Upcoming Seminars & Events

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January 29, 2015
4:30pm - 5:30pm
Endoscopy theory for symplectic and orthogonal similitude groups

The endoscopy theory provides a large class of examples of Langlands functoriality, and it also plays an important role in the classification of automorphic forms. The central part of this theory are some conjectural identities of Harish-Chandra characters between a reductive group and its endoscopic groups. Such identities are established in the real case by Shelstad, but they are still largely unknown in the p-adic case due to our limited knowledge of characters in this case. Arthur uses certain (twisted) stable trace formulas to establish the character identities for symplectic groups and orthogonal groups in the p-adic case. In this talk, I will explain how to extend Arthur's character identities to the similitude groups by using some other cases of the twisted stable trace formula. So our work is an application of the long project of Moeglin and Waldspurger, which establishes the twisted stable trace formula in the general case. 

Speaker: Bin Xu, IAS
Location:
IAS Room S-101
February 2, 2015
3:15pm - 4:30pm
TBA - Nets Katz
Speaker: Nets Katz, Caltech
Location:
Fine Hall 314
February 2, 2015
4:30pm - 5:30pm
Efficient numerical methods for wave scattering in periodic geometries

A growing number of technologies (communications, imaging, solar energy, etc) rely on manipulating linear waves at the wavelength scale, and accurate numerical modeling is key for device design.  I will focus on diffraction problems where time-harmonic scalar waves scatter from piecewise-uniform periodic media.  After reviewing the integral equation method, I explain two innovations that allow our solvers to be high-order, robust, and optimal O(N) complexity: 1) new surface quadrature schemes in 2D and 3D compatible with the fast multipole method, and 2) a simple way to "periodize" the integral equation so that the unknowns live on only a single period of the geometry.  The resulting linear systems are solved iteratively or in a fast direct fashion.  I will present efficient solvers for gratings with up to a thousand periodic interfaces or inclusions.  We are extending the techniques to other boundary value problems such as Stokes flow.  This is joint work with: Min Hyung Cho, Jun Lai, Adrianna Gillman, Leslie Greengard, Andreas Kloeckner, Mike O'Neil, Zydrunas Gimbutas.

Speaker: Alex Barnett, Dartmouth College
Location:
Fine Hall 214
February 3, 2015
4:30pm - 5:30pm
Height Fluctuations in Interacting Dimers

Perfect matchings of Z^2 (also known as non-interacting dimers on the square lattice) are an exactly solvable 2D statistical mechanics model. It is known that the associated height function behaves at large distances like a massless gaussian field, with the variance of height gradients growing logarithmically with the distance. As soon as dimers mutually interact, via e.g. a local energy function favoring the alignment among neighboring dimers, the model is not solvable anymore and the dimer-dimer correlation functions decay polynomially at infinity with a non-universal (interaction-dependent) critical exponent. We prove that, nevertheless, the height fluctuations remain gaussian even in the presence of interactions, in the sense that all their moments converge to the gaussian ones at large distances. The proof is based on a combination of multiscale methods with the path-independence properties of the height function. Joint work with V. Mastropietro and F. Toninelli.

Speaker: Alessandro Giuliani, University of Rome 3
Location:
Jadwin Hall 343
February 3, 2015
4:30pm - 5:30pm
Height Fluctuations in Interacting Dimers

Perfect matchings of Z^2(also known as non-interacting dimers on the square lattice) are an exactly solvable 2D statistical mechanics model. It is known that the associated height function behaves at large distances like a massless gaussian field, with the variance of height gradients growing logarithmically with the distance. As soon as dimers mutually interact, via e.g. a local energy function favoring the alignment among neighboring dimers, the model is not solvable anymore and the dimer-dimer correlation functions decay polynomially at infinity with a non-universal (interaction-dependent) critical exponent. We prove that, nevertheless, the height fluctuations remain gaussian even in the presence of interactions, in the sense that all their moments converge to the gaussian ones at large distances. The proof is based on a combination of multiscale methods with the path-independence properties of the height function. Joint work with V. Mastropietro and F. Toninelli.

Speaker: Alessandro Giuliani, University of Rome 3
Location:
Jadwin Hall 343
February 4, 2015
4:30pm - 5:30pm
Stabilization of control systems: From the water clocks to the regulation of rivers

A control system is a dynamical system on which one can act by using controls. For these systems a fundamental problem is the stabilization issue: Is it possible to stabilize a given unstable equilibrium by using suitable feedback laws? (Think to the classical experiment of an upturned broomstick on the tip of one's finger.) On this problem, we present some pioneer devices and works (Ktesibios, Watt, Maxwell, Lyapunov...), some more recent results, and an application to the regulation of the rivers La Sambre and La Meuse in Belgium. A special emphasize is put on positive or negative effects of the nonlinearities.

Speaker: Jean-Michel Coron, Université Pierre et Marie Curie
Location:
Fine Hall 314
February 5, 2015
2:00pm - 3:30pm
The rare interaction limit in a fast-slow mechanical system

In 2008 Gaspard and Gilbert suggested a two-step strategy to derive the 'macroscopic' heat equation from the 'microscopic' kinetic equation. Their model consisted of a chain of localized and rarely interacting hard disks. For a paradigm billiard model - realizing the first, truly dynamical part of the GG-strategy - we obtain the 'mesoscopic' master equation describing a Markov jump process for the energies of the particles.  Joint work with P. Bálint, P. Nándori and IP. Tóth. 

