Date 
Speaker 
Title & Abstract 
Host 
April 4 
Shi Jin
(Univ. Wisconsin, Madison) 
Title.
Semiclassical Computation of High Frequency Wave in Heterogeneous Media
Abstract. We introduce semiclassical Eulerian methods that are efficient in computing high frequency waves through heterogeneous media. The method is based on the classical Liouville equation in phase space, with discontinous Hamiltonians due to the barriers or material interfaces. We provide physically relevant interface conditions consistent with the correct transmissions and reflections, and then build the interface conditions into the numerical fluxes. This method allows the resolution of high frequency waves without numerically resolving the small wave lengths, and capture the correct transmissions and reflections at the interface. This method can also be extended to deal with diffraction and quantum barriers. 
Bo Li 
April 11 
Jeong Han Kim (Korea Inst. for Advanced Study (KIAS))

Title.
A tale of two models for random graphs
Abstract.
Since ErdosRenyi introduced random graphs in 1959, two closely
related models for random graphs have been extensively studied. In the
G(n,m) model, a graph is chosen uniformly at random from the
collection of all graphs that have n vertices and m edges. In the
G(n,p) model, a graph is constructed by connecting each pair of two
vertices randomly. Each edge is included in the graph G(n,p) with
probability p independently of all other edges.

Jacques Verstraete 
May 16 
Benny Sudakov
(UCLA) 
Title.
Induced Matchings, Arithmetic Progressions and Communication
Abstract. Extremal Combinatorics is one of the central branches of discrete mathematics which deals with the problem of estimating the maximum possible size of a combinatorial structure which satisfies certain restrictions. Often, such problems have also applications to other areas including Theoretical Computer Science, Additive Number Theory and Information Theory. In this talk we will illustrate this fact by several closely related examples focusing on a recent work with Alon and Moitra. 
Jacques Verstraete 
June 10 
Jean Bernard Lasserre

Title.
Abstract. 
Bill Helton & Jiawang Nie 
Date 
Speaker 
Title & Abstract 
Host 
Jan. 10 
Rayan Saab

Title.
Nearoptimal quantization and encoding for oversampled signals
Abstract. Analogtodigital (A/D) conversion is the process by which signals (e.g., bandlimited functions or finite dimensional vectors) are replaced by bit streams to allow digital storage, transmission, and processing. Typically, A/D conversion is thought of as being composed of sampling and quantization. Sampling consists of collecting inner products of the signal with appropriate (deterministic or random) vectors. Quantization consists of replacing these inner products with elements from a finite set. A good A/D scheme allows for accurate reconstruction of the original object from its quantized samples. In this talk we investigate the reconstruction error as a function of the bitrate, of SigmaDelta quantization, a class of quantization algorithms used in the oversampled regime. We propose an encoding of the SigmaDelta bitstream and prove that it yields nearoptimal error rates when coupled with a suitable reconstruction algorithm. This is true both in the finite dimensional setting and for bandlimited functions. In particular, in the finite dimensional setting the nearoptimality of SigmaDelta encoding applies to measurement vectors from a large class that includes certain deterministic and subGaussian random vectors. Time permitting, we discuss implications for quantization of compressed sensing measurements. 
Ery AriasCastro 
Jan. 15
(Tuesday) 
Claus Sorensen
(Princeton Univ.) 
Title.
Abstract. 
Cristian Popescu 
Jan. 17 
Sergey Kitaev
(Strathclyde Univ.) 
Title.
Two involutions on description trees and their applications
Abstract.
Description trees were introduced by Cori, Jacquard and Schaeffer in 1997 to give
a general framework for the recursive decompositions of several families
of planar maps studied by Tutte in a series of papers in the 1960s.
We are interested in two classes of planar maps which can be thought
as connected planar graphs embedded in the plane or the sphere
with a directed edge distinguished as the root. These classes are
rooted nonseparable (or, 2connected) and bicubic planar
maps, and the corresponding to them trees are called, respectively,
$\beta(1,0)$trees and $\beta(0,1)$trees.

