Department of

# Mathematics

Seminar Calendar
for Algebra Seminar events the year of Thursday, October 10, 2019.

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events for the
events containing

More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
    September 2019          October 2019          November 2019
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1  2  3  4  5  6  7          1  2  3  4  5                   1  2
8  9 10 11 12 13 14    6  7  8  9 10 11 12    3  4  5  6  7  8  9
15 16 17 18 19 20 21   13 14 15 16 17 18 19   10 11 12 13 14 15 16
22 23 24 25 26 27 28   20 21 22 23 24 25 26   17 18 19 20 21 22 23
29 30                  27 28 29 30 31         24 25 26 27 28 29 30



Tuesday, April 2, 2019

1:00 pm in 345 Altgeld Hall,Tuesday, April 2, 2019

#### Max-Min theorems for weak containment, square summable homoclinic points, and completely positive entropy

###### Ben Hayes (University of Virginia)

Abstract: I will present a max-min theorem for weak containment in the context of algebraic actions (i.e. actions of a discrete group by automorphisms of a compact group). Namely, given an algebraic action of $G$ on $X$, there is a maximal, closed $G$-invariant subgroup $Y$ of $X$ so that the action of $G$ on $Y$ is weakly contained in a Bernoulli shift. This subgroup is also the minimal subgroup so that any action weakly contained in a Bernoulli shift is "$G$$X/Y-ergodic in the presence of G$$X$" (this will be defined in the talk). Time permitting, I will discussion applications. These include showing that many algebraic actions are weakly contained in a Bernoulli shift, as well as applications to complete positive entropy of algebraic actions.

Friday, August 30, 2019

2:00 pm in 347 Altgeld Hall,Friday, August 30, 2019

#### Organizational Meeting

###### Chelsea Walton (UIUC)

Abstract: This will be a short organizational meeting to introduce the structure of the Algebra seminar. Here is the seminar website: https://faculty.math.illinois.edu/~notlaw/UIUC-Algebra.html. Half of the talk slots will be for (introductory +) research talks, and the other half of the slots will be dedicated to a reading group on Tensor Categories. The format of the reading group will be similar to that for the TQFT reading group in Spring 2019 (https://faculty.math.illinois.edu/~notlaw/teaching.html#past), except that the duration of talk slots will be longer.

Friday, September 6, 2019

2:00 pm in 347 Altgeld Hall,Friday, September 6, 2019

#### Quantum Symmetry in the context of co/representation categories

###### Chelsea Walton (UIUC)

Abstract: In the first 50 minutes, I will provide an introductory talk on quantum symmetry in the context of co/representation categories, which serves as one point of motivation for the reading group on Tensor Categories. I will then give a follow-up research talk in the second 50 minutes on joint work in progress with Elizabeth Wicks and Robert Won on quantum symmetry and weak Hopf algebras.

Friday, September 13, 2019

2:00 pm in 347 Altgeld Hall,Friday, September 13, 2019

#### Tensor Categories Reading Group

###### See seminar site

Abstract: See seminar site.

Friday, September 20, 2019

2:00 pm in 347 Altgeld Hall,Friday, September 20, 2019

#### Hopf Ore Extensions

###### Hongdi Huang (University of Waterloo (visiting UIUC for F19))

Abstract: Brown, O'Hagan, Zhang, and Zhuang gave a set of conditions on an automorphism $\sigma$ and a $\sigma$-derivation $\delta$ of a Hopf $k$-algebra $R$ for when the skew polynomial extension $T=R[x, \sigma, \delta]$ of $R$ admits a Hopf algebra structure that is compatible with that of $R$. In fact, they gave a complete characterization of which $\sigma$ and $\delta$ can occur under the hypothesis that $\Delta(x)=a\otimes x +x\otimes b +v(x\otimes x) +w$, with $a, b\in R$ and $v, w\in R\otimes_k R$, where $\Delta: R\to R\otimes_k R$ is the comultiplication map. In this paper, we show that after a change of variables one can in fact assume that $\Delta(x)=\beta^{-1}\otimes x +x\otimes 1 +w$, with $\beta$ is a grouplike element in $R$ and $w\in R\otimes_k R,$ when $R\otimes_k R$ is a domain and $R$ is noetherian. In particular, this completely characterizes skew polynomial extensions of a Hopf algebra that admit a Hopf structure extending that of the ring of coefficients under these hypotheses. We show that the hypotheses hold for domains $R$ that are noetherian cocommutative Hopf algebras of finite Gelfand-Kirillov dimension.

