# Math Calendar

### Upcoming Events

## The relationship of supernilpotence to nilpotence (4)

Andrew Moorhead, Vanderbilt University

Location: Stevenson 1312

Supernilpotence is a condition on an algebra that is definable with a higher arity commutator that generalizes the classical binary commutator for general algebras. Supernilpotent algebras have received attention lately because of theorems of the flavor ‘nice property true satisfied by finite nilpotent groups’ is satisfied by finite supernilpotent Mal’cev algebras of finite type. For example, it is now know that there is a polynomial time algorithm to solve the equation equation satisfiability problem for such algebras. The exact relationship between supernilpotence and nilpotence had been unclear. We will discuss how supernilpotence implies nilpotence for algebras with a Taylor term, but that in general the two notions are independent.

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Mike Mihalik, Vanderbilt University

Location: Stevenson 1310

## K-groups and Rings of Integers

Adebisi Agboola, UC Santa Barbara

Location: Stevenson 5211

Suppose that F is a number field and that G is a finite group. The inverse Galois problem asks whether or not there exists an extension of F whose Galois group is isomorphic to G. This question is known to have an affirmative answer in many cases, but is unsolved in general. I shall discuss a conjecture in relative algebraic K-theory (in essence, a conjectural Hasse or local-global principle applied to certain relative algebraic K-groups) that implies an affirmative answer to both the inverse Galois problem and to an analogous problem concerning the Galois module structure of rings of integers in tame extensions of F. The K-theoretic conjecture can be proved in many cases (subject to mild technical conditions) e.g. for groups of odd order, giving an analogue of a classical theorem of Shafarevich in this setting. While this approach does not, as yet, resolve any new cases of the inverse Galois problem, it does yield a quite substantial advance in our knowledge concerning the Galois module structure of rings of integers. Tea at 3:33 pm in Stevenson 1425. (Contact Person: Dietmar Bisch)

## Annual Town Hall Meeting of Chair and DGS with Graduate Students

Location: Stevenson 1206

The annual town hall meeting is an informal gathering where Department Chair Mike Neamtu along with Director of Graduate Studies Denis Osin meet with graduate students to answer questions and discuss updates about the graduate program.

## Module Categories, Graph Planar Algebra Embeddings, and Extended Haagerup

Noah Snyder, Indiana University

Location: Stevenson 1432

A natural question that Pinhas Grossman and I have been studying is given a finite collection of finite index N-N bimodules what are all factors M containing N which can be built as a sum of these bimodules. This question is closely related to several “representation theoretic” questions about fusion categories, namely classifying module categories, finding Ocneanu’s “maximal atlas”, and finding Etingof-Nikshych-Ostrik’s “Brauer-Picard groupoid.” Unrelated to all of this, Vaughan Jones asked given a fixed subfactor planar algebra P, can you find all bipartite graphs \Gamma such that P embeds into the Graph Planar Algebra of \Gamma. Emily Peters gave partial evidence that for the Haagerup subfactor there were exactly three such graphs (the two principal graphs, and the broom). My main goal in this talk is to explain why these two questions are basically the same as each other. The key result is a GPA embedding theorem for module categories, which says that P embeds in the GPA(\Gamma) if and only if \Gamma is the fusion graph for some module category. In particular, I will show that it follows from my first paper with Pinhas that Emily’s three graphs are the only graphs with Haagerup GPA embeddings. We are also able to use this approach to answer all these questions for the Extended Haagerup subfactor, showing that there are two new fusion categories EH3 and EH4 which still appear to be exceptional. This is joint work with Grossman, Morrison, Penneys, and Peters as part of our AIM Square.

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Scott Atkinson, Vanderbilt University

Location: Stevenson 1432

## Harmonic Hecke Eigenlines and Mazur’s Problem

Ian Wagner, Emory University

Location: Stevenson 1310

We construct two families of harmonic Maass Hecke eigenforms. Using these families we construct p-adic harmonic Maass forms in the sense of Serre. The p-adic properties of these forms answer a question of Mazur about the existence of an “eigencurve-type” object in the world of harmonic Maass forms.

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James Farre, University of Utah

Location: Stevenson 1310

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Christine Heitsch, Georgia Tech

Location: Stevenson 5211

Tea at 3:33 pm in Stevenson 1425. (Contact Person: Mark Ellingham)

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Alexander Olshanskiy, Vanderbilt University

Location: Stevenson 1308

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Ilya Kapovich, University of Illinois at Urbana-Champaign

Location: Stevenson 5211

Tea at 3:33 pm in Stevenson 1425. (Contact Person: Denis Osin)

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Josh Edge, Indiana University

Location: Stevenson 1432

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Paramita Das, Indian Statistical Institute

Location: Stevenson 1432

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Andrei Okounkov, Columbia University

Location: Stevenson 5211

Tea at 3:33 pm in Stevenson 1425. (Contact Person: Vaughan Jones)

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Shamindra Ghosh, Indian Statistical Institute

Location: Stevenson 1432

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Susan Friedlander, University of Southern California

Location: Stevenson 5211

Tea at 3:33 pm in Stevenson 1425. (Contact Person: Giusy Mazzone)

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Scott Wilson, CUNY Queens College

Location: Stevenson 1310

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Scott Wilson, CUNY Queens College

Location: Stevenson 1310

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Yasu Kawahigashi, University of Tokyo

Location: Stevenson 1432

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Wenqing Hu, Missouri University of Science and Technology.

Location: Stevenson 1307

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Gueo Grancharov, Florida International University

Location: Stevenson 1310

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Willie Wongu, Michigan State University

Location: Stevenson Center 1307

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Dennis Sullivan, Suny at Stony Brook

Location: Stevenson 5211

Tea at 3:33 pm in Stevenson 1425. (Contact Person: Marcelo Disconzi)