## Fall 2021

Learning Group Information:

AG Group, 423 HBH, 3:00pm - 4:00pm, Details [here]

QA Group, 427 HBH, 3:00pm - 4:00pm, Details [here]
August 25, 2021 : Learning Groups [in-person]- see above

September 1, 2021 : AG Speaker [in-person]

Tony Várilly-Alvarado, Rice University

__Title__: Rational surfaces and locally recoverable codes

__Abstract__: Motivated by large-scale storage problems around data loss, a budding branch of coding theory has surfaced in the
last decade or so, centered around locally recoverable codes. These codes have the property that individual symbols in a codeword
are functions of other symbols in the same word. If a symbol is lost (as opposed to corrupted), it can be recomputed, and hence a
code word can be repaired. Algebraic geometry has a role to play in the design of codes with locality properties. In this talk I will
explain how to use algebraic surfaces birational to the projective plane to both reinterpret constructions of optimal codes already
found in the literature, and to find new locally recoverable codes, many of which are optimal (in a suitable sense). This is joint
work with Cecília Salgado and Felipe Voloch.

September 8, 2021 : Learning Groups - see above

September 15, 2021 : QA Speaker [in-person]

Sean Sanford, Indiana University

__Title__: Fusion Categories over Non–Algebraically Closed Fields

__Abstract__: Much of the early work on Fusion Categories was inspired by physicists desire for rigorous foundations of topological
quantum field theory. One effect of this was that base fields other than the complex numbers were rarely considered, if at all. The
relevant features of $\mathbb C$ that make the theory work are the fact that it is characteristic zero, and algebraically closed.
This talk will focus on the interesting things that can be found when the algebraically closed requirement is removed. The content
will be introductory, with lots of examples.

September 22, 2021 : Learning Groups - see above

September 29, 2021 : AG Speaker [in-person]

Alex Barrios, Carleton College

__Title__: Local data of elliptic curves with prescribed isogeny graph

__Abstract__: Given a rational elliptic curve, one can use Tate's algorithm to compute the following local data
at each rational prime: the local conductor exponent, the Néron-Kodaira type, and the local Tamagawa number. This
talk will investigate how the local data changes between two isogenous elliptic curves. We will focus on how the
Néron-Kodaira type and the local Tamagawa number change under isogeny. This has been well-studied in the literature
but remains open for special cases corresponding to a 2- or 3-isogeny. We aim to answer the remaining cases by
explicitly classifying the local data of elliptic curves with a prescribed non-trivial isogeny graph. This is
joint work with Darwin Chimarro, Manami Roy, Nandita Sahajpal, Bella Tobin, and Hanneke Wiersema.

October 6, 2021 : Learning Groups - see above at 3pm

Xingting Wang, Howard University (

Special time at 4pm)

__Title__:
Can a Zhang twist be a cocycle twist?

__Abstract__: In this talk, we will discuss two different twists of algebra structures in the literature, namely Zhang twist
and 2-cocycle twist. We will provide sufficient conditions for them to coincide by introducing the notion of a twisting pair.
We will explore twisting pairs for many well-known examples of Hopf algebras including Manin’s universal quantum group from quantum
symmetry and FRT construction from a solution of the quantum Yang-Baxter equation. This is joint work with Hongdi Huang, Van C. Nguyen, Charlotte Ure and Kent B. Vashaw.

October 13, 2021 : QA Speaker [online]

Zachary Dell, Ohio State University

__Title__: A characterization of braided enriched monoidal categories

__Abstract__: Monoidal categories enriched in symmetric monoidal categories are well studied in the literature.
In recent years attention has been given to the case where the enriching category is merely braided. In this talk I will
give an overview of the existing results characterizing such categories in terms of braided oplax monoidal functors into
the Drinfeld centers of ordinary monoidal categories and describe how this construction extends to an equivalence of
2-categories.

October 20, 2021 : Learning Groups - see above

October 27, 2021 : AG Speaker [online]

Elisa Bellah, University of Oregon

__Title__: Bounding Lifts of Markoff Triples mod p

__Abstract__: In 2016, Bourgain, Gamburd, and Sarnak proved that Strong Approximation holds for the Markoff surface in
most cases. That is, the modulo p solutions to the equation x^2+y^2+z^2=3xyz are covered by the integer points for most primes p.
In this talk, we will discuss how the algorithm given in the paper of Bourgain, Gamburd, and Sarnak can be used to obtain upper
bounds on lifts of Markoff triples modulo p. We will also discuss ongoing work to improve these bounds on average by assuming
the Markoff mod p graphs form an expander family. This is joint work with Elena Fuchs and Lynnelle Ye.

November 3, 2021 : Learning Groups - see above

November 10, 2021 : QA Speaker [online]

Agustina Czensky, University of Oregon

__Title__: On low rank odd-dimensional MTCs

__Abstract__:
Classification of fusion categories by rank is an open (and seemingly out of reach) problem. For modular tensor categories (MTCs),
Bruillard, Ng, Rowell and Wang showed in 2016 that there are finitely many of a fixed rank. Bruillard and Rowell also showed that
odd-dimensional MTCs are pointed up to rank 11, which means that they can be classified by group-theoretical data. In this talk
we will describe joint work with Julia Plavnik were we contribute to this classification problem. We will discuss some useful results
for the classification of low-rank odd-dimensional MTCs, and expand on their classification for ranks 15 to 23.

November 17, 2021 : Learning Groups - see above

November 24, 2021 : (no activity)

December 1, 2021 : AG Speaker [online]

Humberto Diaz, Washington University

__Title__: The Hodge Conjecture for varieties with small Chow group

__Abstract__: The integral Hodge conjecture asserts that every integral Hodge class is the class of an algebraic cycle. It has been known
to be false since the counterexamples of Atiyah and Hirzebruch. Since then, many other types of counterexamples have been produced. In this talk,
I will report on recent work that gives yet another type of counterexample, this time arising from a variety whose Chow group of algebraic cycles
is as small as possible.

December 8, 2021 : QA Speaker [online]

Florencia Orosz, University of Denver

__Title__: Tensor categories arising from the Virasoro algebra

__Abstract__: In this talk we will discuss the tensor structure associated with certain representations of the Virasoro algebra. In particular,
we will show that there is a braided tensor category structure on the category of C1-cofinite modules for the Virasoro vertex operator algebras of
arbitrary central charge. This talk is based on joint work with Thomas Creutzig, Cuibo Jiang, David Ridout and Jinwei Yang.