Jeff Remmel 
3:00 pm, Jan. 22
(Special time and date) 
Alex Lubotzky

Title.
Sieve Methods in Group Theory
Abstract. The sieve methods are classical methods in number theory. Inspired by the 'affine sieve method' developed by Sarnak, Bourgain, Gamburd and others, as well as by works of Rivin and Kowalsky, we develop in a systemtic way a 'sieve method' for group theory. This method is especially useful for groups with 'property tau'. Hence the recent results of BreuillardGreenTao, PyberSzabo, Varju and SalehiGolsefidy are very useful and enables one to apply them for linear groups. We will present the method and some of its applications to linear groups and to the mapping class groups. (Joint work with Chen Meiri). 
Efim Zelmanov 
Feb. 7 
Daniel Tartaru
(UC Berkeley) 
Title.
The two dimensional water wave equation
Abstract. The aim of this talk is to provide an overview of recent developments concerning the motion of a two dimensional incompressible and irrotational fluid with a free surface. The emphasis will be on the case when gravity is present, but surface tension is absent. This is joint work with John Hunter, Mihaela Ifrim and Tak Wong. 
Ioan Bejenaru & Jacob Sterbenz 
Feb. 21

Adrian Vasiu
(SUNY) 
Title.
Cohomological invariants of projective varieties in positive characteristic
Abstract. Let X be a projective smooth variety over an algebraically closed field k. If k has characteristic zero, then the singular (Betti) cohomology groups of X are finitely generated abelian groups and therefore all the invariants associated to them are discrete and in fact do not change under good deformations. If k has positive characteristic, then the crystalline cohomology groups of X have a much richer structure and are called Fcrystals over k. In particular, one can associate to them many subtle invariants which vary a lot under good deformations and which could be of either discrete or continuous nature. We present an accessible survey of the classification of Fcrystals over k via subtle invariants with an emphasis on the recent results obtain by us, by Gabber and us, and by Lau, Nicole, and us. 
Cristian Popescu 
March 7 
Stefaan Vaes
(KU Leuven, Belgium) 
Title.
Von Neumann algebras with a unique Cartan decomposition
Abstract. The subject of this talk is at the crossroads of functional analysis, ergodic theory and group theory. Using a construction by Murray and von Neumann (1943), ergodic actions of countable groups on probability spaces give rise to algebras of operators on a Hilbert space, called von Neumann algebras. In a joint work with Sorin Popa, we proved that such crossed product von Neumann algebras by free groups or, more generally, by hyperbolic groups have a unique Cartan subalgebra. I will explain this result and its consequences for the classification of crossed products by free groups. 
Adrian Ioana 
March 14 
Iskander Taimanov (Russian Acad. Sci.)

The Moutard transformation: an algebraic formalism and applications

Justin Roberts and Efim Zelmanov 
March 21 
Marston Conder
(Auckland Univ., New Zealand)

