Department of

# Mathematics

Seminar Calendar
for Algebra Seminar events the year of Wednesday, September 11, 2019.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
     August 2019           September 2019          October 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    1  2  3  4  5  6  7          1  2  3  4  5
4  5  6  7  8  9 10    8  9 10 11 12 13 14    6  7  8  9 10 11 12
11 12 13 14 15 16 17   15 16 17 18 19 20 21   13 14 15 16 17 18 19
18 19 20 21 22 23 24   22 23 24 25 26 27 28   20 21 22 23 24 25 26
25 26 27 28 29 30 31   29 30                  27 28 29 30 31



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

###### 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

###### See seminar site

Abstract: See seminar site.

Friday, October 4, 2019

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

###### See seminar site

Abstract: See seminar site.

Friday, October 11, 2019

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

###### See seminar site

Abstract: See seminar site.

Friday, October 18, 2019

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

#### To Be Announced

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

Abstract: To be announced.

Friday, October 25, 2019

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

#### To Be Announced

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

Abstract: To be announced.

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

###### 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

###### See seminar site

Abstract: See seminar site.

Friday, December 13, 2019

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