Seminars & Events for 2008-2009

February 12, 2009
4:30pm - 6:30pm
Computational geometry of moduli spaces of curves

A fast algorithm for computing intersection numbers of $\psi$- and $\kappa$-classes on moduli spaces of complex algebraic curves is proposed. As a consequence, the exact large genus asymptotics of these numbers (in particular, Weil-Petersson volumes) is numerically derived.

Speaker: Peter Zogarf, Steklov Mathematical Institute, Russian Academy of Sciences
Location:
Fine Hall 314
February 13, 2009
3:00pm - 5:00pm
Compactness Properties of the Space of Genus-$g$ Helicoids

I will discuss a recent application of the work of Colding and Minicozzi of structure of embedded minimal surfaces in $\Real3$ to the study of compactness properties of the space of genus-$g$ helicoids. I will introduce the theory of Colding and Minicozzi and then show how it can be used to show (among other results) that the space of genus-one helicoids is compact (modulo symmetries).

Speaker: Jacob Bernstein, MIT
Location:
Fine Hall 314
February 16, 2009
4:00pm - 6:00pm
Unusual Classical Ground States of Matter

A classical ground-state configuration of a system of interacting particles is one that minimizes the system potential energy. In the laboratory, such states are produced by slowly cooling a liquid to a temperature of absolute zero, and usually the ground states are crystal structures. However, our theoretical understanding of ground states is far from complete.

Speaker: Salvatore Torquato, Progressive Mathematics Initiative and PACM
Location:
Fine Hall 214
February 16, 2009
4:00pm - 6:00pm
Regularity of singular harmonic maps and axially symmetric stationary electrovacuum spacetimes

According to the Ernst-Geroch reduction, to each axially symmetric stationary vacuum/electro-vacuum spacetime, one can associate an axially symmetric harmonic map with singular boundary behavior. This idea has been exploited in the literature to construct asymptotically flat, axially symmetric stationary spacetimes with disconnected horizons, i.e. having multiple black holes.

Speaker: Luc Nguyen, Rutgers University
Location:
Fine Hall 110
February 17, 2009
4:30pm - 6:30pm
Vojta's conjecture on Blowups and GCD Inequalities

Vojta's conjecture is a deep conjecture in Diophantine geometry, implying for example the Bombieri-Lang conjecture and the abc conjecture. In this talk, I will show some cases of the conjecture for blowup varieties. As a consequence, we derive some interesting inequalities of greatest common divisors.

Speaker: Yu Yasufuku, The City University of New York
Location:
Fine Hall 322
February 18, 2009
2:00pm - 4:00pm
Universality at the spectrum edge for random matrices with independent entries: Soshnikov's theorems and some extensions

We shall discuss the distribution of extreme eigenvalues for several classes of random matrices with independent entries. In particular, we shall discuss the results of Soshnikov and some of their recent extensions, and the combinatorial questions that appear in the proofs. (Based on joint work with Ohad Feldheim).

Speaker: Alexander Sodin, Tel Aviv University
Location:
Jadwin Hall A08
February 18, 2009
4:30pm - 6:30pm
Mathematical Questions Arising from Bose-Einstein Condensation

Bose-Einstein condensation was predicted by Einstein in 1925 and was experimentally discovered 70 years later. This discovery was followed by a flurry of activity in the physics community with many new experiments and with attempts to construct a theory of the newly discovered state of matter. In this talk I will review some recent rigorous results in the subject and outline open problems.

Speaker: Israel Michael Sigal, IAS and University of Toronto
Location:
Fine Hall 314
February 19, 2009
12:30pm - 2:30pm
Bend and break

Our goal is to explain the following theorem due to Mori: Given a compact complex manifold $X$ whose tangent bundle has lots of (holomorphic) determinantal sections (a Fano manifold), any pair of points on it lie in the image of a holomorphic map from the Riemann sphere $P^1$.

Speaker: Bhargav Bhatt, Princeton University
Location:
Fine Hall 314
February 19, 2009
2:00pm - 4:00pm
The decay of Fourier modes of solutions of 2-D Navier-Stokes system

Also:

Numerical results related to the talk by D. Li
presented by Nikolai I. Chernov, University of Alabama

Speaker: Dong Li, IAS
Location:
Fine Hall 401
February 19, 2009
2:30pm - 4:30pm
Randomness extractors - applications and constructions

We will investigate the minimal requirements from a random source under which it is potentially useful for generating perfect randomness. The efficient procedures which utilize such sources, "randomness extractors", turn out to have amazing pseudorandomness properties and are useful in numerous contexts. We'll demonstrate applications in complexity theory, error correction and network design.