Discrete objects with maximum possible symmetry
Abstract. Symmetry is pervasive in both nature and human culture. The notion of chirality (or `handedness') is similarly pervasive, but less well understood. In this lecture, I will talk about a number of situations involving discrete objects that have maximum possible symmetry in their class, or maximum possible rotational symmetry while being chiral. Examples include geometric solids, combinatorial graphs (networks), maps on surfaces, dessins d'enfants, abstract polytopes, and even compact Riemann surfaces (from a certain perspective). I will describe some recent discoveries about such objects with maximum symmetry, illustrated by pictures as much as possible. 
Efim Zelmanov 
Date 
Speaker 
Title & Abstract 
Host 
Oct. 18 
Todd Kemp
(Math, UCSD) 
Title.
Liberating Random Projections
Abstract. Consider two random subspaces of a finitedimensional vector space  i.e. two random projection matrices P and Q. What is the dimension of their intersection? This (random) integer is almost surely equal to its minimal possible value, which corresponds to the subspaces being in general position. Many more delicate questions about the geometry of the configuration are encoded by the principal angles between the subspaces, which are determined by the eigenvalues of the operatorvalued angle matrix PQP. The situation is much more complicated in infinitedimensions. Even the question of whether two random projections are likely to be in general position is difficult to make sense of, let alone answer. Nevertheless, understanding the operatorvalued angle in an infinitedimensional setting is of critical importance to the biggest open problem in free probability theory  the socalled ``Unification Conjecture''  with ramifications for operator algebras, information theory, and random matrices. In this talk, I will discuss recent and ongoing joint work with Benoit Collins, addressing the configuration of random subspaces in an infinitedimensional context. Using a mixture of techniques from stochastic processes, PDEs, and complex analysis, we prove the general position claim and give a complete understanding of the associated geometry. This work proves an important special case of the Unification Conjecture, and has interesting implications for the original finitedimensional setting as well. 
Bruce Driver 
Oct. 25 
Adrian Ioana
(Math, UCSD) 
Title.
Classification and rigidity for von Neumann algebras
Abstract. I will survey some recent progress on the classification of von Neumann algebras arising from countable groups and their measure preserving actions on probability spaces. This includes the finding of the first classes of (superrigid) groups and actions that can be entirely reconstructed from their von Neumann algebras. 
Bruce Driver 
Nov. 1
(Joint CCR & UCSD Math Colloquium) CANCELLED 
Charlie Fefferman
(Princeton Univ.) 
Title.
Extension and interpolation problems
Abstract. Let X be your favorite space of continuous functions on R^n. How can one decide whether a given function f:E>R, defined on a given (arbitrary) subset E of R^n, extends to a function F in X? The question goes back to Whitney 1934. The answers make contact with algebraic geometry and computer science. 
Joe Buhler & Peter Ebenfelt 
Nov. 8  Brendon Rhoades (Math, UCSD) 
Title.
Meet the New Faculty: Parking Spaces
Abstract. A sequence $(a_1, \dots, a_n)$ of positive integers is a {\it parking function} if its nondecreasing rearrangement $(b_1 \leq \dots \leq b_n)$ satisfies $b_i < i+1$ for all $i$. Parking functions were introduced by Konheim and Weiss to study a hashing problem in computer science, but have since received a great deal of attention in algebraic combinatorics. We will define two new objects attached to any (finite, real, irreducible) reflection group which generalize parking functions and deserve to be called parking spaces. We present a conjecture (proved in some cases) which asserts a deep relationship between these constructions. This is joint work with Drew Armstrong at the University of Miami and Vic Reiner at the University of Minnesota. 
Peter Ebenfelt 
Nov. 15  Ioan Bejenaru (Math, UCSD) 
Title.
Meet the New Faculty:
Dispersive Equations
Abstract. This talk will cover some of the main problems in the field of nonlinear dispersive equations. I will discuss the stability, instability and blowup for some simpler models such as the cubic Nonlinear Schr\"odinger equations, as well as for some more delicate geometric equations. 
Peter Ebenfelt 
Nov. 22  No colloquium. Thanksgiving Holiday.  
Nov. 29 
Mitchell Luskin
(Univ. Minnesota/ IPAM, UCLA) 
Title.
AtomistictoContinuum Coupling Methods
Abstract. Many materials problems require the accuracy of atomistic modeling in small regions, such as the neighborhood of a crack tip. However, these localized defects typically interact through long ranged elastic fields with a much larger region that cannot be computed atomistically. Many methods have recently been proposed to compute solutions to these multiscale problems by coupling atomistic models near a localized defect with continuum models where the deformation is nearly uniform. During the past several years, we have given a theoretical structure to the description and formulation of atomistictocontinuum coupling that has clarified the relation between the various methods and the sources of error. Our theoretical analysis and benchmark simulations have guided the development of optimally accurate and efficient coupling methods. 
Randy Bank & Bo Li 
Nov. 30
(Friday) 
Otmar Venjakob
(Univ. Heidelburg, Germany) 
Title.
Are zetafunctions able to solve Diophantine equations?`
Abstract. Motivated by the question whether (some) Diophantine equations are related to special values of $\zeta$ or $L$functions we first describe the origin of classical Iwasawa theory. Then we give a survey on generalizations of these ideas to noncommutative Iwasawa theory, a topic which has been developed in recent years by several mathematicians, including the author. 
Cristian Popescu 
Dec. 6 
Herbert Heyer
(Univ. Tuebingen, Germany) 
Title.
Arithmetic properties of the semigroup of probability measures
Abstract. There are two basic theorems on arithmetic properties of probability measures on Euclidean space: the Levy decomposition of infinitely divisible probability measures as convolutions of Poisson and Gaussian measures, and the Khintchine factorization of arbitrary probability measures in terms of indecomposable measures and measures without indecomposable factors. Both theorems have been generalized by K. R. Parthasarathy to measures on an Abelian locally compact group. Within this framework the role of Gaussian factors will be discussed. Moreover, characterizations of Gaussian measures (in the sense of Cramer and Bernstein) will be presented whose validity depends on the structure of the underlying group. 
Patrick Fitzsimmons 