### Past Events

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

2022-12-02Abstract: 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

2022-11-18

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

2022-11-04

**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

2022-10-21**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.

### [Seminar] Cantor Julia sets, Professor Vyron Vellis, University of Tennessee

2022-10-07**Title:** Cantor Julia sets

**Speaker**: Vyron Vellis,University of Tennessee

**Abstract:** The Julia set of a meromorphic function is the set of “chaotic points”, i.e., the set of all points that have no neighborhood under which the iterates of the function form a normal family. In absence of a rich holomorphic function theory in higher dimensions, the right substitute in complex dynamics are uniformly quasiregular (UQR) maps. Which Cantor sets can appear as Julia sets of UQR maps? How (topologically) complex can such sets be? This talk is based on joint works with Alastair Fletcher and Daniel Stoertz.

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

2022-08-22 to 2022-08-24Speaker: 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 )

2022-07-22### 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

2022-07-01### 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.

### [Catch-All Mathematical Colloquium] The level-set mean curvature flow equation versus the total variation flow equation,Yoshikazu Giga (University of Tokyo )

2022-05-12Title: The level-set mean curvature flow equation versus the total variation flow equation

Abstract: The level-set mean curvature flow equation has been introduced to track an evolving hypersurface by its mean curvature after it develops singularities. A level-set of a solution of the level-set mean curvature flow equation moves its mean curvature. The total variation flow equation is often used to remove noise from images. Although these two equations look similar, analytic properties are quite different; the former equation is a local equation while the latter is a nonlocal equation. In this talk, we compare these two equations as well as a few applications.

**Discussion Theme (for the 2nd part of the event) : **

How to collaborate with researchers other than mathematicians

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 May , 5 pm. Click here to register!