Speaker: Avi Wigderson, IAS
Location:
Fine Hall 224
February 19, 2009
4:30pm - 6:30pm
Two generator subgroups of the pure braid group

A group satisfies the "Tits alternative" if every subgroup is either virtually solvable or contains a nonabelian free group. This is named after J. Tits who proved that all finitely generated linear groups enjoy this property. The Tits alternative was established for braid groups by Ivanov and McCarthy, but now also follows from linearity (due to Bigelow-Krammer).

Speaker: Chris Leininger, University of Illinois, Urbana-Champaign
Location:
Fine Hall 314
February 19, 2009
4:30pm - 6:30pm
Potential automorphy for certain Galois representations to GL(n)

I will describe recent generalizations of mine to a theorem of Harris, Shepherd-Barron, and Taylor, showing that have certain Galois representations become automorphic after one makes a suitably large totally-real extension to the base field.

Speaker: Thomas Barnet-Lamb, Harvard University
Location:
Fine Hall 214
February 20, 2009
3:00pm - 5:00pm
Geometric flows with rough initial data

In a recent joint work with Herbert Koch (University of Bonn) we showed the existence of a global unique and analytic solution for the mean curvature flow (in arbitrary codimensions) and the Willmore flow of entire graphs for Lipschitz initial data with small Lipschitz norm.

Speaker: Tobias Lamm, University of British Columbia
Location:
Fine Hall 314
February 23, 2009
4:00pm - 6:00pm
Classical convolution inequalities and Boltzmann equations for integrable angular section

We study the integrability properties of the gain part of the Boltzmann collision operator using radial symmetrization techniques from harmonic analysis to show Young's inequality in the case of hard potentials and Hardy-Littlewood-Sobolev inequality for soft potentials. The contacts are given by exact formulas depending on the angular cross section.

Speaker: Irene Gamba, University of Texas at Austin
Location:
Fine Hall 110
February 24, 2009
4:30pm - 6:30pm
Localization bounds for multiparticle systems

We discuss the spectral and dynamical properties of quantum systems of N particles on the lattice of arbitrary dimension, with a Hamiltonian which in addition to the kinetic term includes a random potential with parameters of the model are the strength of the disorder and the strength of the interparticle interaction.

Speaker: Simone Warzel, Technische Universität München
Location:
Jadwin Hall 343
February 25, 2009
4:30pm - 6:30pm
Large N limit of random matrices, free probability and the graded algebra of a planar algebra
Speaker: Vaughan Jones, University of California - Berkeley
Location:
Fine Hall 314
February 26, 2009
12:30pm - 2:30pm
Models and Fields: A delicate Passage to Characteristic p

If a polynomial map from $C^n$ to itself is injective, then it is also surjective. The first proof of this elegant result actually used a passage to characteristic p.

Speaker: Jacob Tsimerman, Princeton University
Location:
Fine Hall 314
February 26, 2009
2:30pm - 4:30pm
Finding Lovasz's Needle in an Exponential Haystack

The Lovasz Local Lemma is a subtle and far-reaching probability lemma. Roughly, given a large number of bad events which are "mostly" independent it sieves out an instance when none of the bad events occur. As an illustrative example, consider a huge family of 10-element sets, where each set overlaps at most 100 others.

Speaker: Joel Spencer, Courant Institute for Mathematics, NYC
Location:
Fine Hall 224
February 26, 2009
4:00pm - 6:00pm
Limit lognormal process, Selberg integral as Mellin transform, and intermittency differentiation.

The limit lognormal process is a multifractal stochastic process with the remarkable property that its positive integral moments are given by the celebrated Selberg integral. We will give an overview of the limit lognormal construction followed by a summary of our results on functional Feynman-Kac equations and resulting intermittency expansions that govern its distribution.

Speaker: Dmitry Ostrovsky, Lehigh University
Location:
Fine Hall 401
February 26, 2009
4:30pm - 6:30pm
Topologically invariant Chern numbers of projective varieties

In 1954 Hirzebruch asked which linear combinations of Chern numbers are topological invariants of smooth complex projective varieties. Until recently, this problem was wide open, with few non-trivial results. We give a complete solution in arbitrary dimensions.

Speaker: Dieter Kotschick, Universität München, IAS
Location:
Fine Hall 314

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