Upcoming Seminars & Events

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December 1, 2014
4:30pm - 5:30pm
When Exactly Do Quantum Computers Provide a Speedup?

Twenty years after the discovery of Shor's factoring algorithm, I'll survey what we now understand about the structure of problems that admit quantum speedups.  I'll start with the basics, discussing the hidden subgroup, amplitude amplification, adiabatic, and linear systems paradigms for quantum algorithms.  Then I'll move on to some general results, obtained by Andris Ambainis and myself over the last few years, about quantum speedups in the black-box model.  These results include the impossibility of a superpolynomial quantum speedup for any problem with permutation symmetry, and the largest possible separation between classical and quantum query complexities for any problem.

Speaker: Scott Aaronson , MIT
Location:
Fine Hall 214
December 2, 2014
2:00pm - 3:00pm
TBA - Nori
Speaker: Mahdav Nori , University of Chicago
Location:
IAS Room S-101
December 2, 2014
4:00pm - 5:30pm
Interface dynamics for incompressible flows

The goal of these lectures is to present the main ideas and arguments of recent results concerning global solutions and finite time singularities for interface dynamics. In particular those contour dynamics that are given by basic fluid mechanics systems; Euler´s equation, Darcy´s law and the Quasi-geostrophic equation. These give rise to problems such as water wave, Muskat, and the evolution of sharp fronts of temperature.

Speaker: Diego Cordoba Gazolaz, Princeton University
Location:
Fine Hall 110
December 3, 2014
11:00am - 12:30pm
TBA - McLean

Please note special day.

Speaker: Mark McLean , Stony Brook University
Location:
IAS Room S-101
December 4, 2014
2:00pm - 3:30pm
TBA - Pausader
Speaker: Benoit Pausader , Princeton University
Location:
Fine Hall 601
December 4, 2014
3:00pm - 4:00pm
TBA - Patel
Speaker: Amit Patel, IAS
Location:
Fine Hall 314
December 4, 2014
3:00pm - 4:00pm
On the number of rich lines in truly high dimensional sets

We prove a new upper bound on the number of r-rich lines (lines with at least r points) in a `truly' d-dimensional configuration of points v_1,...,v_n over the complex numbers. More formally, we show that, if the number of r-rich lines is significantly larger than n^2/r^d then there must exist a large subset of the points  contained in a hyperplane. We conjecture that the factor r^d can be replaced with a tight r^{d+1}. If true,  this would generalize the classic Szemeredi-Trotter theorem  which gives a bound of n^2/r^3 on the number of r-rich lines in a planar configuration. This conjecture was shown to hold in R^3 in a seminal work of Guth and Katz (2010) and was recently proved  over R^4 (under some additional restrictions) by Solomon and Sharir.  Although our bound is not optimal, it is the first to hold in arbitrary dimension. For the special case of arithmetic progressions (r collinear points that are evenly distanced) we give a bound that is tight up to low order terms, showing that a d-dimensional grid achieves the largest number of r-term progressions. Joint work with Sivakanth Gopi (Princeton).

Speaker: Zeev Dvir, Princeton University
Location:
Fine Hall 224
December 4, 2014
4:30pm - 6:00pm
Interface Singularities for the Euler Equations

The fluid interface  ``splash'' singularity was introduced by Castro, C\'{o}rdoba,  Fefferman, Gancedo, \& G\'{o}mez-Serrano.  A splash singularity occurs when a fluid interface remains locally smooth but self-intersects in finite time.   In this talk, I will very briefly discuss how we construct splash singularities for the one-phase 3-D Euler and Navier-Stokes equations.  I will then discuss the problem of two-phase Euler flow.   Recently, Fefferman, Ionescu, and Lie have shown that a locally smooth vortex sheet cannot self-intersect in finite time.   I will explain our proof of this result, which is based on elementary arguments and some precise blow-up rates for the gradient of the velocity of the fluid through which the interfaces tries to self-intersect.   This is joint work with D. Coutand. 

Speaker: Steve Shkoller , UC Davis
Location:
Fine Hall 322
December 4, 2014
4:30pm - 5:30pm
Mean Curvature Flow of Cones

For smooth initial hypersurfaces one has short time existence and uniqueness of solutions to Mean Curvature Flow.  For general initial data Brakke showed that varifold solutions exist, but that they need not be unique if the initial data are non smooth.  In this talk I will discuss the multitude of solutions to MCF that exist if the initial hypersurface is a cone that is smooth except at the origin.  Some of the examples go back to older work with Chopp, Ilmanen, and Velazquez, other examples are recent. 

