[Mini-course]: Metric geometry on the configuration space | Professor Kohei Suzuki, Durham University2023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.
*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.
Title: Lectures on Capacities
Speaker: Professor Daniel Spector, National Taiwan Normal University
Lecture 1 Tuesday, June 20 10 am
Lecture 2 Wednesday, June 21st 10 am
Lecture 3 Thursday, June 22nd 10 am
Zoom link: TBA
OIST Workshop | Main organizer: Xiaodan Zhou (Analysis on Metric Spaces) | OIST members are welcome to attend all scientific sessions.
[Seminar] Sharp Uncertainty Principles and their stability, Professor Nguyen Lam, Memorial University of Newfoundland2022年12月2日 (金) 9:00
Abstract: 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.
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.
[Seminar] Whitney Extension and Lusin Approximation for Horizontal Curves in the Heisenberg Group, Professor Andrea Pinamonti, University of Trento2022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.
[Seminar] Korevaar-Schoen-Sobolev spaces and critical exponents on metric measure spaces, Professor Fabrice Baudoin, University of Connecticut2022年10月21日 (金) 9:00 〜 10:00
[Mini-course] BV functions in Carnot groups | Speaker Dr. Sebastiano Nicolussi Golo, University of Jyväskylä2022年8月22日 (月) 15:00 〜 2022年8月24日 (水) 17:00
Speaker: Dr. Sebastiano Nicolussi Golo, University of Jyväskylä
Title: BV functions in Carnot groups
Language: English, no interpretation.
Please register before July 18, 5 pm. Click here to register!
Speaker: Professor Motoko Kotani, Tohoku University
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.
Have fun in interacting with people from different interests.
Speaker: Professor Changyu Guo, Shangdong University
Title: Conservation law for harmonic mappings in higher dimensions
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.