Department of

Mathematics


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

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
     August 2019           September 2019          October 2019    
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              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
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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

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

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.