Colloquia, AY 20122013
Thursdays 4:10 pm in 5211 Stevenson Center, unless otherwise noted
Tea at 3:30 pm in 1425 Stevenson Center
August 23, 2012 
The Fall 2012 Faculty Assembly, no colloquium


August 29, 2012 
Martin, Gaven (New Zealand Institute for Advanced Study) New approaches to modelling nonlinear phenomena This is a very general talk which will not be at all technical and will be painted with a broad brush. When deforming a material body (e.g. heating, bending, stretching or otherwise stressing), physics In this talk I will discuss some recent work with others about a special interesting case modelling nonlinear phenomena in elastic media by Contact person: 
September 13, 2012 
Nigel Higson (Penn State University) Contractions of Lie Groups and Representation Theory Let K be a closed subgroup of a Lie group G. The contraction of G to K Contact person: 
October 11, 2012 
Nicolas Monod (ÉCOLE POLYTECHNIQUE FÉDÉRALE DE LAUSANNE) Fixed points and derivations This expository lecture will lead to a new fixed point Contact person: 
October 25, 2012 
Klaus Boehmer (PhilippsUniversität Marburg) On Finite Element Methods for Fully Nonlinear Second Order Elliptic Equations in R^n This was an open problem for more than 20 years in the communities of Numerical Contact person: 
November 1, 2012 
Department Meeting, no colloquium

