Department of

Mathematics


Seminar Calendar
for events the day of Friday, February 9, 2018.

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Friday, February 9, 2018

12:00 pm in 443 Altgeld Hall,Friday, February 9, 2018

Symmetrization Techniques in Functional Analysis

Derek Kielty (UIUC Math)

Abstract: Optimization problems are of great importance in analysis. Often times an optimization problem has many symmetries built into it. It is a natural and important question to determine if the optimizers inherit all of the symmetries of the optimization problem itself. Symmetrization techniques play an important role in answering this question. In this talk I will give a basic introduction to symmetrization techniques and discuss their applications to functional analysis. The prerequisites for this talk are strong calculus muscles and a bit of Math 540 notation.

4:00 pm in 345 Altgeld Hall,Friday, February 9, 2018

More on ``A Vietoris-Smale mapping theorem for the homotopy of hyperdefinable sets'' by Achille and Berarducci

Elliot Kaplan (UIUC Math)

Abstract: I will continue to discuss the paper ``A Vietoris-Smale mapping theorem for the homotopy of hyperdefinable sets'' by Alessandro Achille and Alessandro Berarducci [arXiv]. I will sketch the proofs of the two main theorems, in which they show that under certain conditions, the definable homotopy groups of a space $X$ definable in an o-minimal structure are isomorphic to the (usual) homotopy groups of the quotient of $X$ by a certain kind of type-definable equivalence relation $E$. This is the second talk on this paper.

4:00 pm in 241 Altgeld Hall,Friday, February 9, 2018

What are spectra?

Tsutomu Okano (UIUC)

Abstract: This is an introductory talk on stable homotopy theory. I will begin by discussing stable phenomena in homotopy theory that led to the definition of spectra. Spectra represent generalized cohomology theories, such as various kinds of K-theories and cobordism theories. This implies that results about cohomology theories can be proven in the category of spectra, using analogies from topological spaces. Unfortunately, the earlier category of spectra was defective in formal properties and it was not until the 1990's that suitable categories of spectra were defined. This formality leads to the study of other sorts of homotopy theories, such equivariant and motivic homotopy theories.