Date 
Speaker 
Title & Abstract 
Host 
April 3, 2014
Special place: AP&M 2402 
Chris Bishop (SUNY Stony Brook) 
Title.
Conformal Maps and Optimal Meshes
Abstract.
The Riemann mapping theorem says that every simply connected proper plane domain can be conformally mapped to the unit disk. This result is over a 100 years old, but the study and computation of such maps is still an active area. In this talk, I will discuss the computational complexity of constructing a conformal map from the disk to an ngon and show that it is linear in n, with a constant that depends only on the desired accuracy. As one might expect, the proof uses ideas from complex analysis, quasiconformal mappings and numerical analysis, but I will focus mostly on the surprising roles played by computational planar geometry and 3dimensional hyperbolic geometry.

Peter Ebenfelt 
Special time:
2:00  3:00, Thursday, May 8 
Vera Serganova
(UC Berkeley) 
Title.
Finitedimensional representations of classical algebraic supergroups
Abstract.
Studying Lie superalgebras and supergroups was initially motivated by applications in physics. In the recent years interesting connections with other branches of mathematics were discovered. The goal of the talk is to review some of these results.

Efim Zelmanov 
May 8 
Burt Totaro
(UCLA) 
Title.
The fundamental group of an algebraic variety, and hyperbolic complex manifolds
Abstract. It is a mystery which groups can occur as fundamental groups of smooth complex projective varieties. It is conceivable that whenever the fundamental group is infinite, the variety has some "negative curvature" properties. We discuss a result in this direction, in terms of "symmetric differentials". There are interesting open questions even about the special case of compact quotients of the unit ball in C^n. (Joint work with Yohan Brunebarbe and Bruno Klingler.) 
James McKernan 
Special time:
4:00  5:00, Friday, May 23 
YaXiang Yuan
(Chinese Acad. Sci.) 
Title.
Abstract. 
Jiawang Nie 
June 5 
Robert Krasny
(Univ. Michigan) 
Title.
Lagrangian Particle Methods for Vortex Dynamics
Abstract. In this talk I'll discuss how Lagrangian particle methods are being used to study the dynamics of fluid vortices. These methods use the BiotSavart integral to recover the velocity from the vorticity and they track the flow map using adaptive particle discretizations. I'll present computations of vortex sheet motion in 2D flow, with reference to KelvinHelmholtz instability, the Moore singularity, spiral rollup, and chaotic dynamics. Other examples include vortex rings in 3D flow, and vortex dynamics on a rotating sphere. 
Bo Li 
Date 
Speaker 
Title & Abstract 
Host 
January 9 
Andrew Blumberg
(UT Austin) 
Title.
Algebraic Ktheory and the geometry of module categories
Abstract.
Algebraic Ktheory is a deep and subtle invariant of rings and schemes, carrying information about arithmetic and geometry. When applied to the group ring of the loop space of a manifold, it captures information about the diffeomorphism group. Over the past 25 years, the study of algebraic Ktheory has been revolutionized by the introduction of trace methods, which use trace (or Chern character) maps to the simpler but related theories of (topological) cyclic and Hochschild homology.