November 15, 2012 
Scott Morrison (the Australian National University ) Small index subfactors Over the last two decades our understanding of small index subfactors has improved substantially. We have discovered a slew of examples, some related to finite groups or quantum groups, and other `sporadic’ examples. At present we have a complete classification of (hyperfinite) subfactors with index at most 5, and a few results that push past 5. I’ll explain the main techniques behind these classification results, and also spend a little time describing how we construct the sporadic examples. (Joint work with many people!) Contact person: 
November 29, 2012 
Justin Tatch Moore (Cornell University) Nonassociative Ramsey Theory and the amenability problem for Thompson’s group In 1973, Richard Thompson considered the question of whether his newly defined group $F$ was amenable. The motivation for this problem stemed from his observation — later rediscovered by Brin and Squire — that $F$ did not contain a free group on two generators, thus making it a candidate for a counterexample to the von NeumannDay problem. While the von NeumannDay problem was solved by Ol’shanskii in the class of finitely generated groups and Ol’shanskii and Sapir in the class of finitely presented groups, the question of $F$’s amenability was sufficiently basic so as to become of interest in its own right. In this talk, I will analyze this problem from a Ramseytheoretic Contact person: 
December 6, 2012 
Kasso A. Okoudjou (University of Maryland ) Scalable frames Frames provide a mathematical framework for stably representing signals as linear combinations of basic building blocks that constitute an overcomplete collection. Finite frames are frames for finite dimensional spaces, and are especially suited for many applications in signal processing. The inherent redundancy of frames can be exploited to build compression and transmission algorithms that are resilient not only to lost of information but also to noise. For instance, tight frames constitute a particular class of frames that play important roles in many applications. After giving an overview of finite frame theory, I will consider the question of modifying a general frame to generate a tight frame by rescaling its frame vectors. A frame that positively answers this question will be called scalable. I will give various characterizations of the set of scalable frames, and present some topological descriptions of this set. (This talk is based on joint work with G. Kutyniok, F. Philipp and E. Tuley). Contact person: 
January 8, 2013 
A Special Lecture
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January 10, 2013 
A Special Lecture
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January 15, 2013 
A Special Lecture
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January 18, 2013 
A Special Lecture
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February 7, 2013 
Barry Simon (Cal Tech) Tales of our Forefathers
This is not a mathematics talk but it is a talk for mathematicians. Too often, we think of historical mathematicians as only names assigned to theorems. With vignettes and anecdotes, I’ll convince you they were also human beings and that, as the Chinese say, “May you live in interesting times” really is a curse. Contact person: 
February 14, 2013 
Chris Heil (Georgia Institute of Technology) Music, TimeFrequency Shifts, and Linear Independence
Fourier series provide a way of writing almost any signal as a Contact person: 
February 21, 2013 
Loukas Grafakos (University of Missouri) Gabor ridge functions: theory and applications We discuss a directionally sensitive timefrequency decomposition and representation of functions. The coefficients of this representation allow one to measure the “amount” of frequency the function (signal, image) contains in a certain time interval, and also in a certain direction. This has been previously achieved using a version of wavelets called ridge lets, but in this work we discuss an approach based on timefrequency or Gabor elements. Applications to image processing are discussed. Contact person: 
February 28, 2013 
Yves de Cornulier (Universite ParisSud 11) Actions on trees and ends of groups
A metric space is multiended if it admits a bounded subset whose complement has at least two unbounded connected components. For instance, the line is multiended but higherdimensional Euclidean spaces are not. In the late sixties, Stallings has given a remarkable characterization of those finitely generated groups whose Cayley graph is multiended; the only such torsionfree groups are free products of two nontrivial groups! A key part of the proof is the construction of a action on a tree; in the seventies, the study of general group actions on trees was achieved by Bass and Serre. In the meantime, the study of multiended Schreier graphs was started by Abels and Houghton, and a remarkable connection with nonpositively curved cube complexes was discovered by Sageev twenty years later. While outstanding applications of cube complexes have been made since then, I will try to focus on the question of understanding which finitely generated groups admit a multiended Schreier graph. Contact person: 
March 14, 2013 
Marcus Khuri (SUNY at Stony Brook) Geometric Inequalities in General Relativity
Perhaps the most outstanding open problem in mathematical relativity is the so called Cosmic Censorship conjecture, which roughly asserts that singularities in the evolution of spacetime must always be hidden inside black holes, and moreover that spacetime must eventually settle down to a stationary final state. Based on heurisitc physical arguments, R. Penrose derived a series of geometric inequalities relating total mass, area of the event horizon, electricromagnetic charge, and angular momentum, all of which serve as necessary conditions for the validity of Cosmic Censorship. In this talk, we will detail recent advances in the rigorous mathematical formulation and proofs of some of these inequalities. Contact person: 
March 18, 2013, Special Colloquium SC 1308 
XiuXiong Chen (SUNY at Stony Brook) Kaehler Einstein metrics on Fano manifolds
In 1980s, Yau conjectured that the existence of Kaehler Einstein metric on Fano manifold is related to an algebraic geometric condition of “stability”. The recent work with Donaldson, Sun Song confirmed this conjecture. In the talk, we will review history of this problems as well as this subject, and we also will review earlier work of G. Tian and others on this problems. We will outline the strategy of proof, which involves deforming through metrics with cone singularities. If time permits, we will give more details about various aspects of the proof. Contact person: 
March 21, 2013 
Paul Schupp (UIUC) Asymptotic density and the theory of computability
Eighty years after the beginning of the general theory of computability, ideas from the “asymptotic point of view” prevalent in several areas of mathematics have begun to interact with computability theory. This will be a very general talk, developing the necessary ideas from scratch. I will try to give an idea of how this point of view leads to new questions and new answers. Contact person: 
March 28, 2013 
Marston Conder (University of Auckland, New Zealand), AMSNZMS Maclaurin Lecturer 2013 Discrete objects with maximum possible symmetry
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. Contact person: 
April 4, 2013 
The Spring 2013 Faculty Assembly, no colloquium

April 11, 2013 
Oleg R. Musin (University of Texas at Brownsville) The kissing problem in three and four dimensions
The kissing number k(n) is the maximal number of equal nonoverlapping spheres in ndimensional space that can touch another sphere of the same size. This problem in dimension three was the subject of a famous discussion between Isaac Newton and David Gregory in 1694. In three dimensions the problem was finally solved only in 1953 by Sch\”utte and van der Waerden. It was proved that the bounds given by Delsarte’s method are not good enough to solve the problem in 4dimensional space. Delsarte’s linear programming method is widely used in coding theory. In this talk we will discuss a solution of the kissing problem in four dimensions which is based on an extension of the Delsarte method. This extension also yields a new proof of k(3)<13. We also going to discuss our recent solution of the strong thirteen spheres problem. It is a joint work with Alexey Tarasov. Contact person: 
April 18, 2013 
Math Awards ceremony, no colloquium

Colloquium Chair (20122013): Dechao Zheng
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