Department of

# Mathematics

Seminar Calendar
for events the day of Friday, November 13, 2020.

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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, November 13, 2020

1:00 pm in Zoom,Friday, November 13, 2020

#### Cyclicity preserving operators

###### Jeet Sampat   [email] (Washington University in St Louis - Math)

Abstract: For certain spaces of analytic functions in several complex variables, we will show that bounded linear operators that preserve shift-cyclic functions (i.e. Tf is shift-cyclic whenever f is shift-cyclic) are necessarily weighted composition operators. Examples of spaces for which this result holds true consist of the Hardy space, Dirichlet type spaces, Drury-Arveson space etc. In the case of Hardy spaces we will show that this condition is also sufficient. That is, all bounded weighted composition operators preserve cyclic functions in the Hardy spaces.

3:00 pm in Zoom (Email na17 [AT] illinois [DOT] edu for details),Friday, November 13, 2020

#### Gatekeeping in Calculus and Other Stories: Investigating the Influence of Race and Gender on Instructor Beliefs and Student Experiences

###### Taylor McNeill (Vanderbilt University)

Abstract: In this seminar we'll discuss how conceptions of mathematics instruction as race- and gender-neutral can impede inclusive teaching in undergraduate pre-calculus and calculus. Drawing on a larger study that explores instructors’ and students’ perceptions of instructional events, which white women and racially minoritized students identified as discouraging, I’ll share a case study centered on an event that exhibits the well-documented gatekeeping function of calculus. Instructors’ and students’ contrasting perceptions of this event reveal how instructors’ views of pre-calculus and calculus teaching as socially neutral can erase underrepresented students’ racialized and/or gendered experiences of instruction. I will also share ongoing work that investigates the influence of instruction and other mathematics cultural practices on the experiences of students and faculty minoritized by race, gender, and/or sexuality.

4:00 pm in Zoom,Friday, November 13, 2020

#### Minimal Surfaces and Its Applications

###### Xiaolong Hans Han

Abstract: In this talk, we will talk about some basic definitions of minimal surfaces, its stability and connection to Heegaard splitting. We also explain transversal vs. non-transversal intersections of minimal surfaces and how to do surgery. We then use results of existence and intersections of minimal surfaces to provide some applications in 3-manifolds. Depending on time, we will outline applications of minimal surfaces to prove non-sharpness of a recent inequality by Brock and Dunfield.

4:00 pm in Zoom (email ruiyuan at illinois for info),Friday, November 13, 2020

#### GraphSAT -- a novel decision problem combining SAT and graph theory

###### Vaibhav Karve (UIUC Math)

Abstract: Graph theorists often care about forbidden-graph characterizations of graph properties. For example, Kuratowski's theorem says that a graph is planar iff it does not "contain" K5 or K3,3. We replace "planar" by a new graph property inspired by Boolean Satisfiability (SAT) and look for similar forbidden graphs in the hope that it will tell us something about SAT. We will also talk about various ways to translate "containment" to GraphSAT and as a result we will encounter a host of other decision problems on the way. We will show a full forbidden-graph characterization of 2-GraphSAT and partial results for 3-GraphSAT. This talk requires no prerequisites other than familiarity with complexity classes P, NP, NP-complete etc. This is joint work with Anil Hirani (UIUC Math)

4:00 pm in via Zoom,Friday, November 13, 2020

#### Computing with braids

###### Eric Samperton (UIUC Math)

Abstract: This talk will be a mash-up of some basic ideas in topology and computer science. The braid group on n strands is a mathematical abstraction of the collection of “braid patterns” one can form by braiding n ropes around each other. It plays an important role in many parts of topology and group theory. I’ll begin by introducing the braid group, it’s relation to knot theory, and the important concept of a "group action.” We’ll then see how various actions of the braid group can be used to simulate computers—both quantum and classical. We’ll learn some basic theoretical computer science along the way.

For Zoom info, please email Derek Thomas (drthoma2@illinois.edu)