Speaker: Sigurd Angenent, University of Wisconsin, Madison
Location:
Fine Hall 214
December 4, 2014
4:30pm - 5:30pm
Level raising mod 2 and arbitrary 2-Selmer ranks

We prove a level raising mod p=2 theorem for elliptic curves over Q, generalizing theorems of Ribet and Diamond-Taylor. As an application, we show that the 2-Selmer rank can be arbitrary in level raising families. We will begin by explaining our motivation from W. Zhang's approach to the p-part of the BSD conjecture. Explicit examples will be given to illustrate different phenomena compared to odd p. This is joint work with Bao V. Le Hung.

Speaker: Chao Li , Harvard University
Location:
IAS Room S-101
December 4, 2014
4:30pm - 5:30pm
Heegaard Floer homologies and cuspidal curves
Speaker: Maciej Borodzik, University of Warsaw
Location:
Fine Hall 314
December 4, 2014
5:45pm - 6:45pm
Geometry of the space of probability measures

The space of probability measures, on a compact Riemannian manifold, carries the Wasserstein metric coming from optimal transport. Otto found a remarkable formal Riemannian metric on this infinite-dimensional space. It is a challenge to make rigorous sense of the ensuing formal calculations, within the framework of metric geometry. I will describe what is known about geodesics, curvature, tangent spaces (cones) and parallel transport. 

Speaker: John Lott, University of California, Berkeley
Location:
Fine Hall 214
December 5, 2014
1:30pm - 2:30pm
TBA - Xu
Speaker: Guangbo Xu , UCI
Location:
Fine Hall 322
December 5, 2014
2:00pm - 3:00pm
TBA - Saint-Raymond

This is a joint Analysis - Analysis of Fluids and Related Topics seminar.

Speaker: Laure Saint-Raymond , ENS, France
Location:
Fine Hall 214
December 5, 2014
2:00pm - 3:00pm
TBA - Saint-Raymond

This is a joint Analysis of Fluids and Related Topics - Analysis seminar.

Speaker: Laure Saint-Raymond , ENS, France
Location:
Fine Hall 214
December 5, 2014
3:00pm - 4:00pm
Pluriclosed flow and generalized Kahler geometry

In joint work with G. Tian I introduced a natural evolution equation generalizing the Kahler Ricci flow to complex, non-Kahler manifolds.  Moreover we showed that this equation preserves "generalized Kahler geometry."  In this talk I will discuss further results on this flow in the generalized Kahler setting, including a sharp long time existence result for complex surfaces.  These results lead to strong rigidity and classification results for generalized Kahler structures. 

Speaker: Jeff Streets, University of California Irvine
Location:
Fine Hall 314
December 5, 2014
4:00pm - 5:30pm
Interface dynamics for incompressible flows

The goal of these lectures is to present the main ideas and arguments of recent results concerning global solutions and finite time singularities for interface dynamics. In particular those contour dynamics that are given by basic fluid mechanics systems; Euler´s equation, Darcy´s law and the Quasi-geostrophic equation. These give rise to problems such as water wave, Muskat, and the evolution of sharp fronts of temperature.

Speaker: Diego Cordoba Gazolaz, Princeton University
Location:
Fine Hall 110
December 8, 2014
3:15pm - 4:30pm
Discrete maximal functions in higher dimensions
Speaker: Bartosz Trojan , Uniwersytet Wroclawski, Poland
Location:
Fine Hall 314
December 9, 2014
11:00am - 12:00pm
The Euclidean Distance Degree

The nearest point map of a real algebraic variety with respect to Euclidean distance is
an algebraic function. The Euclidean distance degree is the number of critical points for
this optimization problem. We focus on varieties seen in engineering applications, and
we discuss tools for exact computation. Our guiding example is the Eckart-Young Theorem
which relates the nearest point map for low rank matrices with the singular value
decomposition. This is joint work with Jan Draisma, Emil Horobet, Giorgio Ottaviani,
Rekha Thomas. [Preprint: http://front.math.ucdavis.edu/1309.0049 ]

Speaker: Bernd Sturmfels, U.C. Berkeley
Location:
Sherrerd Hall 125
December 9, 2014
4:00pm - 5:30pm
Interface dynamics for incompressible flows

The goal of these lectures is to present the main ideas and arguments of recent results concerning global solutions and finite time singularities for interface dynamics. In particular those contour dynamics that are given by basic fluid mechanics systems; Euler´s equation, Darcy´s law and the Quasi-geostrophic equation. These give rise to problems such as water wave, Muskat, and the evolution of sharp fronts of temperature.

Speaker: Diego Cordoba Gazolaz, Princeton University
Location:
Fine Hall 110

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