
Date Time 
Location  Speaker 
Title – click for abstract 

08/19 1:00pm 
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Yi Wang Vanderbilt University 
HeltonHowe trace formula on submodules
HeltonHowe trace formula gives an explicit description of the traces of antisymmetric sums of Toeplitz operators on the Bergman space. On a submodule of the Bergman module with relatively nice zero locus, previous results show that the cross commutators between the generalized Toeplitz operators with coordinate symbols belong to some Schatten class. A natural question is whether the same HeltonHowe trace formula remain true for such submodules. We answer this question in affirmative, using finite rank approximation and dilation techniques. Abstract 

08/26 1:00pm 
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Giovanni Landi Trieste University 
Solutions to the quantum YB equation and related deformations
We present natural families of coordinate algebras of noncommutative Euclidean spaces and noncommutative products of Euclidean spaces. These coordinate algebras are quadratic ones associated with an Rmatrix which is involutive and satisfies the quantum Yang–Baxter equation. As a consequence they enjoy a list of nice properties, being regular of finite global dimension. Notably, we have spherical manifolds, and noncommutative quaternionic planes as well as noncommutative quaternionic tori. On these there is an action of the classical quaternionic torus SU(2)×SU(2) in parallel with the action of the torus U(1)×U(1) on a complex noncommutative torus. Abstract 

09/02 1:00pm 
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Bruno de Mendonca Braga University of Virginia 
Coarse equivalences of metric spaces and outer automorphisms of Roe algebras
Given a metric space $X$, the Roe algebra of $X$, denoted by $\mathrm{C}^*(X)$, is a $ \mathrm{C} ^*$algebra which encodes many of $X$'s large scale geometric properties. In this talk, I will discuss some uniform approximability results for maps between Roe algebras (we call those "coarselike properties"). I will then talk about applications of these uniform approximability results to isomorphisms between Roe algebras. In particular, given a uniformly locally finite metric space $X$, we obtain that the canonical map from the group of coarse equivalences of $X$ modulo the relation of closeness to the group of outer automorphisms of $ \mathrm{C} ^*(X)$ is surjective if $X$ has property A. This is a joint work with Alessandro Vignati. Abstract 

09/09 1:00pm 
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Anna Duwenig University of Wollongong 
Noncommutative Poincaré Duality of the Irrational Rotation Algebra
The irrational rotation algebra is known to be selfdual in a KKtheoretic sense. The required Khomology fundamental class was constructed by Connes out of the Dolbeault operator on the 2torus, but there has not been an explicit description of the dual element. In this talk, I will geometrically construct that Ktheory class by using a pair of transverse Kronecker flows on the 2torus.This is based on joint work with Heath Emerson (University of Victoria). Abstract 

09/16 1:00pm 
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Kristin Courtney University of Münster (WWU) 
C*structure on images of completely positive order zero maps
A completely positive (cp) map is called order zero when it preserves orthogonality. Such maps enjoy a rich structure, which has made them a key component of completely positive approximations of nuclear C*algebras. Motivated by generalized inductive limits arising from such cp approximations, we consider the structure of the image of a cp order zero map. It turns out that this is captured by a few key properties that one can ask of a selfadjoint subspace of a C*algebra. We will discuss these properties and the implications for generalized inductive sequences. This is joint work with Wilhelm Winter. Abstract 

09/23 1:00pm 
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Rudolf Zeidler University of Göttingen 
Scalar curvature comparison via the Dirac operator
In recent years, Gromov proposed studying the geometry of positive scalar curvature (abbreviated by "psc") via various metric inequalities. In particular, he proposed the following conjecture: Let $M$ be a closed manifold which does not admit a metric of psc. Then for any Riemannian metric on $V = M \times [1,1]$ of scalar curvature $\geq n(n1)$ the estimate $d(\partial_ V, \partial_+ V) \leq 2\pi/n$ holds, where $\partial_\pm V = M \times \{\pm 1\}$ and $n = \dim V$.
Previously, Rosenberg and Stolz conjectured similarly that if $M$ does not admit psc, then $M \times \mathbb{R}$ does not admit a complete metric of psc and $M \times \mathbb{R}^2$ does not admit a complete metric of uniformly psc.
In this talk, we will discuss a new geometric phenomenon consisting of a precise quantitative interplay between distance estimates and scalar curvature bounds which underlies these three conjectures. We will explain that this phenomenon arises if $M$ admits an obstruction to psc using the index theory of Dirac operators. Abstract 

