Department of

# Mathematics

Seminar Calendar
for events the day of Friday, October 18, 2019.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Friday, October 18, 2019

2:00 pm in 245 Altgeld Hall,Friday, October 18, 2019

#### Careers for Math Students in the Life Sciences and Medicine

###### Howard Aizenstein, Tandy Warnow, James O'Dwyer, Olgica Milenkovic

Abstract: Are you interested in learning more about the role of mathematics in the fields of biology, biochemistry, or medicine? Come hear from a distinguished panel of applied mathematicians whose research addresses societally relevant problems in the biological sciences. Panelists: Howard Aizenstein, Charles F. Reynolds III and Ellen G. Detlefsen Endowed Chair in Geriatric Psychiatry and Professor of Bioengineering and Clinical and Translational Science at the University of Pittsburgh; Tandy Warnow, Founder Professor of Computer Science and Associate Head for Computer Science, UIUC;; James O'Dwyer, Associate Professor, Department of Plant Biology, UIUC; and Olgica Milenkovic, Professor and Donald Biggar Willett Scholar, Department of Electrical and Computer Engineering, UIUC

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.

4:00 pm in 141 Altgeld Hall,Friday, October 18, 2019

#### Lines in Space

###### Brian Shin (UIUC)

Abstract: Consider four lines in three-dimensional space. How many lines intersect these given lines? In this expository talk, I'd like to discuss this classical problem of enumerative geometry. Resolving this problem will give us a chance to see some interesting algebraic geometry and algebraic topology. If time permits, I'll discuss connections to motivic homotopy theory.

4:00 pm in 347 Altgeld Hall,Friday, October 18, 2019

#### Where Automata Theory Meets Metric Geometry

###### Alexi Block Gorman (UIUC Math)

Abstract: The results in this talk illustrate and expand on connections between automata theory and metric geometry. We will begin by defining automata, Buchi automata, fractals, and iterated function systems. We say that a function is regular if there is a Buchi automaton that accepts precisely the set of base n representations of points in the graph of the function. We show that a continuous regular function (with closed and bounded domain) "looks linear" almost everywhere, if you zoom in enough. As a result, we show that every differentiable regular function is a shift of linear function (or hyperplane, in higher dimensions).