Noncommutative Geometry & Operator Algebras Seminar
Spring 2006
Organizers: Dietmar Bisch, Guoliang Yu
Tuesdays, 4:00pm-5:00pm in SC 1432
Date: 1/17/06
no meeting due to special colloquium
Date: 1/24/06
Speaker: Daoxing Xia, Vanderbilt University
Title: Determinant formula for trace class perturbations of Heisenberg
commutation relations
Date: 1/31/06
Speaker: Marcin Jankiewicz, Vanderbilt University (Physics)
Title: Extensions of Monster Moonshine to c=24k Conformal Field
Theories
Abstract:
We present a family of conformal field theories (or candidates for
CFTs) that is build on extremal partition functions. Spectra of these
theories can be decomposed into the irreducible representations of the
Fischer-Griess Monster sporadic group. Interesting periodicities in the
coefficients of extremal partition functions are observed and
interpreted as a possible extension of Monster moonshine to c=24k
holomorphic field theories.
Date: 2/2/06 (Thursday), Mathematics Colloquium,
4:10-5:00pm in SC 5211
Speaker: Yehuda Shalom, Tel Aviv University (visiting Princeton)
Title: Analytic methods in group theory
Abstract:
We shall try to explain how analytic tools, involving spectral analysis,
ergodic theory and probability on groups, combine together to yield
purely algebraic properties of some interesting classes of groups. We
shall also use the main result, which is entirely elementary in its
statement, as a motivation to discuss some aspects of the fundamental
notions of amenability and property (T), assuming no prior familiarity.
The talk should be accessible to every graduate student.
Date: 2/3/06 (Friday), Special Seminar,
SC 1432, 4:10-5:00pm
Speaker: Yehuda Shalom, Tel Aviv University (visiting Princeton)
Title: Factor and normal subgroups theorems for lattices in products of
groups
Abstract:
I think it would be good to concentrate on one of the main results
which I will describe in the colloquium talk (February 2). It will be an
independent self contained
talk, yet will benefit from the "big picture" motivation presented in the
colloquium talk.
Date: 2/7/06
Speaker: Liangqing Li, University of Puerto Rico (visiting Vanderbilt)
Title: Reduction from dimension three to dimension two for
local spectra of simple AH algebras
Abstract:
In the classification of simple AH algebras, an important
step is the reduction of thedimension of local spectra of the
algebras to dimension three. In this talk I will present a
reduction theorem to reduce the dimension of local spectra from
three to two, using sub-homogeneous algebras. This reduction can
be used to unify the classification of simple AH algebras (due to
Elliott-Gong-Li) and the classification of inductive limit algebras
of matrix algebras over circles with dimension drops (due to
Thomsen).
Date: 2/14/06
Speaker: Dmitri Nikshych, University of New Hampshire
Title: A rigidity theorem for semisimple tensor categories
Abstract:
This talk is based on a joint work with Pavel Etingof and
Viktor
Ostrik.
Tensor categories arise as "non-commutative symmetries" in many
areas of mathematics and physics -- conformal field theory, operator
algebras,
representation theory of quantum groups, and low-dimensional topology.
In this talk I will describe the foundations of the algebraic theory of
semisimple
tensor categories and will prove that such categories and functors between
them
do not admit non-trivial deformations. In particular, the number of
tensor
categories
realizing a given set of fusion rules is finite. I will also introduce the
notion
of a Frobenius-Perron dimension of an object in tensor category and
discuss
its arithmetic properties and applications to classification problems.
Date: 2/21/06
Speaker: Guihua Gong, University of Puerto Rico (visiting Vanderbilt)
Title: AH algebras with ideal property
Abstract:
In this talk, I will discuss a class of AH algebras
which including simple AH algebras and real rank zero AH algebras
as subclasses. We will give a reduction theorem for this class of
C*-algebras, this is a joint work with Cornel Pasnicu and Liangqing Li.
Date: 2/28/06
Speaker: Teodor Banica, Universite Paul Sabatier (Toulouse)
Title: Spectral measures of small index graphs
Abstract:
This is a report on joint work with Dietmar Bisch. Inspired from deep
results in subfactor theory - ADE classification, planar algebras, annular
structure - we associate to any bipartite graph of norm \leq 2 a
probability measure supported on the unit circle. We compute this measure
for ADE graphs, and we get remarkably simple formulae. We also show that
there is a purely analytic approach to this construction by using the
equation \Delta = U+U^{-1}, where \Delta is the discrete Laplacian.
Date: 3/7/06
no meeting (spring break)
Date: 3/14/06
Speaker: Teodor Banica, Universite Paul Sabatier (Toulouse)
Title: Integration over free quantum groups
Abstract:
This is a report on joint work with Benoit Collins. It is known that the
spectral measures of characters of the free quantum groups A_0,A_u,A_s are
semicircular, circular, and free Poisson. These can be regarded as order 0
results, and our purpose is to get now into order 1 problems. The main
result so far is a formulation of the problem in terms of meander
determinants of Di Francesco et al., with a nice application to A_s(4).
