### Past Events

### [Seminar] Sub-Gaussian heat kernel bounds and singularity of energy measures for symmetric diffusions,Professor Naotaka Kajino (Kyoto University)

2022年4月22日 (金) 10:00 〜 11:00### Abstract:

This talk will present the result of a joint work with Mathav Murugan(University of British Columbia) that, for a symmetric diffusion on a complete locally compact separable metric space, two-sided sub-Gaussian heat kernel bounds imply the singularity of the energy measures with respect to the reference measure.

For self-similar (scale-invariant) diffusions on self-similar fractals, the singularity of the energy measures is known to hold in many cases by Kusuoka (1989, 1993), Ben-Bassat, Strichartz and Teplyaev (1999),

Hino (2005), and Hino and Nakahara (2006), but these results heavily relied on the self-similarity of the space.

It was conjectured, and had remained open for the last two decades to prove, that the singularity of the energy measures should follow, without assuming the self-similarity, just from two-sided sub-Gaussian

heat kernel bounds of the same form as those for diffusions on typical self-similar fractals. The main result of this talk answers this conjecture affirmatively.

The first half of the talk will be devoted to a brief introduction to self-similar diffusions (and their associated Dirichlet forms) on self-similar fractals and to sub-Gaussian heat kernel bounds for symmetric diffusions, so that the talk will (hopefully) be accessible even to those without prior knowledge about diffusions on fractals.

### [Seminar] Supercaloric functions for the parabolic p-Laplace equation in the fast diffusion case, Juha Kinnunen, Aalto University

2022年3月8日 (火) 16:00This talk discusses a generalized class of supersolutions, so-called \(p\)-supercaloric functions, to the parabolic \(p\)-Laplace equation. This class of functions is defined as lower semicontinuous functions that are finite in a dense set and satisfy the parabolic comparison principle. Their properties are relatively well understood in the slow diffusion case \(p>2\), but little is known in the fast diffusion case \(1

### [Mini-course] Curvature and Optimal transport | Professor Asuka Takatsu, Tokyo Metropolitan University

2022年3月8日 (火) 10:00 〜 2022年3月10日 (木) 11:00### Speaker: Professor Asuka Takatsu, Tokyo Metropolitan University

### Title: Curvature and Optimal transport

Abstract

In this series of lectures, I first review the notion of curvature (Gaussian curvature and Ricci curvature).

In particular, I recall some comparison theorems (Toponogov's triangle comparison theorem, Bishop--Gromov volume comparison theorem etc).

Then I introduce a generalized notion of curvature in non-smooth spaces.

### [Catch-All Math Colloquium] Monge-Ampère equations related to optimal transport and geometric optics, Jun Kitagawa, Michigan State University

2022年2月22日 (火) 15:00 〜 17:00### Monge-Ampère type equations are fully nonlinear elliptic partial differential equations that arise when considering the deformation of volume induced by some kind of transformation. In this talk I will discuss two such cases, the optimal transport problem, and geometric optics problems. The former discusses the most efficient way of transporting some resource to another location, and the second is a simplified model for optical instruments (such as lenses or mirrors) in which light is treated as a particle rather than a wave. I will attempt to focus more on heuristics rather than technical details; no knowledge of PDEs is assumed. A portion of this talk is based on joint work with N. Guillen.

Please register before February 17, 5 pm. Click here to register!

### The colloquium will be held once a month online. Each event consists of a one-hour talk on mathematics followed by a one-hour diversity panel discussion session. February speaker is Jun Kitagawa from Michigan State University.

In the mathematics part, we will hear an exciting overview talk for a general audience. In the discussion session, we will hear about the speaker's experience 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.

### Catch-All Mathematical Colloquium

2022年1月19日 (水) 15:00 〜 17:00### 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. Please register before January 14, 5 pm. Click here to register!

In the mathematics part, we will hear an exciting overview talk for a general audience. January speaker is Ade Irma Suriajaya from Kyushu University. In the discussion session, we will hear about the speaker's experience 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.

Part I Expository math talk 3-4 pm

Speaker: Ade Irma Suriajaya Kyushu University

Talk Title : Goldbach’s Conjecture and the Riemann Hypothesis in Number Theory, and Their Relations to Zeta Functions

Abstract: Number Theory has a very long history that dates back to thousands of years ago. The main goal of this study is to understand properties of numbers which can essentially be reduced to understanding prime numbers. Number Theory has evolved over time and yet we are still left with several important old problems. Among, Goldbach’s conjecture which is celebrating its 280th anniversary this year (by the time of my talk in 2022) and the Riemann hypothesis which is now over 160 years old remain unsolved. In this talk, I would like to explain what these problems are about and briefly introduce a few recent works which are related to them, especially how the distribution of zeros of the Riemann zeta function comes into play. My talk will be given in the perspective of Analytic Number Theory.

Abstract: Part II Diversity Panel Discussion 4-5 pm

### Analysis on Metric Spaces Seminar

2021年12月10日 (金) 9:00 〜 10:00**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.

**Click here to register.**

### Catch-All Mathematical Colloquium

2021年11月24日 (水) 15:00 〜 17:00### 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

### Catch-All Mathematical Colloquium

2021年10月21日 (木) 9:00 〜 11:00The 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年10月14日 (木) 15:00 〜 16:00Analysis 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 Summer Analysis on Metric Spaces Seminar

2021年8月27日 (金) 9:00 〜 10:00#### Title : CURVE SHRINKING FLOW IN CARNOT GROUPS

#### Speaker: Luca Capogna, Smith College