### Analysis on Metric Spaces Seminar

2021-12-10
Zoom
Title: Helgason-Fourier analysis techniques on hyperbolic spaces and sharp geometric and functional inequalities

Speaker: Professor Guozhen Lu, University of Connecticut

Abstract: In this talk, we will report some recent progress on sharp geometric and functional inequalities by using the Helgason-Fourier analysis techniques on hyperbolic and symmetric spaces. These techniques allow us to establish sharp higher order Hardy-Sobolev-Maz'ya and Hardy-Adams inequalities on upper half spaces, complex Siegel domains and quaternionic and octanionic hyperbolic spaces. Some applications to PDEs will also be given.

2021-11-24
zoom

### This colloquium will be held once a month. It will be held online for the time being. Each event consists of a one-hour talk on mathematics followed by a one-hour diversity panel discussion session.

In the mathematics part, we will hear an exciting overview talk for a general audience. November speaker is Masato Mimura from Tohoku University. In the discussion session, we will hear about the speaker's experience as a mathematician, especially in choosing fields of research. You can take inspiration from them and exchange ideas with other participants in a small group. After the sessions are over, there will be a tea time where participants can chat freely.

You can join Part I only or both parts of the colloquium. Please register before November 19, 5 pm. Click here to register!

Part I Expository math talk 3-4 pm

Speaker: Masato Mimura 見村万佐人 (Tohoku University 東北大学)

Talk Title : The Green--Tao theorem for number fields

Abstract:  The celebrated Green--Tao theorem states that an upper dense subset of the set of rational primes contains arbitrarily long arithmetic progressions. Later, Tao proved that an upper dense subset of the set of Gaussian primes, namely, prime elements in the integer ring $\mathbb{Z}[\sqrt{-1}]$ of the number field $\mathbb{Q}(\sqrt{-1})$ contains arbitrarily shaped constellations. (We will explain the precise statement in the talk.) In the paper, Tao asked whether the same conclusion holds in the setting of arbitrary number fields. In this joint work with Wataru Kai (Tohoku U.), Akihiro Munemasa (Tohoku U.), Shin-ichiro Seki (Aoyama Gakuin U.) and Kiyoto Yoshino (Tohoku U.), we answer Tao's question in the affirmative. We have an application to the setting of a binary quadratic form. More precisely, given a form $F$, we study combinatorics on the set of pair of integers $(x,y)$ for which $F(x,y)$ is a rational prime. No serious background of number theory is required for this talk.

Part II Diversity Panel Discussion 4-5 pm

### Fractals and the dynamics of Thurston maps

2021-11-19
Zoom

#### Speaker: Professor Mario Bonk, UCLATitle: Fractals and the dynamics of Thurston maps

Abstract:

A Thurston map is a branched covering map on a topological 2-sphere for which the forward orbit of each critical point under iteration is finite.  Each such map gives rise to a fractal geometry on its underlying 2-sphere. The study of these maps and their associated  fractal structures links diverse  areas of mathematics such as dynamical systems, classical conformal analysis, hyperbolic geometry, Teichmüller theory,  and analysis on metric spaces.  In my talk I will report on some recent developments.

### Catch-All Mathematical Colloquium

2021-10-21
Zoom

The colloquium will be held once a month. It will be held online for the time being. Each event consists of a one-hour talk on mathematics followed by a one-hour diversity panel discussion session.

In the mathematics part, we will hear an exciting overview talk for a general audience. October speaker is Megumi Harada, Professor of McMaster University. In the discussion session, we will hear about the speaker's personal journey as a mathematician. You can take inspiration from them and exchange ideas with other participants in a small group. After the sessions are over, there will be a tea time where participants can chat freely.

You can join Part I only or both parts of the colloquium. Please register before Oct 18th, 5 pm. Click here to register!

### Quasiconformal and Sobolev mappings in metric measure spaces

2021-10-14
Zoom

Analysis on Metric Spaces Fall Seminar

Title: Quasiconformal and Sobolev mappings in metric measure spaces

Speaker: Panu Lahti, Chinese Academy of Sciences

Abstract: Starting from Gehring, the equivalence between the metric, geometric, and analytic def- initions of quasiconformality has been investigated by various authors. There are many results stating that if a mapping is metrically quasiconformal, perhaps only in a relaxed sense, then it is analytically quasiconformal, or at least a Sobolev mapping. In recent joint work with Xiaodan Zhou, we have shown an improved version of such a result, which seems to detect more Sobolev mappings than previous results in the literature. I will discuss these results as well as the general strategy of the proofs.

2021-10-08
Zoom seminar

2021-08-27
On Zoom

2021-08-11
Zoom

2021-07-16
on Zoom

2021-06-25
On Zoom