Date: 3/16/06 (Thursday), Mathematics Colloquium,
4:10-5:00pm in SC 5211
Speaker: Richard Kadison, University of Pennsylvania
Title: Re-examining the Pythagorean Theorem - A Functional Analyst's
View
Abstract:
In the colloquium talk we'll study some surprising
twists and connections with operator algebras, symmetric
spaces, Schur's work - on reviewing the basic theorem. We'll
start at the beginning.
In the second lecture, we'll study the Schur-Horn extension
and Pythagoras in II1 factors, as well as connections with
the work of Kostant, Atiyah, and Guillemin-Sternberg. This
may be a bit more technical.
Date: 3/17/06 (Friday), Special NCGOA Seminar,
3:10-4:00pm in SC 1431
Speaker: Richard Kadison, University of Pennsylvania
Title: Re-examining the Pythagorean Theorem - A Functional Analyst's
View, Part II
Abstract:
In the colloquium talk we'll study some surprising
twists and connections with operator algebras, symmetric
spaces, Schur's work - on reviewing the basic theorem. We'll
start at the beginning.
In the second lecture, we'll study the Schur-Horn extension
and Pythagoras in II1 factors, as well as connections with
the work of Kostant, Atiyah, and Guillemin-Sternberg. This
may be a bit more technical.
Date: 3/21/06
Speaker: Guihua Gong, University of Puerto Rico (visiting Vanderbilt)
Title: Classification of simple AH algebras: why K group together
with tracial space is enough?
Abstract:
In this talk, I will explain why ordered K-group
together with space of tracial states is enough to classify sipmple
AH algebras by discussing a special case: simple inductive limits of
matrix algebras over interval (which is due to G. Elliott).
Date: 3/23/06 (Thursday), Mathematics Colloquium,
4:10-5:00pm in SC 5211
Speaker: Jonathan Rosenberg, University of Maryland
Title: An analogue of the Novikov Conjecture in complex algebraic geometry
Abstract:
We introduce an analogue of the Novikov Conjecture on higher signatures in the context of the algebraic geometry of (nonsingular) complex projective varieties. This conjecture asserts that certain "higher Todd genera" are birational invariants, and implies birational invariance of certain extra combinations of Chern classes (beyond just the classical Todd genus) in the case of varieties with large fundamental group (in the topological sense). The conjecture is, in a certain sense, best possible, and unlike the usual Novikov Conjecture, it is already known to be true in all cases, though some variants are still open. An interesting biproduct of this work is a curious analogy between the homotopy category of smooth manifolds and the birational category of smooth projective varieties.
Date: 3/28/06
Speaker: Remus Nicoara, Vanderbilt University
Title: A continuous family of non-isomorphic, irreducible,
hyperfinite subfactors with the same standard invariant
Abstract:
We construct a 1-parameter family of irreducible subfactors of the
hyperfinite II$_1$ factor, which are non-isomorphic, have Jones index 6
and have all the same standard invariant. This is joint work with
Dietmar Bisch and Sorin Popa.
********* Starting this week the seminar
will meet at 4:10pm *********
Date: 4/4/06
Speaker: Rongwei Yang, SUNY at Albany
Title: Functional spectrum of contractions
Abstract:
The idea of functional spectrum associates a closed subset of
the Hardy space with a contractive operator. In generic cases,
there is a cononical imbedding of the ordinary spectrum into the
functional spectrum. Functional spectrum has much richer structure and
they enable a finer analysis of contractive operators. In this talk, we will
see some elementary facts and examples.
Date: 4/11/06
no meeting
Date: 4/18/06
Speaker: Guoliang Yu, Vanderbilt University
Title: The coarse geometric Novikov conjecture for a class of
expanders
Abstract: I will first explain what is the coarse geometric Novikov
conjecture and why it is interesting. I will then outline a proof of
the conjecture for a class of expanders. This is joint work with
G. Gong and Q. Wang.
Date: 4/25/06
Speaker: Kunyu Guo, Fudan University
Title: Essentially normal Hilbert modules and K-homology
Abstract:
This talk mainly concerns homogeneous and quasi-homogeneous submodules
of essentially normal Hilbert modules. When the
submodules are essentially normal, their spectrum, essential
spectrum are described by zero varieties of the submodules. In
dimensions $d=2,\,\,3$, the $C^*$-extensions determined by the
corresponding quotient modules give nontrivial information of
algebraic varieties--$K$-homology invariant. In dimension $d=2$,
and in the case of finite multiplicity, it is proved that each
homogeneous submodule is $p$-essentially normal for $p>2$. In
particular, the \textbf{Arveson's Conjecture} is true when $d=2$.
The talk also will describe recent progress in $p$-essential
normality of submodules of Hilbert modules in general. This is a
joint work with K.Wang.