Dragos Oprea 
Special time
2:00  3:00, Friday, January 10 
Yaniv Plan

Title.
Lowdimensionality in mathematical signal processing
Abstract. Natural images tend to be compressible, i.e., the amount of information needed to encode an image is small. This conciseness of information  in other words, low dimensionality of the signal  is found throughout a plethora of applications ranging from MRI to quantum state tomography. It is natural to ask: can the number of measurements needed to determine a signal be comparable with the information content? We explore this question under modern models of lowdimensionality and measurement acquisition. 
Ery AriasCastro 
January 23 
Jacob Bedrossian
(NYU) 
Title.
Inviscid damping and the asymptotic stability of planar shear flows
in the 2D Euler equations
Abstract. We prove asymptotic stability of shear flows close to the planar, periodic Couette flow in the 2D incompressible Euler equations. That is, given an initial perturbation of the Couette flow small in a suitable regularity class, specifically Gevrey space of class smaller than 2, the velocity converges strongly in L2 to a shear flow which is also close to the Couette flow. The vorticity is asymptotically mixed to small scales by an almost linear evolution and in general enstrophy is lost in the weak limit. Joint work with Nader Masmoudi. The strong convergence of the velocity field is sometimes referred to as inviscid damping, due to the relationship with Landau damping in the Vlasov equations. Recent work with Nader Masmoudi and Clement Mouhot on Landau damping may also be discussed. 
Bo Li 
January 30 
Rayan Saab
(UCSD) 
Title.
A compressive sampling of compressed sensing and related areas
Abstract.
Compressed sensing is a signal acquisition paradigm that utilizes the sparsity of a signal (a vector in R^N with s << N nonzero entries ) to efficiently reconstruct it from very few (say n, s < n << N) generalized linear measurements. These measurements often take the form of inner products with random vectors drawn from appropriate distributions, and the reconstruction is typically done using convex optimization algorithms or computationally efficient greedy algorithms.

Peter Ebenfeld 
February 6
CANCELLED 
Toti Daskalopoulos
(Columbia Univ.) CANCELLED 
Title.
Ancient solutions to geometric flows
Abstract.
We will discuss ancient solutions to nonlinear parabolic equations, such as the semilinear heat equation, the Ricci flow on surfaces, the Yamabe flow and the mean curvature flow. We will address the problem of classification of ancient solutions, the existence and classification of solitons as well as the construction or other ancient nonsoliton solutions.
CANCELLED 
Lei Ni 
February 13 
Claus Sorensen
(UCSD) 
Title.
A gentle introduction to local Langlands in families
Abstract. This talk will be geared towards a general audience. Assuming only familiarity with padic numbers, we will first discuss the local Langlands correspondence for GL(n), and explain why it's a wideranging generalization of local class field theory. Then we will follow Emerton and Helm in trying to extrapolate it to a correspondence between representations over more general local rings  whereupon we reformulate the conjectural Ihara lemma in this language. The latter is a big open problem for n>2, which occurred in work of Clozel, Harris, and Taylor, in their attempt to mimic the proof of Fermat's Last Theorem in the context of GL(n). 
Peter Ebenfelt 
Joint Biostat/Math
Colloq.
3:30 Friday, Feb. 21 
Don Rubin
(Harbard) 
Title.
Abstract. 
Dimitris Politis 
March 13 
Gunther Cornelissen
(Utrecht and Caltech) 
Title.
Graph spectra and diophantine equations
Abstract. I will show how to find uniform finiteness results for certain diophantine equations in terms of the Laplace spectrum of an associated graph. The method is to bound the "gonality" of a curve (minimal degree of a map onto a line) by the "stable gonality" of an associated stable reduction graph, and then to bound this stable gonality of the graph (some kind of minimal degree of a map to a tree) in terms of spectral data. The latter bound is a graph theoretical analogue of a famous inequality of Li and Yau in differential geometry. An example of an application is to bound the degree of the modular parametrisation of elliptic curves over function fields. (Joint work with Fumiharu Kato and Janne Kool.) 
Cristian Popescu 
Date 
Speaker 
Title & Abstract 
Host 
October 24 
Todd Kemp
(UCSD) 
Title.
Brownian Motion on Lie Groups: Limits and Fluctuations in High Dimension
Abstract.
Brownian motion is continuous random motion, discovered by early 19th Century botanist Robert Brown, studied by Albert Einstein in one of the three 1905 papers that led to his Nobel prize, and finally put on firm mathematical footing by Norbert Wiener in the 1920s. It is intimately tied to local and global geometry, and is an important tool in studying heat flow on more general manifolds.