Speaker: Domokos Szász, Budapest University of Technology
Location:
Fine Hall 601
February 5, 2015
3:00pm - 4:00pm
TBA - Alex Scott
Speaker: Alex Scott, Oxford University
Location:
Fine Hall 224
February 5, 2015
4:30pm - 5:30pm
On the formal degrees of square-integrable representations of odd special orthogonal and metaplectic groups

The formal degree conjecture relates the formal degree of an irreducible square-integrable representation of a reductive group over a local field to the special value of the adjoint gamma-factor of its L-parameter. We prove the formal degree conjecture for odd special orthogonal and metaplectic groups in the generic case, which combined with Arthur's work on the local Langlands correspondence implies the conjecture in full generality. This is joint work with Erez Lapid and Zhengyu Mao. 

Speaker: Atsushi Ichino, Kyoto University
Location:
IAS Room S-101
February 9, 2015
3:00pm - 4:00pm
TBA - Willie Wong

Please note special time.

Speaker: Willie Wong, EPFL
Location:
Fine Hall 314
February 9, 2015
4:00pm - 5:00pm
TBA - Andre' Lisibach

Please note special time.

Speaker: Andre' Lisibach, ETH
Location:
TBD
February 9, 2015
4:30pm - 5:30pm
Disordered Hyperuniform Materials: New States of Matter

While there are four commonly observed states of matter (solid crystal, liquid, gas, and plasma), we have known for some time now that there exist many other forms of matter. For example, both quasicrystals and liquid crystals are states of matter that possess properties that are intermediate between those of crystals and conventional liquids. The focus of my talk will be disordered hyperuniform many-body systems [1], which can be regarded to be new distinguishable states of disordered matter in that they behave more like crystals or quasicrystals in the manner in which they suppress large-scale density fluctuations, and yet are also like liquids and glasses because they are statistically isotropic structures with no Bragg peaks. Thus, disordered hyperuniform systems can be regarded to possess a "hidden order" that is not apparent on short length scales while being structurally rotationally invariant. I will describe a variety of different examples of such disordered states of matter, both equilibrium and nonequilibrium varieties. I will demonstrate that there exist classical ground states that are hyperuniform and disordered in a high-density regime down to some critical density, below which the system undergoes a phase transition to ordered states [2]. Disordered hyperuniform systems appear to be endowed with novel physical properties, including complete photonic band gaps comparable in size to those in photonic crystals [3] and improved electronic band-gap properties. Moreover, we have recently shown that photoreceptor cell patterns (responsible for detecting light) in avian retina have evolved to be disordered and hyperuniform [4].

1. S. Torquato and F. H. Stillinger, "Local Density Fluctuations,
Hyperuniform Systems, and Order Metrics," Phys. Rev. E, 68, 041113 (2003).

2. R. D. Batten, F. H. Stillinger and S. Torquato, "Classical Disordered
Ground States: Super-Ideal Gases, and Stealth and Equi-Luminous
Materials," J. Appl. Phys., 104, 033504 (2008).

3. M. Florescu, S. Torquato and P. J. Steinhardt, "Designer Disordered
Materials with Large, Complete Photonic Band Gaps," Proc. Nat. Acad. Sci.,
106, 20658 (2009).

4. Y. Jiao, T. Lau, H. Haztzikirou, M. Meyer-Hermann, J. C. Corbo, and S.
Torquato, "Avian Photoreceptor Patterns Represent a Disordered
Hyperuniform Solution to a Multiscale Packing Problem," Phys. Rev. E, 89,
022721 (2014).

Speaker: Sal Torquato , Princeton University
Location:
Fine Hall 214
February 10, 2015
4:30pm - 5:30pm
TBA - Michael Kiessling
Speaker: Michael Kiessling, Rutgers University
Location:
Jadwin Hall 343
February 12, 2015
4:30pm - 6:00pm
TBA - Gautam Iyer
Speaker: Gautam Iyer, Carnegie Mellon
Location:
Fine Hall 322
February 12, 2015
4:30pm - 5:30pm
TBA - Baldwin
Speaker: John Baldwin, Boston College
Location:
Fine Hall 314
February 13, 2015
1:30pm - 2:30pm
TBA - Luis Diogo
Speaker: Luis Diogo, Columbia University
Location:
IAS Room S-101
February 16, 2015
3:15pm - 4:30pm
TBA - Yannis Angelopoulos
Speaker: Yannis Angelopoulos, University of Toronto
Location:
Fine Hall 314
February 16, 2015
4:30pm - 5:30pm
Hypothesis Testing on Random Networks

I will discuss some new hypothesis testing problems on random graph models. A popular example is the problem of detecting community structure in a graph. Here we will consider more exotic situations, such as testing one of the basic assumption in social network analysis: whether the graph has "geometric structure". We will also talk about dynamical models of random graphs (such as preferential attachment), and how to test different hypotheses on the "history" of these graphs.

Speaker: Sebastien Bubeck, Princeton University - ORFE
Location:
Fine Hall 214
February 19, 2015
2:30pm - 3:30pm
Existence of Lefschetz fibrations on Stein/Weinstein domains

Please note special day and location.   I will describe joint work with E. Giroux in which we show that every Weinstein domain admits a Lefschetz fibration over the disk (that is, a singular fibration with Weinstein fibers and Morse singularities). We also prove an analogous result for Stein domains in the complex analytic setting. The main tool used to prove these results is Donaldson's quantitative transversality.

Speaker: John Pardon, Stanford University
Location:
TBD
February 19, 2015
4:30pm - 6:00pm
TBA - Lenya Ryzhik
Speaker: Lenya Ryzhik, Stanford University
Location:
Fine Hall 322

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