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

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

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

Speaker: 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 )

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

[Seminar] Conservation law for harmonic mappings in higher dimensions

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. 

Click here to register

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

Title: 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!

[Seminar] Variational problems with gradient constraint, Professor Xiao Zhong, University of Helsinki

Speaker: Professor Xiao Zhong, University of Helsinki

Title: Variational problems with gradient constraint

Abstract:

I will talk about three different classes of variational problems with gradient constraint.
They arise from elastic-plastic torsion, hypersurfaces in the Lorentz-Minkowski spaces with
given mean curvature and dimer models.

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

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.

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

This 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

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.