### Past Events

### [Mini-course]: Metric geometry on the configuration space | Professor Kohei Suzuki, Durham University

2023年8月29日 (火) 10:00 〜 2023年9月1日 (金) 11:00### Title: Metric geometry on the configuration space

### Speaker: Professor Kohei Suzuki, Durham University

Abstract: The configuration space Y(X) over a base space X is the space of all Radon point measures on X. The space Y(X) has been studied in many fields such as algebraic geometry (e.g., the hyperplane arrangement with X=Grassmannian), algebraic topology (e.g., the braid group with X=Euclidean plane), representation theory (e.g., the L^2-representation of diffeomorphism groups on manifolds X), statistical physics (e.g., interacting particle diffusions with X=Euclidean space). In this series of lectures, I will focus on the metric geometry of Y(X) induced by the 2-Wasserstein distance. As Y(X) does not support the volume doubling property, the established theory of PI spaces does not apply. The goal of the series is to elaborate on

- Metric geometry on Y(X);
- Curvature analysis on Y(X);
- Applications to infinite particle diffusion processes (including e.g. infinite particle Dyson Brownian motion);
- Open questions.

Lecture 1 | **L4E01** August 29, 2023 10:00 - 11:00

Lecture 2 | **L4E01 **August 30, 2023 10:00 - 11:00

Lecture 3 | **L4F01 **August 31, 2023 10:00 - 11:00

Lecture 4 | **B700 **September 1, 2023 10:00 - 11:00

### Register here

*After registering, you will receive a confirmation email containing information about joining the meeting.

### This lecture be accessible to senior math undergraduate and anyone above the level.

### [Mini-course]: Lectures on Capacities | Professor Daniel Spector, National Taiwan Normal University

2023年6月20日 (火) 10:00 〜 2023年6月22日 (木) 11:00### Title: Lectures on Capacities

### Speaker: Professor Daniel Spector, National Taiwan Normal University

Zoom registration: https://oist.zoom.us/meeting/register/tJErce-tpj0jGNN5TM3gwMnRnGHaY5lNZ5Qk#/registration

### Lecture 1 Tuesday, June 20 10 am

### Lecture 2 Wednesday, June 21st 10 am

### Lecture 3 Thursday, June 22nd 10 am

### Zoom link: TBA

### [Hybrid] OIST Workshop "Potential theory and random walks in metric spaces"

2023年5月30日 (火) (All day) 〜 2023年6月2日 (金) (All day)OIST Workshop | Main organizer: Xiaodan Zhou (Analysis on Metric Spaces) | OIST members are welcome to attend all scientific sessions.

OIST campus will be closed on Thursday and Friday due to the typhoon. All talks will be online on Thursday and Friday. You can obtain a zoom link from here.

### [Seminar] Sharp Uncertainty Principles and their stability, Professor Nguyen Lam, Memorial University of Newfoundland

2022年12月2日 (金) 9:00Abstract: The Heisenberg uncertainty principle, which is a fundamental result in quantum mechanics, and related inequalities such as the hydrogen and Hardy uncertainty principles, belong to the family of geometric inequalities known as the Caffarelli-Kohn-Nirenberg inequalities. In this talk, we discuss some recent results about the optimal uncertainty principles, Caffarelli-Kohn-Nirenberg inequalities, and their quantitative stability. The talk is based on recent joint works with C. Cazacu, J. Flynn and G. Lu.

### [Seminar] Poincare inequalities on the Vicsek set, Professor Chen Li, Louisiana State University

2022年11月18日 (金) 10:00

Abstract:

The Vicsek set is a tree-like fractal on which neither analog of curvature nor differential structure exists, whereas the heat kernel satisfies sub-Gaussian estimates. I will talk about Sobolev spaces and scale invariant $L^p$ Poincar\'e inequalities on the Vicsek set. Several approaches will be discussed, including the metric approach of Korevaar-Schoen and the approach by limit approximation of discrete p-energies.

Zoom: https://oist.zoom.us/meeting/register/tJEpdu-uqTwrGdFV5IrA0woMhvhlxVa_5ttw

### [Seminar] Whitney Extension and Lusin Approximation for Horizontal Curves in the Heisenberg Group, Professor Andrea Pinamonti, University of Trento

2022年11月4日 (金) 17:00

**Abstract: **Whitney extension results characterize when one can extend a mapping from a compact subset to a smooth mapping on a larger space. Lusin approximation results give conditions under which one can approximate a rough map by a smoother map after discarding a set of small measure. We first recall relevant results in the Euclidean setting, then describe recent work extending them to horizontal curves in the Heisenberg group. We focus on C^m curves.

**Zoom:** https://oist.zoom.us/meeting/register/tJMpduGtqzooG9PA85LMRCwswpo5ODm2nU49

### [Seminar] Korevaar-Schoen-Sobolev spaces and critical exponents on metric measure spaces, Professor Fabrice Baudoin, University of Connecticut

2022年10月21日 (金) 9:00 〜 10:00**Title**: Korevaar-Schoen-Sobolev spaces and critical exponents on metric measure spaces

**Speaker:**Fabrice Baudoin, University of Connecticut

**Abstract:**We will review some of the recent developments in the theory of Korevaar-Schoen-Sobolev spaces. While this theory is equivalent to that of Cheeger and Shanmugalingam if the space supports a Poincare inequality, it offers new perspectives in situations, like fractals, where such inequalities are not available.

### [Mini-course] BV functions in Carnot groups | Speaker Dr. Sebastiano Nicolussi Golo, University of Jyväskylä

2022年8月22日 (月) 15:00 〜 2022年8月24日 (水) 17:00Speaker: Dr. Sebastiano Nicolussi Golo, University of Jyväskylä

Title: BV functions in Carnot groups

Language: English, no interpretation.

### [Catch-All Mathematical Colloquium] Professor Motoko Kotani (Tohoku University )

2022年7月22日 (金) 15:00 〜 17:00### 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. Please register before July 18, 5 pm. Click here to register!

**Speaker**: Professor Motoko Kotani, Tohoku University

**Title**: Discrete geometric analysis and its application

**Abstract:**Discrete geometric analysis is an attempt to discretize geometric analysis. Mathematics is often said “a common language of science”. As our world consists of atoms, which we consider as discrete objects, developing language to describe discrete objects, their geometric structures in particular, is important. I would like to discuss our challenge to establish discrete geometric analysis and its application to other science.

Part II

Have fun in interacting with people from different interests.

### [Seminar] Conservation law for harmonic mappings in higher dimensions

2022年7月1日 (金) 10:00 〜 11:00### Speaker: Professor Changyu Guo, Shangdong University

**Title**: Conservation law for harmonic mappings in higher dimensions

**Abstract**:

It has been a longstanding open problem to find a direct conservation law for harmonic mappings into manifolds. In the late 1980s, Chen and Shatah independently found a conservation law for weakly harmonic maps into spheres, which can be interpreted by Noether's theorem. This leads to Helein's celebrated regularity theorem on weakly harmonic maps from surfaces. For general target manifolds, Riviere discovered a direct conservation law in two dimension in 2007, allowing him to solve two well known conjectures of Hildebrandt and Heinz. As observed by Riviere-Struwe in 2008, due to lack of Wente's lemma, Riviere's approach does not extend to higher dimensions. In a recent joint work with Chang-Lin Xiang, we successfully found a conservation law, in the spirit of Riviere, for a class of weakly harmonic maps (around regular points) into general closed manifolds in higher dimensions.