
Date Time 
Location  Speaker 
Title – click for abstract 

09/05 2:00pm 
BLOC 628 
Michael Brannan Texas A&M University 
Quantum permutations and their matrix models
A quantum permutation matrix is an N x N matrix P whose entries are orthogonal projections on some common Hilbert space H with the property that the rows and columns of P sum to the identity operator on H. In the special case where H is the one dimensional Hilbert space, a quantum permutation matrix simply corresponds to an ordinary permutation matrix, and in this case can be thought of as describing a symmetry of an N point set. In this talk I will explain how arbitrary quantum permutation matrices describe the ``quantum symmetries'' of an N point set. Putting all of these quantum permutation matrices together in a cohesive way yields the structure of a quantum group, which is commonly called the Quantum Permutation Group on N letters. Unlike the classical permutation groups, quantum permutation groups turn out to highly infinite and noncommutative objects  in many ways they behave algebraically like the C* and von Neumann algebras associated to nonabelian free groups. Despite the inherent infiniteness of quantum permutation groups, I will show how these objects can nonetheless be wellapproximated by finitedimensional structures. In particular, these objects turn out to be residually finite as discrete quantum groups, and this residual finiteness can in fact be achieved using certain very simple finitedimensional matrix models which I will describe. (Joint work with Alexandru Chirvasitu and Amaury Freslon.) 

09/12 2:00pm 
BLOC 628 
Hao Guo Texas A&M University 
Index of Equivariant CalliasType Operators
I will discuss a class of Diractype operators, called equivariant Calliastype operators, on manifolds equipped with a Lie group action, where the orbit space is noncompact. It turns out that these operators are Fredholm with an index in the Ktheory of the group C*algebra and can be constructed by adding an ordinary (nonFredholm) Dirac operator to an element of the Ktheory of the equivariant Higson corona of the manifold. One can apply the index theory of such operators to prove an obstruction theorem for invariant metrics of positive scalar curvature. 

09/26 2:00pm 
BLOC 628 
Li Gao Texas A&M University 
Pseudodifferential Operators and the local index formula on Moyal Planes
Moyal planes are noncommutative deformation of Euclidean spaces given by canonical commutation relations (CCR). They are prototypes of noncommutative noncompact manifolds. In the recent work of GonzalezPerez, Junge and Parcet, the Pseudodifferential operators on Moyal planes were studied. In this talk, I will talk about the application of Pseudodifferential operators of Moyal plane to the local index formula. We will consider the setting that for a Moyal plane, its covariant derivatives also satisfy CCR relations. This is a joint work with Marius Junge and Edward McDonald. 

10/03 3:00pm 
BLOC 220 
Alan Reid Rice University 
(Joint seminar with Groups and Dynamics Seminar) Distinguishing certain triangle groups by their finite quotients
We prove that some arithmetic Fuchsian triangle groups are profinitely rigid in the sense that they are determined by their set of finite quotients amongst all finitely generated residually finite groups. These include the (2,3,8) triangle group.


10/10 2:00pm 
BLOC 628 
Dean Baskin Texas A&M University 
Diffraction for the Dirac equation with Coulomblike potentials
The Dirac equation describes the relativistic evolution of
electrons and positrons. We consider the (timedependent!) Dirac equation
in three spatial dimensions coupled to a potential with Coulomb
singularities. We show that singularities of the solutions are typically
diffracted by the singularities of the potential and compute the symbol of
the diffracted wave.
In this talk I will 1) describe what I mean by diffraction in a simpler
setting, 2) describe our results for the Dirac equation, and 3) ask the
audience for help understanding these results in a more geometric way.
This talk is based on joint work with Oran Gannot and Jared Wunsch. 

10/12 4:00pm 
BLOC 220 
Rufus Willett University of Hawaii 
Representation stability and topology (Joint with Linear Analysis Seminar)
Let G be a discrete group with a fixed finite generating set
S. A map from G into some (finite dimensional) unitary group U(n) is an
epsilonrepresentation if it is a group homomorphism up to epsilon error
(for the operator norm) on the finite set S. Thus a
quasirepresentation is a close to being a representation in some sense.
The group G is stable if every epsilon representation is close to an
actual representation, in a precise sense. For example, free groups are
fairly obviously stable. However, a famous result of Voiculescu shows
that the rank two free abelian group is not stable. In his thesis,
Loring gave this a topological interpretation: it turns out that
Voiculescu’s result is moreorless equivalent to Bott periodicity.
I’ll try to explain all this, and how topological information can be
used to produce many other examples of nonstable groups. 

10/31 2:00pm 
BLOC 628 
Zhenhua Wang University of Houston 
Noncommutative topology and operator *algebras
An operator $*$algebra is an operator algebra with a completely isometric conjugate linear involution. In this talk, we will talk about general theory of operator $*$algebras such as characterizations of operator $*$algebras, the relationship to their $C^*$covers and real positivity. In the second part of my talk, noncommutative topology in the involutive setting will be discussed. This is joint work with David Blecher. 

11/07 2:00pm 
BLOC 628 
Clement Dell'Aiera University of Hawaii 
Dynamical Property T
We will present a notion of topological property T for group actions
which generalizes Kazhdan's property T for groups and geometric property
T of Willett and Yu. This is work in progress with Rufus Willett. 

11/14 2:00pm 
BLOC 628 
Robin Deeley University of Colorado Boulder 
Relative constructions in Khomology and KKbordism
The BaumDouglas model for Khomology provides a geometric counterpart to the analytic construction of Kasparov. In the framework of index theory, the former is more related to the topological index, while the latter is more related to the analytic index. I will discuss various relative constructions in geometric (i.e., BaumDouglas) Khomology and each case the associated index theoretic invariant. If time permits, some more analytic constructions involving Hilsum's notion of KKbordism will also be discussed. The results in this talk are (in part) joint work with Magnus Goffeng and Bram Mesland. 

11/28 2:00pm 
BLOC 628 
Jinmin Wang Texas A&M University 
Higher rho invariant and pairings with higher cyclic cocyles
In this talk, I will introduce a pairing map between Ktheory of obstruction algebra and higher cyclic cocyles for the group algebras of hyperbolic groups. The main focus of this pairing is to establish a connection between two different approaches to the index theory of manifolds with boundaries. This is joint work with Xiaoman Chen, Zhizhang Xie and Guoliang Yu. 

12/05 2:00pm 
BLOC 628 
Jeffrey Kuan Texas A&M University 
Noncommutative random walks on the dual of gl_n
We construct two noncommutative versions of random walks on the dual of gl_n. The observables are elements of the universal enveloping algebra U(gl_n) [in the first construction] and of the quantum group U_q(gl_n) [in the second construction]. We take asymptotics to find two different generalizations of the twodimensional Gaussian free field. 