09/30 1:00pm 
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Simone Cecchini University of Göttingen 
A long neck principle for Riemannian spin manifolds with positive scalar curvature
We present results in index theory on compact Riemannian spin manifolds with boundary in the case when the topological information is encoded by bundles which are supported away from the boundary.
As a first application, we establish a ``long neck principle'' for a compact Riemannian spin nmanifold with boundary X, stating that if scal(X) ≥ n(n1) and there is a nonzero degree map f into the nsphere which is area decreasing, then the distance between the support of the differential of f and the boundary of X is at most π/n. This answers, in the spin setting, a question recently asked by Gromov.
As a second application, we consider a Riemannian manifold X obtained by removing a small nball from a closed spin nmanifold Y. We show that if scal(X) ≥ σ >0 and Y satisfies a certain condition expressed in terms of higher index theory, then the width of a geodesic collar neighborhood Is bounded from above from a constant depending on σ and n.
Finally, we consider the case of a Riemannian nmanifold V diffeomorphic to N x [1,1], with N a closed spin manifold with nonvanishing Rosenebrg index.
In this case, we show that if scal(V) ≥ n(n1), then the distance between the boundary components of V is at most 2π/n. This last constant is sharp by an argument due to Gromov. Abstract 

10/07 1:00pm 
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Bogdan Nica IUPUI 
On norms of averaging operators on geometric groups
Given a finite subset S of an infinite discrete group, consider the operator \lambda(S)=\sum_{g\in S} \lambda(g). I will discuss the problem of estimating the operator norm of \lambda(S) in certain `geometric' situations. Abstract 

10/14 1:00pm 
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Paolo Piazza Università di Roma La Sapienza 
Higher genera and C*indices on Gproper manifolds
Higher general for a Gproper manifold without boundary can be defined in analogy with Galois coverings and they are, by definition, geometric objects. To understand their stability properties we need to connect them to higher C^*indices of suitable Dirac operators. This is possible but under additional assumptions on the group G, for example G semisimple and connected and more generally G satisfying the Rapid Decay condition and G/K of nonpositive sectional curvature. I will begin my talk by explaining these results. I will then move to manifolds with boundary and explain how it is possible to define higher genera in this more complicated situation. Crucial to the analysis is a higher C^*index theorem of AtiyahPatodiSinger type. All these results, the last very recent, are in collaboration with Hessel Posthuma. Abstract 

10/21 1:00pm 
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Jonathan Block University of Pennsylvania 
Singular foliations and characteristic classes
We revisit the residue theorem of Baum and Bott computing characteristic classes for certain objects in terms of residues calculated along the singularities of a foliation using techniques from higher homotopy structures. Abstract 

10/28 1:00pm 
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Matthew Lorentz University of Hawai‘i at Mānoa 
The Hochschild cohomology of uniform Roe algebras
Recently Rufus Willett and I showed that all bounded derivations on Uniform Roe Algebras associated to a bounded geometry metric space X are inner in our paper “Bounded Derivations on Uniform Roe Algebras”. This is equivalent to the first Hochschild cohomology group $H^1(C^*_u(X), C^*_u(X))$ vanishing. It is then natural to ask if all the higher groups $H^n(C^*_u(X), C^*_u(X))$ vanish. To investigate the continuous cohomology of a Uniform Roe Algebra we employ the technique of “reduction of cocycles” where we modify a given cocycle by a coboundary to obtain certain properties. I will discuss this procedure and give examples of calculating the higher cohomology groups. Abstract 

11/04 1:00pm 
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Rudy Rodsphon Northeastern University 
A KKtheoretical perspective on quantization commutes with reduction
We propose a reframing of ParadanVergne's approach to the quantization commutes with reduction problem in KKtheory, more especially the index theoretic part that leads to their "Witten nonabelian localization formula". While our method is similar to theirs at least in spirit, interesting conceptual simplifications occur, and it makes the relationship to
MaTianZhang's analytic methods quite apparent.
Time permitting, I'll also sketch another possible way to derive this localization formula, which is purely functorial. Abstract 

11/11 1:00pm 
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Nigel Higson Penn State University 
The Oka principle and Novodvorskii’s theorem
In the early days of Banach algebra Ktheory, Novodvorskii proved that the Gelfand transform for any commutative Banach induces an isomorphism in Banach algebra Ktheory. This is a version of the Oka principle in several complex variables, which identifies equivalence classes of structures, including vector bundles, in the holomorphic and continuous categories in a variety of contexts. Since the Oka principle has long been proposed as a mechanism to understand and indeed prove the BaumConnes conjecture, Novodvorskii’s theorem continues to be of interest in noncommutative geometry. I shall give a more or less selfcontained proof of Novodvorskii’s theorem, along with a rough sketch of possible future extensions into the noncommutative realm. This is joint work with Jacob Bradd. Abstract 