Department of

# Mathematics

Seminar Calendar
for events the day of Friday, February 2, 2018.

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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, February 2, 2018

12:00 pm in 443 Altgeld Hall,Friday, February 2, 2018

#### CANCELED- A short proof of the Schwartz Kernel Theorem

Abstract: Schwartz’ kernel theorem is a foundational result in the theory of distributions, going on to inspire many further techniques in analysis, e.g. Pseudodifferential Operators. And, like many other inspiring results, much is made of the statement and its consequences without considering much detail of the proof. In this talk I’ll give a proof of the theorem suggested in lecture notes of Richard Melrose.

4:00 pm in 345 Altgeld Hall,Friday, February 2, 2018

#### On "A Vietoris-Smale mapping theorem for the homotopy of hyperdefinable sets" by Achille and Berarducci

###### Elliot Kaplan (UIUC Math)

Abstract: I will discuss the paper "A Vietoris-Smale mapping theorem for the homotopy of hyperdefinable sets" by Alessandro Achille and Alessandro Berarducci [arXiv]. In this paper, they compare the definable homotopy groups of a space $X$ definable in an o-minimal structure (denoted $\pi_n(X)^\mathrm{def}$) with the (usual) homotopy groups of the quotient $X/E$, where $E$ is a certain kind of type-definable equivalence relation on $X$. Under certain assumptions, these groups are actually isomorphic. These types of quotients were first studied by Pillay in the case that $X$ is actually a definable group. This is the first talk that I will give on this paper.

4:00 pm in 241 Altgeld Hall,Friday, February 2, 2018

#### Integrable systems in algebraic geometry

###### Matej Penciak (UIUC)

Abstract: In this talk I'll introduce the definition of an algebraic integrable system. The definition axiomatizes what it means to have an integrable system in algebraic geometry. After connecting the definition to the more common notion in differential geometry, I'll give a few examples of my favorite integrable systems. Possible examples are the Hitchin system on the space of Higgs bundles, the Calogero-Moser system, the Toda lattice hierarchy, and, if time permits, I'll try to give a hint of how all these systems are related via the gauge theory in physics.