Bruce Driver 
October 31 
Jesse Peterson
(Vanderbilt Univ.) 
Title.
Character rigidity for lattices in higher rank groups
Abstract. A character on a group is a class function of positive type. For finite groups, the classification of characters is directly connected to the representation theory of the group and plays a key role in the classification of finite simple groups. Based on the rigidity results of Mostow, Margulis, and Zimmer, it was conjectured by Connes that for lattices in higher rank Lie groups the space of characters should be completely determined by the finite dimensional representations of the lattice. In this talk, I will give an introduction to this conjecture (which has now been solved in a number of cases), and I will discuss its relationship to ergodic theory, abstract harmonic analysis, invariant random subgroups, and von Neumann algebras. 
Adrian Ioana & Hans Wenzl 
November 7 
James McKernan
(UCSD) 
Title.
Boundedness of Fano varieties
Abstract.
Fano varieties are in some sense the simplest type of
algebraic varieties. They are the algebraic analogue of manifolds
with positive curvature, such as spheres. In low dimensions one can
classify Fano varieties (where for an algebraic geometer low means up
to dimension three) and as the dimension increases, they form bounded
families, so that one can in principle classify Fano varieties in all
dimensions.

Peter Ebenfeld 
November 14 
Elham Izadi
(UCSD) 
Title.
Hodge theory and abelian varieties
Abstract. I will give a brief introduction to Hodge theory and discuss Hodgetheoretic problems involving abelian varieties. 
Peter Ebenfeld 
November 21 
Herbert Heyer
(Univ. Tuebingen, Germany) 
Title.
Limit theorems for probability measures on convolution structures of growing dimension
Abstract. Some central limit results on stochastic processes in a compact connected 2point homogeneous space E(d) of growing dimension d are reformulated within the theory of polynomial convolution structures. This approach stresses the algebraictopological relationship between those structures and the asymptotic properties of the stochastic processes under consideration, in particular of random walks and Gaussian processes on E(d) with d \to \infty. 
Pat Fitzsimmons 
3:00  4:00
(special time) November 25 
Elena Fuchs
(UC Berkeley) 
Title.
Thin groups: arithmetic and beyond
Abstract. In 1643, Ren\'{e} Descartes discovered a formula relating curvatures of circles in Apollonian circle packings, constructed by Apollonius of Perga in 200 BC. This formula has recently led to a connection between the construction of Apollonius and orbits of a certain socalled \emph{thin} subgroup $\Gamma$ of $\textrm{GL}_4(\mathbb Z)$. This connection is key in recent results on the arithmetic of Apollonian packings, which I will describe in this talk. A crucial ingredient in the proofs is the spectral gap coming from families of expander graphs associated to $\Gamma$  this gap is far less understood in the case of thin groups than that of nonthin groups. Motivated by this problem, I will then discuss the ubiquity of thin groups and present results on thinness of monodromy groups of hypergeometric equations in the case where these groups act on hyperbolic space. 
Alina Bucur and Kiran Kedlaya 
3:00  4:00
(special time) December 5 
James Demmel
(UC Berkeley) 
Title.
Communication Avoiding Algorithms for Linear Algebra and Beyond
Abstract. Algorithms have two costs: arithmetic and communication, i.e. moving data between levels of a memory hierarchy or processors over a network. Communication costs (measured in time or energy per operation) already greatly exceed arithmetic costs, and the gap is growing over time following technological trends. Thus our goal is to design algorithms that minimize communication. We present algorithms that attain provable lower bounds on communication, and show large speedups compared to their conventional counterparts. These algorithms are for direct and iterative linear algebra, for dense and sparse matrices, as well as direct nbody simulations. Several of these algorithms exhibit perfect strong scaling, in both time and energy: run time (resp. energy) for a fixed problem size drops proportionally to the number of processors p (resp. is independent of p). Finally, we describe extensions to algorithms involving arbitrary loop nests and array accesses, assuming only that array subscripts are affine functions of the loop indices. 
Jiawang Nie 
4:00  5:00
December 5 
Lu Wang
(Johns Hopkins Univ.) 
Title.
Rigidity of Selfshrinkers of Mean Curvature Flow
Abstract.
The study of mean curvature flow not only is fundamental in geometry, topology and analysis, but also has important applications in applied mathematics, for instance, image processing. One of the most important problems in mean curvature flow is to understand the possible singularities of the flow and selfshrinkers, i.e., selfshrinking solutions of the flow, provide the singularity models.

Ben Chow and Lei Ni 