Department of

Mathematics


Seminar Calendar
for events the day of Friday, November 1, 2019.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Friday, November 1, 2019

2:00 pm in 347 Altgeld Hall,Friday, November 1, 2019

Categorification and quantum symmetry

Colleen Delaney (Indiana University)

Abstract: One variation on the theme of ``quantum symmetry" is a categorical group action on a unitary modular tensor category, which can be interpreted physically as a global symmetry of a 2-dimensional topological quantum phase of matter. Much of our understanding of tensor category theory and hence topological phases comes from categorification: from generalizing theorems we have about rings to theorems about categories. For example, categorifying an easy theorem in commutative ring theory, the work of Etingof, Nikshych, and Ostrik established an equivalence between categorical G-actions on modular tensor categories (MTCs), and so-called G-crossed braided extensions of MTCs. Physicists Barkeshli, Bonderson, Cheng, and Wang then recognized that this correspondence can be understood as a tensor-categorical formulation of gauge coupling, wherein G-crossed braided extensions of MTCs give an algebraic theory of symmetry-enriched topological (SET) phases of matter. While the abstract theory of Etingof, Nikshych, and Ostrik is well understood, even constructing the de-categorified part of G-crossed braided extensions of MTCs, namely their fusion rings, is challenging problem in general. We will give a two-part talk, starting with an introduction to the algebraic theory of SET phases described above. In the second part of the talk we describe a topological phase-inspired approach to constructing the fusion rings of certain G-crossed extensions called permutation extensions and share work in progress with E. Samperton in constructing their categorifications.

3:00 pm in 341 Altgeld Hall,Friday, November 1, 2019

Connections of Fixed-Point Theorems with Complexity

Basilis Livanos (UIUC CS)

Abstract: In this talk, we study how fixed-point theorems arise in the field of complexity theory and their deep connections with complexity classes like TFNP which contain problems who are guaranteed to have a solution. In the process, we provide an introduction to complexity theory and also a generalization of Bessaga's and Meyers's converse theorems to Banach's fixed-point theorem. The talk will be introductory and no prior knowledge of complexity theory will be needed.

4:00 pm in 345 Altgeld Hall,Friday, November 1, 2019

O-minimal complex analysis (Part 4)

Elliot Kaplan (UIUC)

Abstract: I will continue discussing Peterzil and Starchenko's treatment of definable functions on the algebraic closure of an o-minimal field.

4:00 pm in 141 Altgeld Hall,Friday, November 1, 2019

Flexibility vs Rigidity in hyperbolic geometry

Xiaolong Han (UIUC)

Abstract: "Most" closed surfaces have a hyperbolic structure. We can ask similar questions in higher dimensions. In this talk, I will talk about some interesting phenomena and duality by looking at examples and theorems in hyperbolic geometry. I will also talk about rigidity, like how having isomorphic first fundamental group implies existence of diffeomorphism / isometry. The talk will mostly use intuition and requires no prior knowledge of hyperbolic geometry.

4:00 pm in 347 Altgeld Hall,Friday, November 1, 2019

Games That Take Forever (Literally)

Jenna Zomback   [email] (UIUC Math)

Abstract: Do you have a winning strategy for playing tic tac toe? What about chess? In a two player game (with no ties), we say that Player 1 has a winning strategy if she can always make sure that she wins the game, regardless of what Player 2 does. In this talk, we will make this definition a bit more formal, and we'll prove that in any game that ends after finitely many steps, one of the players has a winning strategy. We'll also discuss infinite games (that end after infinitely many steps), and what it means to have a winning strategy in these games. If time allows, we'll prove that in special types of infinite games, one of the players has a winning strategy.

5:00 pm in 241 Altgeld Hall,Friday, November 1, 2019

Stochastic Differential Equations and Unitaries

Marius Junge (University of Illinois at Urbana-Champaign)

Abstract: TBD