
Date Time 
Location  Speaker 
Title – click for abstract 

08/28 2:00pm 
BLOC 628 
Sherry Gong UCLA 
On the KronheimerMrowka concordance invariant
We will talk about Kronheimer and Mrowka’s knot concordance invariant, $s^\sharp$. We compute the invariant for various knots. Our computations reveal some unexpected phenomena, including that $s^\sharp$ differs from Rasmussen's invariant $s$, and that it is not additive under connected sums. We also generalize the definition of $s^\sharp$ to links by giving a new characterization of the invariant in terms of immersed cobordisms.


09/13 4:00pm 
BLOC 220 
Caterina Consani Johns Hopkins University 
[Colloquium] Under and above Spec(Z)
The talk will describe some recent geometric constructions related to the algebraic spectrum of the integers and the adele class space of the rationals which are part of a joint work with A. Connes. 

10/02 2:00pm 
BLOC 628 
Clément Dell'Aiera University of Hawai'i 
Exhaustivity of representations at infinity of Roe algebras
Exhaustive representations were introduced by Nistor and Prudhon, motivated by characterizations of Fredholm operators and spectral theory of Nbody Hamiltonians. Coarse geometry deals with the geometry at infinity of metric spaces with bounded geometry via the Roe algebra. In particular, Spakula and Willlett show how to construct a family of representations of the Roe algebra which can be thought of "the representations at infinity". We will be studying when this family is exhaustive. This is joint work with Yu Qiao. 

10/09 2:00pm 
BLOC 628 
Chunlan Jiang Hebei Normal University 
Similarity invariants of essentially normal CowenDouglas operators and Chern polynomials
In this talk, I will discuss our resent work on a class of essentially normal operators by using the geometry method from the CowenDouglas theory and a BrownDouglasFillmore theorem in the CowenDouglas theory. More precisely, the Chern polynomials and the second fundamental forms are
the similarity invariants (in the sense of Herrero) of this class of essentially normal operators. 

10/16 2:00pm 
BLOC 628 
Jianchao Wu Texas A&M University 
The Ktheory of C*algebras associated to certain infinite dimensional spaces
Noncommutative geometry provides a potent approach to the study of the algebraic geometry (e.g., Ktheory) of infinite dimensional manifolds. In this talk, I will outline the construction of C*algebras associated to HilbertHadamard spaces, understood as a kind of (typically infinite dimensional) nonpositively curved manifolds. Under mild assumptions, these C*algebras retain a remnant of Bott periodicity, which we exploit to prove the Novikov conjecture of geometrically discrete groups of diffeomorphisms. This is joint work with Sherry Gong and Guoliang Yu. 

10/23 2:00pm 
BLOC 628 
Rufus Willett University of Hawai'i 
Decompositions and Ktheory
We introduce a notion of 'local decomposability' for a C*algebra, inspired by the theory of nuclear dimension (due to Winter and Zacharias) and of dynamical complexity (due to Guentner, Yu and the speaker). We derive the existence of a sortof controlled MayerVietoris sequence in this setting, inspired by work of OyonoOyono and Yu in controlled Ktheory (although not using that language), and give applications to BaumConnes theory and to the Künneth formula.


10/30 2:00pm 
BLOC 628 
Quanlei Fang The City University of New York 
Revisiting Arveson’s Dirac operator of a commuting tuple
About twenty years ago, Arveson introduced an abstract Dirac operator based on Taylor spectrum and functional calculus. He showed that every Dirac operator is associated with a commuting tuple. The Dirac operator of a commuting tuple has inspired several interesting problems in multivariable operator theory. In this talk, we will revisit the Dirac operator and discuss some related problems. 

11/06 2:00pm 
BLOC 628 
Jintao Deng Texas A&M University 
The Novikov conjecture and group extensions
The Novikov conjecture is an important problem in higher dimensional topology. It claims that the higher signatures of a compact smooth manifold are invariant under orientation preserving homotopy equivalences. The Novikov conjecture is a consequence of the strong Novikov conjecture in the computation of the Ktheory of group C*algebras. In this talk, I will talk about the Novikov conjecture for groups which are extensions of coarsely embeddable groups. 

11/13 2:00pm 
BLOC 628 
Tatiana Nagnibeda University of Geneva 
Various types of spectra and spectral measures on Schreier and Cayley graphs
We will be interested in the Laplacian on graphs associated
with finitely generated groups: Cayley graphs and more generally
Schreier graphs corresponding to some natural group actions. The
spectrum of such an operator is a compact subset of the closed interval
[1,1], but not much more can be said about it in general. We will
discuss various techniques that allow to construct examples with
different types of spectra: connected, union of two intervals, totally
disconnected…, and how this depends on the choice of the generating set
in the group. Types of spectral measures that can arise in these
examples will also be discussed. 

11/13 3:00pm 
BLOC 220 
Paul Schupp University of Illinois at Urbana Champaign 
Closures of Turing Degrees
This talk is on aspect of my general project with Carl
Jockusch on “the coarsification of computability theory”, that is,
bringing the asymptoticgeneric point of view of geometric group theory
into the theory of computability. Classically, computability theory
studies Turing degrees, that is, equivalence classes of subsets of N
which are computationally equivalent. Coarse computability studies how
closely arbitrary subsets of N can be approximated by computable sets.
The idea of coarse computabilty leads to a natural definition of the
closure of a Turing degree in the space S of coarse similarity classes
of subsets of N with the Besicovich metric. It turns out that S is an
interesting space. We will discuss interactions of the topology of S and
properties of Turing degrees. 

