Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, March 9, 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, March 9, 2021

10:00 am in Zoom,Tuesday, March 9, 2021

#### Open problems in additive combinatorics

###### Ben Green (Oxford University)

Abstract: There will be discussion on some open problems, the audience is encouraged to look some in advance.

11:00 am in Zoom,Tuesday, March 9, 2021

#### Cyclotomic Galois extensions in the chromatic homotopy

###### Tomer Schlank (Hebrew University)

Abstract: The chromatic approach to stable homotopy theory is "divide and conquer". That is, questions about spectra are studied through various localizations that isolate pure height phenomena and then are put back together. For each height n, there are two main candidates for pure height localization. The first is the generally more accessible K(n)-localization and the second is the closely related T(n)-localization. It is an open problem whether the two families of localizations coincide. One of the main reasons that the K(n)-local category is more amenable to computations is the existence of well understood Galois extensions of the K(n)-local sphere. In the talk, I will present a generalization, based on ambidexterity, of the classical theory of cyclotomic extensions, suitable for producing non-trivial Galois extensions in the T(n)-local and K(n)-local context. This construction gives a new family of Galois extensions of the T(n)-local sphere and allows to lift the well known maximal abelian extension of the K(n)-local sphere to the T(n)-local world. I will then describe some applications, including the study of the T(n)-local Picard group, a chromatic version of the Kummer theory, and interaction with algebraic K-theory. This is a joint project with Shachar Carmeli and Lior Yanovski.

for Zoom info, please email vesna@illinois.edu

2:00 pm in Zoom,Tuesday, March 9, 2021

#### Ramsey numbers of Sparse Digraphs

###### Xiaoyu He (Stanford University)

Abstract: The Ramsey number $r(H)$ of a digraph $H$ is the minimum $N$ such that every $N$-vertex tournament contains $H$ as a subgraph. Note that $r(H)$ only exists if $H$ has no oriented cycle, so we will assume H is acyclic. In 1934, Rédei showed that every tournament has a Hamiltonian path, which implies $r(H)=n$ when $H$ is the oriented path on $n$ vertices. For which other $n$-vertex digraphs $H$ is it true that $r(H) = O(n)$?

A famous result of Lee, proving a conjecture of Burr and Erdős, says that any sparse undirected graph has Ramsey number linear in $n$. It is natural to ask whether the analogous statement also holds for digraphs, and surprisingly we show that it is false. For any $C > 1$, we construct a family of bounded-degree digraphs $H$ with $r(H) > n^C$. In the other direction, we prove linear and nearly-linear upper bounds for $r(H)$ for several natural families of bounded-degree digraphs, including random digraphs and digraphs of bounded height.

Joint work with Jacob Fox and Yuval Wigderson.

6:00 pm in Zoom | Register at http://bit.ly/MathWithoutBorders,Tuesday, March 9, 2021

#### Opening remarks

###### Various speakers (see abstract) (Various)

Abstract: Opening remarks for the Kyushu-Illinois Strategic Partnership Colloquia Series, "Mathematics Without Borders – Applied and Applicable," featuring Susan Martinis, vice chancellor for research and innovation, Stephen G. Sligar Professor of Molecular and Cellular Biology, Illinois; Reitumetse Mabokela, vice provost for international affairs and global strategies, professor of higher education, Illinois; Yoshio Hisaeda, executive vice president for research, professor of applied chemistry, Kyushu; Toshiyuki Kono, executive vice president for international affairs, professor of law, Kyushu.

Register at https://zoom.us/webinar/register/WN_tddbR8ciTHKKji-QCvbjkA

6:10 pm in Zoom | Register at http://bit.ly/MathWithoutBorders,Tuesday, March 9, 2021

#### “Water Waves: breaking, peaking and disintegration”

###### Vera Mikyoung Hur (University of Illinois Urbana-Champaign, Department of Mathematics)

Abstract: Water waves describe the situation where water lies below a body of air and are acted upon by gravity. Describing what we may see or feel at the beach or in a boat, they are a perfect specimen of applied mathematics. They encompass wide-ranging wave phenomena, from whitecapping to tsunamis and to rogue waves. The interface between the water and the air is free, and poses profound and subtle difficulties for rigorous analysis, numerical computation and modeling. I will discuss some recent developments and future research directions, particularly, a rich variety of wave phenomena in rotational flows, and their instability, and also statistical and machine learning approaches to rogue waves.

Register at https://zoom.us/webinar/register/WN_tddbR8ciTHKKji-QCvbjkA

7:20 pm in Zoom | Register at http://bit.ly/MathWithoutBorders,Tuesday, March 9, 2021

#### “Visual Design Analysis with Machine Learning”

###### Seiichi Uchida, professor (Faculty of Information Science and Electrical Engineering, Kyushu University )

Abstract: Visual designs are image data, such as fonts, logos, and typographies, and often carefully created for showing specific impressions. In this talk, several on-going attempts of visual design analysis at my lab will be introduced. For the trials, we employ various machine learning techniques to deal with the complex relationships between image appearance and impression.