Department of

# Mathematics

Seminar Calendar
for Topology Seminar events the year of Thursday, January 23, 2020.

.
events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
    December 2019           January 2020          February 2020
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1  2  3  4  5  6  7             1  2  3  4                      1
8  9 10 11 12 13 14    5  6  7  8  9 10 11    2  3  4  5  6  7  8
15 16 17 18 19 20 21   12 13 14 15 16 17 18    9 10 11 12 13 14 15
22 23 24 25 26 27 28   19 20 21 22 23 24 25   16 17 18 19 20 21 22
29 30 31               26 27 28 29 30 31      23 24 25 26 27 28 29



Friday, January 24, 2020

4:00 pm in 141 Altgeld Hall,Friday, January 24, 2020

#### Organizational Meeting

Abstract: We will draft a schedule of the seminar talks this semester. Please join us and sign up if you want to speak (you don't have to decide on a topic or abstract now). As usual, there will be cookies. All are welcome!

Friday, January 31, 2020

4:00 pm in 141 Altgeld Hall,Friday, January 31, 2020

#### Introduction to Orbifolds

###### Brannon Basilio (UIUC)

Abstract: We can generalize the notion of a manifold to include singularities; thus we can define a new object called orbifolds. In this talk, we will give an introduction to the notion of orbifolds, including examples, covering orbifold, Euler number of an orbifold, and the classification theorem of 2-orbifolds.

Friday, February 7, 2020

4:00 pm in 141 Altgeld Hall,Friday, February 7, 2020

#### A probabilistic approach to quantizing Yang-Mills theory

###### Kesav Krishnan (UIUC)

Abstract: I will introduce the problem of rigorously quantizing Yang Mills Theory, and how probability theory can be used to that end. If time permits, I will talk about the discrete gauge-string duality as introduced by Sourav Chatterjee

Tuesday, February 11, 2020

11:00 am in 243 Altgeld Hall,Tuesday, February 11, 2020

#### Vanishing and Realizability

###### Shane Clark (University of Kentucky)

Abstract: The Reidemeister trace of an endomorphism of a CW complex is a lower bound for the number of fixed points (up to homotopy) of that endomorphism. For an endomorphism $f$, the Reidemeister trace of $f^n$ is a lower bound for the number of fixed points of $f^n$, however it can be a far from an optimal lower bound. One method of addressing this discrepancy constructs an equivariant map, the n^{th} Fuller trace $f$, which carries information about the periodic points of a map $f$. However, we must ask how much information is retained by this equivariant construction? In this talk we show that the n^{th} Fuller trace of $f$ is a complete invariant for describing a minimum set of periodic points for maps of tori.

Friday, February 14, 2020

4:00 pm in 141 Altgeld Hall,Friday, February 14, 2020

#### Bounds on volumes of mapping tori

###### Heejoung Kim (UIUC)

Abstract: For a surface $S$ and a homeomorphism $f: S\to S$, the mapping torus of $S$ by $f$ is defined by $M_f=(S\times [0,1])/((x,0)\sim (f(x), 1))$. In particular, for a closed surface $S$ of genus at least 2 and a pseudo-Anosov element $f$ of the mapping class group of $S$, $M_f$ is a hyperbolic manifold. Brock provided bounds of the hyperbolic volume of $M_f$ from a hyperbolic structure on $M_f$ by using its Weil-Petersson metric. And then Agol gave a sharp upper bound for the volume in terms of the translation distance on the pants graph $P(S)$ which is associated with pants decomposition on $S$. In this talk, we will discuss mapping class groups and Agol's proof on the upper bound.

Friday, February 21, 2020

4:00 pm in 141 Altgeld Hall,Friday, February 21, 2020

#### Unifying Galois Theories with Categorification

###### Robert (Joseph) Rennie (UIUC)

Abstract: Since its inception nearly two centuries ago, what we call "Galois Theory" (say in an undergraduate algebra course) has led to many analogous results, and thus attained the status of a sort of metatheorem. In Galois' case, this concept was applied to fields, yielding an equivalence between some lattice of field extensions and a lattice of subgroups of a corresponding "galois group" ... under certain conditions. Later on, the same concept was shown to be present in Topology, with extensions being replaced by their dual notion of covering spaces, and the galois group being replaced by the fundamental group... again, under certain conditions. Even later, Galois' results for fields were generalized to arbitrary rings, introducing new associated data along the way. In this talk, we explore the process of formally unifying all of these "Galois Theories" into one Galois Principle, with the aim of developing an intuition for identifying some of its infinite use-cases in the wilds of Math (e.g. Algebra, Topology, and Logic). Along the way, I aim to discuss explicitly and to motivate categorification to the working mathematician using the results of this talk as concrete examples.

Tuesday, February 25, 2020

11:00 am in 243 Altgeld Hall,Tuesday, February 25, 2020

#### \'Etale K-theory

###### Akhil Mathew (U Chicago)

Abstract: I will explain some general structural results about algebraic K-theory and its \'etale sheafification, in particular its approximation by Selmer K-theory. This is based on some recent advances in topological cyclic homology. Joint work with Dustin Clausen.

Friday, February 28, 2020

4:00 pm in 141 Altgeld Hall,Friday, February 28, 2020

#### Arnold-Liouville Theorem

###### Jungsoo (Ben) Park (UIUC)

Abstract: This talk will be an introduction to fundamental concepts of symplectic geometry. Furthermore, we will delve into the proof of Arnold-Liouville theorem: https://en.wikipedia.org/wiki/Liouville–Arnold_theorem.

Tuesday, March 10, 2020

11:00 am in 243 Altgeld Hall,Tuesday, March 10, 2020

#### To Be Announced

###### Mark Behrens (Notre Dame Math)

Tuesday, March 24, 2020

11:00 am in 243 Altgeld Hall,Tuesday, March 24, 2020

#### To Be Announced

###### Christina Osborne (OSU Math)

Tuesday, April 7, 2020

11:00 am in 243 Altgeld Hall,Tuesday, April 7, 2020

#### To Be Announced

###### Ben Antieau (UIC )

Tuesday, April 21, 2020

11:00 am in 243 Altgeld Hall,Tuesday, April 21, 2020