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for events the day of Monday, March 12, 2018.

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Monday, March 12, 2018

9:00 am in Altgeld Hall,Monday, March 12, 2018

Mathematics Graduate School Open House

1:00 pm in 163 Noyes Laboratory,Monday, March 12, 2018

Kirwan-Ness stratifications for Cyclic quivers

Itziar Ochoa de Alaiza Gracia (Illinois Math)

Abstract: Mathematical and physical problems can often be simplified by making use of symmetries: for example, by taking a space with symmetries and forming a quotient (“dividing out by the symmetries”). Starting with elementary examples, I will explain difficulties that can arise in forming such quotients, and outline a scientific procedure in algebraic geometry that builds reasonable quotients by cutting up spaces into “stable” and “unstable” orbits. I will then explain that, by refining the “stable/unstable” dichotomy to measure “just how unstable each orbit is,” one can get a lot of topological/geometric information about the quotient.

3:00 pm in 345 Altgeld Hall,Monday, March 12, 2018

The geometry of the moduli stack of formal groups

Ningchuan Zhang (UIUC Math)

Abstract: The geometry of $\mathcal{M}_{fg}$, the moduli stack of formal groups, reflects many important concepts and results in chromatic homotopy theory. In this talk, I’ll first give the basic definition of stacks. After that, I’ll define $\mathcal{M}_{fg}$ and talk about its geometry: sheaves, substacks and Lubin-Tate deformation theory. I’ll also explain how the geometry of $\mathcal{M}_{fg}$ is related to chromatic homotopy theory.

3:00 pm in 243 Altgeld Hall,Monday, March 12, 2018

Morse theory and a stack of broken lines

Hiro Tanaka (Harvard)

Abstract: I'll talk about a stack encoding the moduli space of gradient trajectories on a point (which is, I promise, less trivial than it sounds). It turns out that Morse theory on any manifold defines a sheaf on this stack, and that this sheaf in turn allows us to encode Morse theory as a deformation problem. I'll touch on the generalization to Floer theory, too. These constructions conjecturally allow one to construct Floer theory and Morse theory with coefficients in spectra when appropriate obstructions vanish. This is joint work with Jacob Lurie.

4:00 pm in 245 Altgeld Hall,Monday, March 12, 2018

Some of my (embarrassing) stories from working in algebraic combinatorics

Alex Yong   [email] (Department of Mathematics, University of Illinois at Urbana-Champaign)

Abstract: In recent years (and in my opinion), the field of algebraic combinatorics has centered around three topics: Cluster algebras, Macdonald polynomials and Schubert calculus. My own specialization is in the latter (Professors Di Francesco and Kedem are experts in the other two). A standard way to introduce Schubert calculus is to ask "How many lines in three space meet four given lines?". The answer "2" and the rigorous foundation for this claim was the subject of Hilbert's fifteenth problem. I refer you to the recent PBS Infinite Series video (link here) for some quick preparation. I'll speak about my own experiences in the subject in the form of three short stories: "The AMS talk about nothing", "Wishing becomes doing", and "Conference coffee, but not conveyor belt sushi".

5:00 pm in 241 Altgeld Hall,Monday, March 12, 2018

More on equivalence relations

Anush Tserunyan (UIUC)

Abstract: We will finish the previous results and start with L_2-Betti numbers.