Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, May 4, 2021.

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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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Tuesday, May 4, 2021

11:00 am in Zoom,Tuesday, May 4, 2021

#### Splitting $BP\langle 2 \rangle \wedge BP \langle 2 \rangle$ at odd primes

###### Elizabeth Tatum (UIUC)

Abstract: In the 1980’s, Mahowald and Kane used Brown-Gitler spectra to construct splittings of $bo \wedge bo$ and $l \wedge l$. In this talk, we will construct an analogous splitting for the spectrum $BP\langle 2 \rangle \wedge BP \langle 2 \rangle$ at odd primes.

2:00 pm in Zoom,Tuesday, May 4, 2021

#### On sizes of 1-cross intersecting set pair systems

###### Mina Nahvi (UIUC)

Abstract: Let $\{(A_i,B_i)\}_{i=1}^m$ be a set pair system. Furedi, Gyarfas and Kiraly called it $1$-cross intersecting if the size of intersection of $A_i$ and $B_j$ is $1$ when $i$ and $j$ are distinct, and $0$ if $i=j$. They studied such systems and their generalizations, and in particular considered $m(a,b,1)$, the maximum size of a $1$-cross intersecting set pair system in which $|A_i|\leq a$ and $|B_i|\leq b$ for all $i$.

Answering one of their questions, Holzman recently proved that if $a,b\geq 2$, then $m(a,b,1)\leq (29/30)((a+b) \text{ choose } a)$. He also conjectured that the factor $29/30$ in his bound can be replaced by $5/6$. The goal of this talk is to sketch the proof of this improved bound.

This is joint work with Grace Mc.Court and Alexandr V Kostochka.

2:00 pm in Zoom Meeting (email daesungk@illinois.edu for info),Tuesday, May 4, 2021

#### Towards optimal gradient bounds for torsion functions in the plane

###### Jeremy Hoskins (University of Chicago)

Abstract: In this talk we consider a natural question going back to Saint Venant in 1856: if a beam of constant cross-section is twisted, how large is the maximum shear stress? As it turns out, this problem can be formulated as a basic question about elliptic PDEs which arises in a number of settings, including electrostatics, constrained maximization of the lifetime of Brownian motion started close to the boundary, and optimal Hermite-Hadamard inequalities for subharmonic functions on convex domains. In this talk we will present upper and lower bounds for the largest possible shear stress for convex domains, and discuss extremal shapes.

4:00 pm in Zoom | Register at https://illinois.zoom.us/meeting/register/tZcsdeyhpjMvHdQSDeyJv0zk34B2Z-lzD-wZ ,Tuesday, May 4, 2021

#### Spring 2021 Department Faculty Meeting

###### (UIUC Department of Mathematics)

Abstract: The Spring 2021 Department Faculty Meeting will be held virtually on Tuesday, May 4, 2021, at 4 p.m. CT. Advance registration will be required: https://illinois.zoom.us/meeting/register/tZcsdeyhpjMvHdQSDeyJv0zk34B2Z-lzD-wZ