
Date Time 
Location  Speaker 
Title – click for abstract 

01/22 1:00pm 
Zoom 951 5490 42 
Emil Prodan Yeshiva University 
NonCommutative Geometry and Materials Science
Starting with the pioneering works of Jean Bellissard in the 1980’s,
NonCommutative Geometry has emerged as one of sharpest tools in the arsenal of a theoretical materials scientist. Perhaps for this audience, the most important questions are why NonCommutative Geometry and how much of it?
Using well understood examples, where specially designed materials display extraordinary behaviours in extreme conditions, I will try to convince the audience that one has to walk the entire sequence: algebra of observables → Ktheory →pairing with cyclic cohomology → local index formula, plus one additional step which I call “pushing into the Sobolev.” Furthermore, among such extraordinary behaviours is a certain relation between the dynamics of degrees of freedominside the bulk and at the boundary of a sample, dubbed the bulkboundary correspondence principle. It is captured by a certain extension of C*algebras and, as such, KKtheory offers a natural framework and supplies the necessary tools to investigate such phenomena. If the time permits, I will also discuss recent efforts trying to steer these tools from their usual use of explaining observed behaviours towards the discovery of new dynamical behaviours in materials science. Abstract 

01/29 1:00pm 
Zoom 951 5490 42 
Pierre Albin University of Illinois at UrbanaChampaign 
The subRiemannian limit of a contact manifold
Contact manifolds, which arise naturally in mechanics, dynamics, and geometry, carry natural Riemannian and subRiemannian structures and it was shown by Gromov that the latter can be obtained as a limit of the former. Subsequently, Rumin found a complex of differential forms reflecting the contact structure that computes the singular cohomology of the manifold. He used this complex to describe the behavior of the spectra of the Riemannian Hodge Laplacians in the subRiemannian limit. As many of the eigenvalues diverge, a refined analysis is necessary to determine the behavior of global spectral invariants. I will report on joint work with Hadrian Quan in which we determine the global behavior of the spectrum by explaining the structure of the heat kernel along this limit in a uniform way. Abstract 

02/05 1:00pm 
Zoom 951 5490 42 
Jens Hemelaer University of Antwerp 
Toposes in arithmetic noncommutative geometry
We give an introduction to topos theory from a geometric point of view, focusing on toposes that arise from a discrete group acting on a topological space. In particular, we will look at lattices over a global field, and see how the topos classifying them is related to the ring of finite adeles of the global field. In the case where the class group is trivial, this topos is equivalently described as a topos of presheaves on a monoid, leading to toposes that are analogous to (the underlying topos) of the Arithmetic Site of Connes and Consani. We then discuss how the different toposes are related to each other. Are there interesting geometric morphisms between them? When are these morphisms embeddings, or local homeomorphisms?
The talk is based on joint work in progress with Morgan Rogers and joint work in progress with Aurélien Sagnier. Abstract 

02/12 1:00pm 
Zoom 951 5490 42 
Henry Yuen Columbia University 
Testing lowdegree polynomials in the noncommutative setting
In lowdegree testing the following question is considered: given a multivariate function over a finite field, if a sufficiently large fraction of “local views” of the function are consistent with lowdegree polynomials, does this imply that the function is _globally_ consistent with a single lowdegree polynomial? Many lowdegree testing theorems have been proved over the years, and have had important applications in theoretical computer science, including complexity theory and property testing.
Lowdegree testing also plays an important role in the recent quantum complexity result MIP* = RE. Here, lowdegree testing is considered in the _noncommutative_ setting: “local views” of a function are given via a sequence of measurements on a state, but the measurement operators do not necessarily commute with each other. Despite noncommutativity, there is still a sense in which local consistency with lowdegree polynomials implies global consistency with lowdegree polynomials.
In this talk, I will give an introduction to lowdegree testing and discuss its analysis. This is based on joint work with Ji, Natarajan, Vidick, and Wright. (https://arxiv.org/abs/2009.12982 ) Abstract 

02/19 1:00pm 
Zoom 951 5490 42 
Eckhard Meinrenken University of Toronto 
Differential Geometry of Weightings
The idea of assigning weights to local coordinate functions appears in many areas of mathematics, such as singularity theory, microlocal analysis, subRiemannian geometry, or the theory of hypoelliptic operators, under various terminologies. In this talk, I will describe some differentialgeometric aspects of weightings along submanifolds. This includes a coordinatefree definition, and the construction of weighted normal bundles and weighted deformation spaces. As an application, I will discuss the osculating tangent bundle for Lie filtrations, and the corresponding tangent groupoid of ChoiPonge, van ErpYuncken, and HajHigson. (Based on joint work with Yiannis Loizides.) Abstract 

02/26 1:00pm 
Zoom 951 5490 42 
Alcides Buss Universidade Federal de Sanata Catarina 
Amenable actions of groups on C*algebras
In this lecture I will explain recent developments in the theory of amenability for actions of groups on C*algebras and Fell bundles, based on joint works with Siegfried Echterhoff, Rufus Willett, Fernando Abadie and Damian Ferraro. Our main results prove that essentially all known notions of amenability are equivalent. We also extend Matsumura’s theorem to actions of exact locally compact groups on commutative C*algebras and give a counterexample for the weak containment problem for actions on noncommutative C*algebras. Abstract 