Department of

# Mathematics

Seminar Calendar
for events the day of Wednesday, February 20, 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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31


Wednesday, February 20, 2019

3:00 pm in 243 Altgeld Hall,Wednesday, February 20, 2019

#### To Be Announced

###### Elisabeth Moyer (University of Chicago, Geophysical Sciences)

3:00 pm in 2 Illini Hall,Wednesday, February 20, 2019

#### The Geometry of Spectral Curves

###### Matej Penciak (Illinois Math)

Abstract: One way of encoding the data of an integrable system is in terms of the spectral curves. From the curves, it is possible to obtain the constants of motion as integrals over cycles in the curves. In this talk, I will explain some of these classical aspects of integrable systems through some worked out examples. I will also introduce an action-coordinate (AC) duality for integrable systems. I will show how AC duality can be used to relate well-known integrable systems and even construct new integrable systems from old ones. Finally, I hope to describe what the action this AC duality has on spectral curves for some integrable systems of interest.

4:00 pm in 245 Altgeld Hall,Wednesday, February 20, 2019

#### Some necessary uses of logic in mathematics

###### Ilijas Farah (York University)

Abstract: Every now and then, a difficult mathematical problem turns out to be difficult for a particularly objective reason: Provably, it cannot be solved by using 'conventional' means. Some classical examples are proving the Continuum Hypothesis, trisecting an angle, and solving the quintic equation. I’ll discuss more recent examples of such problems, giving some emphasis to the problems arising from the study of operator algebras.

4:00 pm in 343 Altgeld Hall,Wednesday, February 20, 2019

#### Connecting Boolean (un)satisfiability to Graph Theory

###### Vaibhav Karve (Illinois Math)

Abstract: Given a Boolean formula can we find consistent assignments (True or False)for variables such that the formula is satisfied? This is the Boolean Satisfiability problem, a problem of great historic value in computer science. It is the first problem that was proven to be NP-complete. In this talk, I will introduce Satisfiability and explain what the terms P, NP, NP-complete... mean. I will then demonstrate a (surprising)connection between Boolean formulas and graph theory which will help us gain a more visual understanding of when a class of formulas is satisfiable or unsatisfiable. There will be lots of small graphs in this talk.