# Math Calendar

### Upcoming Events

## Talk Title TBA

Kevin Schreve, University of Chicago

Location: Stevenson 1308

## Department Welcome Event

Location: Stevenson 5211

Interim Chair Mark Ellingham will introduce new members of the department. Refreshments will be served afterwards in the Common Room, SC 1425.

## Classical Symmetries and Quantum Subgroups

Cain Edie-Michell, Vanderbilt University

Location: Stevenson 1432

In the early 2000’s Ocneanu initiated the classification of quantum subgroups of a Lie algebra $\mathfrak{g}$ by providing a complete classification of quantum subgroups of the algebras $\mathfrak{sl}_2$ and $\mathfrak{sl}_3$. Despite a large effort since then, little progress has been made for the other simple Lie algebras. However, recent results of Gannon and Schopieray have blown this problem wide open, by providing effective bounds on the levels at which quantum subgroups can appear for a given Lie algebra $\mathfrak{g}$. Hence there has been a recent revival in the program to classify all quantum subgroups, and in particular, to construct examples that are predicted to exist. In this talk I will describe the connection between symmetries of the category of level $k$ integrable representations of $\mathfrak{g}$, and the quantum subgroups of $\mathfrak{g}$ appearing at level $k$. In particular I will give constructions of the conjectured charge conjugation quantum subgroups of $\mathfrak{sl}_n$ at all levels, and of a sporadic quantum subgroup of $\mathfrak{g}_2$ which appears at level 4.

## Talk Title TBA

Mihalis Kolountzakis, University of Crete

Location: Stevenson 5211

Tea at 3:33 pm in Stevenson 1425. (Host: Akram Aldroubi)

## Talk Title TBA

Jacob Sterbenz, University of California at San Diego

Location: Stevenson 5211

Tea at 3:33 pm in SC 1425. (Contact Person: Alex Powell)

## Attractors of the Einstein-Klein-Gordon System

Zoe Wyatt, University of Edinburgh

Location: Stevenson 1307

A key question in general relativity is whether solutions to the Einstein equations, viewed as an initial value problem, are stable to small perturbations of the initial data. For example, previous results have shown that the Milne spacetime, which represents an expanding universe emanating from a big bang singularity with a linear scale factor, is a stable solution to the Einstein equations. With such a slow expansion rate, particularly compared to related models with accelerated expansion (such as the exponentially expanding de Sitter spacetime modelling our universe), there are interesting questions one can ask about stability of this spacetime. Previous results have shown that the Milne model is a stable solution to the vacuum Einstein, Einstein-Klein-Gordon and Einstein-Vlasov systems. Motivated by techniques from the last result, I will present a new proof of the stability of the Milne model to the Einstein-Klein-Gordon system and compare our method to a recent result of J. Wang. This is joint work with David Fajman (Vienna).

## Minimal Index and Dimension for Inclusions of von Neumann Algebras with Finite-Dimensional Centers

Luca Giorgetti, Vanderbilt University

Location: Stevenson 1432

The notion of index for inclusions of von Neumann algebras goes back to the seminal work of Jones on subfactors of type II1. More generally, one can define the index of a conditional expectation associated with a subfactor and look for expectations that minimize the index. This minimal value is a number and it is called the minimal index of the subfactor. We report on our analysis of the minimal index for inclusions of arbitrary von Neumann algebras (not necessarily factorial, nor finite) with finite-dimensional centers (multi-factor inclusions). The theory is controlled by a matrix associated with the inclusion, that we call matrix dimension, whose squared L^2 norm equals the minimal index and which determines a further invariant, that we call spherical state of the inclusion, via Perron-Frobenius theory. We mention the properties of finite multi-factor inclusions, especially multi-matrices, for which the spherical state coincides on the relative commutant with the Markov trace (super-extremal inclusions). We also mention how the matrix dimension can be purely algebraically defined for 1-arrows in rigid 2-C*-categories and how it determines the so-called standard solutions of the conjugate equations, and we address some open questions. Based on joint work with R. Longo, arXiv:1805.09234.

## The Strong Cosmic Censorship Conjecture in General Relativity

Jonathan Luk, Stanford University

Location: Stevenson 5211

The Einstein equations in general relativity admit explicit black hole solutions which have the disturbing property that global uniqueness fails. As a way out, Penrose proposed the strong cosmic censorship conjecture, which says that this phenomenon of global non-uniqueness is non-generic. We will discuss this conjecture and some recent mathematical progress. This talk is based on joint works with Mihalis Dafermos, Sung-Jin Oh, Jan Sbierski and Yakov Shlapentokh-Rothman. Tea at 3:33 pm in Stevenson 1425. (Contact Person: Jared Speck)

## A Plethora of Embeddings into an Ultraproduct of II_1 Factors

Srivatsav Kunnawalkam Elayavalli, Vanderbilt University

Location: Stevenson 1432

We will report on some results (joint with S. Atkinson) regarding new characterizations of amenability for Connes embeddable II_1 factors. First we introduce the notion of self-tracial stability and discuss immediate connections with amenability. Secondly we will discuss an interesting strengthening of the well known Jung’s tubularity result. The core of this is a technical argument of Kishimoto. There are also some interesting model theoretic questions that come out of this. Finally we build on work of N. Brown and N. Ozawa to answer a question of Popa concerning the “vastness” of the space of embeddings of a non-amenable II_1 factor into the ultraproduct of a given collection of II_1 factors. We will end with interesting questions in the group theory setting. See arxiv: 1907.03359 for submitted paper.

## Talk Title TBA

Rachel Skipper, The Ohio State University

Location: Stevenson 1308

## Around Cantor Uniqueness Theorem

Alexander Olevskii, Tel Aviv University

Location: Stevenson 5211

After a short introduction to Riemann’s uniqueness theory I will discuss the following problem, going back to early 60-s: Can a (non-trivial) trigonometric series

\sum c(n) e^inx , c( n) = o(1),

have a subsequence of partial sums which converges to zero everywhere? Joint work with Gady Kozma. Tea at 3:33 pm in SC 1425. (Host: Akram Aldroubi)

## Talk Title TBA

Vu Hoang, The University of Texas at San Antonio

Location: Stevenson 1307

## Talk Title TBA

Jean Pierre Mutanguha, University of Arkansas

Location: Stevenson 1308

## Talk Title TBA

Mihaela Ifrim, University of Wisconsin Madison

Location: Stevenson 1307

## Talk Title TBA

Daniel Studenmund, Notre Dame

Location: Stevenson 1308