Department of

Mathematics


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

3:00 pm in 341 Altgeld Hall,Friday, October 18, 2019

The geometry of real hypersurfaces in complex space

Martino Fassina (UIUC Math)

Abstract: Real hypersurfaces are the boundaries of complex domains, and their geometry is therefore crucial in understanding the theory of functions of several complex variables. I will focus in particular on the following question: does the hypersurface contain some local analytic structure? More generally, how closely ambient complex analytic varieties can contact the hypersurface? The talk will be elementary, and with plenty of pictures.

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).