The case of matrix rings $R$ is considered.

Speaker: Henry Thackeray , Princeton University
Location:
Fine Hall 314
October 2, 2014
2:00pm - 3:30pm
On well-posedness and small data global existence for a damped free boundary fluid-structure model

We address a fluid-structure system which consists of the incompressible Navier-Stokes equations and a damped linear wave equation defined on two dynamic domains. The equations are coupled through transmission boundary conditions and additional boundary stabilization effects imposed on the free moving interface separating the two domains.

Speaker: Mihaela Ignatova , Princeton University
Location:
Fine Hall 214
October 2, 2014
3:00pm - 4:00pm
Finiteness properties for the fundamental groups of complex algebraic varieties

We describe some relations obtained in joint work with S.Papadima and A. Suciu between finiteness properties of fundamental groups and resonance and characteristic varieties. 

Speaker: Alex Dimca, IAS
Location:
Fine Hall 314
October 2, 2014
3:00pm - 4:00pm
Bipartite decomposition of graphs

For a graph G, let bc(G) denote the minimum possible number of pairwise edge disjoint complete bipartite subgraphs of G so that each edge of G belongs to (exactly) one of them. The study of this quantity and its variants received a considerable amount of attention and is related to problems in communication complexity and geometry.

Speaker: Noga Alon, Tel Aviv University and IAS, Princeton
Location:
Fine Hall 224
October 2, 2014
4:30pm - 5:30pm
The standard L-function for G_2: a "new way" integral

We consider a Rankin-Selberg integral representation of a cuspidal (not necessarily generic) representation of the exceptional group G2. Although the integral unfolds with a non-unique model, it turns out to be Eulerian and represents the standard L-function of degree 7. We discuss a general approach to the integrals with non-unique models.

Speaker: Nadia Gurevich , Ben Gurion University
Location:
IAS Room S-101
October 2, 2014
4:30pm - 5:30pm
Dynamics and polynomial invariants of free-by-cyclic groups

The theory developed by Thurston, Fried and McMullen provides a near complete picture of the various ways a hyperbolic 3-manifold M can fiber over the circle.

Speaker: Ilya Kapovich, University of Illinois
Location:
Fine Hall 314
October 2, 2014
4:30pm - 6:00pm
Onsager's Conjecture

In 1949, Lars Onsager in his famous note on statistical hydrodynamics conjectured that weak solutions to the Euler equation belonging to Hölder spaces with Hölder exponent greater than 1/3 conserve energy; conversely, he conjectured the existence of solutions belonging to any Hölder space with exponent less than 1/3 which dissipate energy.

Speaker: Tristan Buckmaster, NYU - Courant Institute
Location:
Fine Hall 322
October 3, 2014
2:00pm - 3:00pm
Regularity of manifolds with bounded Ricci curvature and the codimension $4$ conjecture

This talk will concern joint work with Aaron Naber on the regularity of noncollapsed Riemannian manifolds $M^n$ with bounded Ricci curvature $|{\rm Ric}_{M^n}|\leq n-1$, as well as their Gromov-Hausdorff limit spaces, $(M^n_j,d_j)\stackrel{d_{GH}}{\longrightarrow}(X,d)$, where $d_j$ denotes the Riemannian distance.

Speaker: Jeff Cheeger, NYU
Location:
Fine Hall 314
October 6, 2014
3:15pm - 4:30pm
On two extremal problems for the Fourier transform

One of the most fundamental facts about the Fourier transform is the Hausdorff-Young inequality, which states that for any locally compact Abelian group, the Fourier transform maps $L^p$ boundedly to $L^q$, where the two exponents are conjugate and $p \in [1,2]$.

Speaker: Michael Christ , UC Berkeley
Location:
Fine Hall 314

Pages