Spring 2021

- Date:
**1/29/21****Srivatsav Kunnawalkam Elayavalli**, Vanderbilt University- Title: On Heirs
- Abstract: We will introduce the notion of types and heirs in the context of embeddings into ultraproducts. As an application, we will prove that if any two embeddings of a Connes embeddable II_1 factor M into its own ultrapower are equivalent by an automorphism, then M is isomorphic to R. Time permitting, we will discuss the situation of embeddings into R^omega. Based on joint work with S. Atkinson and I. Goldbring.

- Date:
**2/5/21****Brent Nelson**, Michigan State University- Title: Free Stein dimension and von Neumann algebras
- Abstract: Let (M,\tau) be a tracial von Neumann algebra and A a finitely generated *-subalgebra of M. The free Stein dimension of (A,\tau) is the von Neumann dimension of a module determined by certain closable derivations on A. This quantity was originally defined as a free probabilistic invariant associated to the non-commutative distribution of generators for A with respect to \tau, but the perspective given by derivations on A is better suited for applications to von Neumann algebras such as detecting L^2-rigidity. In this talk, I will provide an introduction to free Stein dimension and show how its quantitative behavior can reveal structural properties of the von Neuman algebra A''. I will also discuss how to use the free Stein dimension to define a von Neumann algebra invariant, and present examples of when this invariant can be explicitly computed.

- Date:
**2/12/21****Corey Jones**, North Carolina State University- Title: Anomalous symmetries of geometric C*-algebras.
- Abstract: Given a group G and a U(1)-valued 3-cocycle w, an anomalous action on a C*-algebra is a generalization of a cocycle action of G, where the cocycle equations "hold up to w". We use the techniques of Eilenberg-MacLane, V. Jones, and Sutherland to show for every n>1 and every finite group G, every anomaly can be realized on the stabilization of a commutative C*-algebra of continuous functions on some closed connected n-manifold M. We also show that although there are no anomalous symmetries of Roe C*-algebras of coarse spaces, for every finite group G, every anomaly can be realized on the Roe corona of some bounded geometry metric space X with property A.

- Date:
**2/19/21****Julia Plavnik**, Indiana University- Title: Zesting link invariants
- Abstract: It was conjectured that modular categories were determined by its modular data (S- and T-matrices). In 2017, Mignard and Schauenburg presented a family of counterexamples to this conjecture, which led to the study of link invariants beyond modular data to distinguish these categories. In this talk we will discuss ribbon zesting, which is a construction of modular categories, and how it is related to the family of Mignard-Schauenburg counterexamples. To better understand this relation, we look into how zesting affects link invariants such as the W-matrix and the B-tensor. This talk is based on joint work in progress with Colleen Delaney and Sung Kim.

- Date:
**2/26/21**(11:10am - 12:30pm central)**Erik Christensen**, University of Copenhagen- Title: From spectral triples to rapid decay
- Abstract: A question on the domain of definition for a spectral triple has caused an interest in the Schur product of operator valued matrices. It then turned out that this is a completely bounded bilinear operator, which is a special case of the Hadamard product in a crossed product of a C*-algebra by a discrete group. This observation lead to an extension of the concept named rapid decay from group algebras to crossed products.

- Date:
**3/5/21****Ben Hayes**, University of Virginia- Title: A multiplicative ergodic theorem for von Neumann algebra valued cocycles
- Abstract: I'll discuss joint work with Lewis Bowen and Frank Lin. In it, we generalize the classical Multiplicative Ergodic Theorem (MET) of Oseledets to cocycles taking values in a semi-finite von Neumann algebra. In contrast with previous work, the limiting operator we get is typically not the exponential of a compact operator and often has diffuse spectrum.

- Date:
**3/12/21**(11:10am - 12:30pm central)**Sam Mellick**, ENS de Lyon- Title: Point processes on groups, their cost, and fixed price for G x Z.
- Abstract: Invariant point processes on groups are a rich class of probability measure preserving (pmp) actions. In fact, every essentially free pmp action of a nondiscrete locally compact second countable group is isomorphic to a point process. The cost of a point process is a numerical invariant that, informally speaking, measures how hard it is to "connect up" the point process. This notion has been very profitably studied for discrete groups, but little is known for nondiscrete groups. This talk will not assume any sophisticated knowledge of probability theory. I will define point processes, their cost, and discuss why every point process on groups of the form G x Z has cost one. Joint work with Miklós Abért.

- Date:
**3/19/21****Sayan Das**, UC Riverside- Title: Property (T) factors with trivial fundamental group.
- Abstract: Motivated by Connes' rigidity conjecture, S. Popa conjectured in 2005 that fundamental groups of any property (T) group factor must be trivial. In this talk I shall give examples of Property (T) group factors with trivial fundamental group. This talk is partially based on a joint work with Ionut Chifan, Krishnendu Khan and Cyril Houdayer.

- Date:
**3/26/21**(11:10am - 12:30pm central)**Liviu Păunescu**, Institute of Mathematics of the Romanian Academy

- Date:
**4/2/21****Rachel, Norton**, Fitchburg State University

- Date:
**4/9/21****Noah Snyder**, University of Indiana

- Date:
**4/16/21****Alex Margolis**, Vanderbilt University

- Date:
**4/23/21****Cain Edie-Michell**, Vanderbilt University

- Date:
**4/30/21** - End of Spring Semester.