11/13 4:00pm 
BLOC 220 
Tullio CeccheriniSilberstein University of Sannio 
Hecke algebras of multiplicityfree induced representations
Given a finite group G and a subgroup K, one says that (G,K) is a
Gelfand pair provided the associated permutation representation
(\lambda, L(G/K)) is multiplicityfree (that is, decomposes into
pairwise nonequivalent irreducible subrepresentations). This condition
is equivalent to the algebra End_G(L(G/K)) of interwining operators
being commutative. Observe that \lambda is nothing but the induced
representation Ind_K^G \iota_K of the trival representation \iota_K of
K. In [CSST] we consider triples (G,K,\theta), where \theta is, more
generally, an irreducible Krepresentation and introduce a Hecketype
algebra H(G,K,\theta)  analogous to End_G(L(G/K))  and show that that
Ind_K^G\theta is multiplicityfree if and only if H (G,K,\theta) is
commutative. We apply our results in the context of the representation
theory of GL_2(q), the general linear group of a field with q elements.
[CSST] Harmonic analysis and spherical functions for multiplicityfree
induced representations of finite groups. Springer (to appear) arXiv:
1811.09526.


11/20 2:00pm 
BLOC 628 
Peter Hochs University of Adelaide 
A localised equivariant index for proper actions and an APS index theorem.
Roe defined a localised version of the coarse index of an elliptic operator that is invertible outside a subset Z of the manifold M it is defined on. An equivariant version of this index was defined for proper and free actions by discrete groups by Xie and Yu. With Guo and Mathai, we extended this to proper actions by any locally compact group G. If Z/G is compact, then this index takes values in the Ktheory of the group C* algebra of G, and generalises the BaumConnes analytic assembly map. It also generalises an equivariant index of Calliastype operators constructed earlier by Guo. Another special case is an equivariant index for proper, cocompact actions on manifolds with boundary, generalising the AtiyahPatodiSinger (APS) index and its equivariant version. With BaiLing Wang and Hang Wang, we obtained an equivariant APS index theorem in this context. Using a version for maximal group C*algebras and Roe algebras, we obtain a link with an index on invariant sections defined earlier with Mathai. 

11/22 3:00pm 
BLOC 624 
Ilya Kachkovskiy Michigan State University 
Almost commuting matrices
Suppose that $X$ and $Y$ are two selfadjoint matrices with the commutator $[X,Y]$ of small operator norm. One would expect that $X$ and $Y$ are close to a pair of commuting matrices. Can one provide a distance estimate which only depends on $\[X,Y]\$ and not on the dimension? This question was asked by Paul Halmos in 1976 and answered positively by Huaxin Lin in 1993 by indirect C*algebraic methods, which did not provide any explicit bounds. It was conjectured by Davidson and Szarek that the distance estimate would be of the form $C\[X,Y]\^{1/2}$. In the talk, I will explain some background on this and related problems, and the main ideas of the proof of this conjecture, obtained jointly with Yuri Safarov. If time permits, I will discuss some current work in progress. 

11/25 2:00pm 
BLOC 628 
Ilan Hirshberg BenGurion University 
Mean cohomological independence dimension and radius of comparison.
I will report on joint work in progress with N. Christopher Phillips.
In 2010, Giol and Kerr published a construction of a minimal dynamical system whose associated crossed product has positive radius of comparison. Subsequently, Phillips and Toms conjectured that the radius of comparison of a crossed product should be roughly half the mean dimension of the underlying system. Upper bounds were obtained by Phillips, HinesPhillipsToms and very recently by Niu, however there were no results concerning lower bounds aside for the examples of Giol and Kerr. In the nondynamical context, work of Elliott and Niu suggests that the right notion of dimension to consider is cohomological dimension, rather than covering dimension (notions which coincide for CW complexes). Motivated by this insight, we introduce an invariant which we call "mean cohomological independence dimension" (more precisely, a sequence of such invariants), for actions of countable amenable groups on compact metric spaces, which are related to mean dimension, and obtain lower bounds for the radius of comparison for crossed products in terms of this invariant. 

12/04 2:00pm 
BLOC 628 
Mizanur Rahaman Institute for Quantum Computing / University of Waterloo 
Bisynchronous Games and Factorizable Maps
In the theory of nonlocal games, the graph isomorphism game stands out to be an intriguing one. Specially when the algebra of this game is considered. This is because this game establishes a close connection between the algebra of the game and the theory of quantum permutation groups. It turns out that the graph isomorphism game is an example of a bisynchronous game. In this talk, I will introduce these games and the corresponding correlations arising from the perfect strategies for such games. Moreover, when the number of inputs is equal to the number of outputs, each bisynchronous correlation gives rise to a completely positive map which will be shown to be factorizable in the sense of HaagerupMusat. This is a joint work with Vern Paulsen. 

12/11 2:00pm 
BLOC 628 
Chris Phillips University of Oregon 
Simplicity of reduced Banach algebras of free groups and their relatives