Friday, September 27, 2019

2:00 pm in 347 Altgeld Hall,Friday, September 27, 2019

#### Tensor Categories Reading Group

###### See seminar site

Abstract: See seminar site.

Friday, October 4, 2019

2:00 pm in 347 Altgeld Hall,Friday, October 4, 2019

#### Tensor Categories Reading Group

###### See seminar site

Abstract: See seminar site.

Friday, October 11, 2019

2:00 pm in 347 Altgeld Hall,Friday, October 11, 2019

#### Tensor Categories Reading Group

###### See seminar site

Abstract: See seminar site.

Friday, October 18, 2019

2:00 pm in 347 Altgeld Hall,Friday, October 18, 2019

#### Brown-Goodearl conjecture for PI weak Hopf algebras

###### James Zhang (University of Washington, Seattle)

Abstract: Brown and Goodearl conjectured that every noetherian Hopf algebra is Artin-Schelter Gorenstein. This conjecture is known to be true for many cases, in particular, for affine polynomial identity Hopf algebras. Weak Hopf algebras are an important generalization of Hopf algebras, and the category of modules over a weak Hopf algebra has a monoidal structure. Let $W$ be a weak Hopf algebra that is a finitely generated module over its affine center. We prove that $W$ has finite self-injective dimension and is a direct sum of Artin-Schelter Gorenstein algebras. Therefore Brown-Goodearl conjecture holds in this special weak Hopf setting. We will also give some motivations and consequences of Brown-Goodearl conjecture. This is joint work with Dan Rogalski and Robert Won.

Friday, October 25, 2019

2:00 pm in 347 Altgeld Hall,Friday, October 25, 2019

#### Noncommutative algebra from a geometric point of view

###### Xingting Wang (Howard University)

Abstract: In this talk, I will discuss how to use algebro-geometric and Poisson geometric methods to study the representation theory of 3-dimensional Sklyanin algebras, which are noncommutative analogues of polynomial algebras of three variables. The fundamental tools we are employing in this work include the noncommutative projective algebraic geometry developed by Artin-Schelter-Tate-Van den Bergh in 1990s and the theory of Poisson order axiomatized by Brown and Gordon in 2002, which is based on De Concini-Kac-Priocesi’s earlier work on the applications of Poisson geometry in the representation theory of quantum groups at roots of unity. This is joint work with Milen Yakimov and Chelsea Walton.

Friday, November 1, 2019

2:00 pm in 347 Altgeld Hall,Friday, November 1, 2019

#### To Be Announced

###### Colleen Delaney (Indiana University)

Abstract: To be announced.

Friday, November 8, 2019

2:00 pm in 347 Altgeld Hall,Friday, November 8, 2019

#### To Be Announced

###### Cris Negron (University of North Carolina)

Abstract: To be announced.

Saturday, November 9, 2019

9:00 am in 245 Altgeld Hall,Saturday, November 9, 2019

#### Quasy-Con

###### Various regional speakers (various)

Abstract: "Quasy-Con" is an informal Quantum Symmetries Conference in the U.S. Midwest, which will be held on November 9-10, 2019. See site for more details: https://faculty.math.illinois.edu/~notlaw/QuaSy-Con2019.html.

Friday, November 15, 2019

2:00 pm in 347 Altgeld Hall,Friday, November 15, 2019

#### Tensor Categories Reading Group

###### See seminar site

Abstract: See seminar site.

Friday, November 22, 2019

2:00 pm in 347 Altgeld Hall,Friday, November 22, 2019

#### To Be Announced

###### Robert Laugwitz (University of East Anglia / University of Nottingham)

Abstract: To be announced.

Friday, December 6, 2019

2:00 pm in 347 Altgeld Hall,Friday, December 6, 2019

#### Tensor Categories Reading Group

###### See seminar site

Abstract: See seminar site.

Friday, December 13, 2019

2:00 pm in 347 Altgeld Hall,Friday, December 13, 2019

#### Tensor Categories Reading Group

###### See seminar site

Abstract: See seminar site.
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