2025 Analysis on Metric Space Seminar: "Almost splitting and quantitative stratification for super Ricci flow" by Professor Yohei Sakurai, Saitama University

Speaker: Professor Yohei Sakurai, Saitama University

Title: Almost splitting and quantitative stratification for super Ricci flow

Abstract:

I will discuss almost rigidity properties of super Ricci flow whose Muller quantity is non-negative.
I will present almost splitting and quantitative stratification theorems that have been established by Bamler for Ricci flow. This talk is based on the joint work with Keita Kunikawa (Tokushima university).

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2025 Analysis on Metric Space Seminar: " Fluid structure interaction and Sobolev spaces on changing domains" by Professor Malte Kampschulte, Charles University

Speaker: Professor ​Malte Kampschulte, Charles University in Prague.

Title: Fluid structure interaction and Sobolev spaces on changing domains

Abstract:

Dynamic interaction between fluids and solids occurs everywhere, from a fish swimming in the water to an airplane wing bending in the wind. When studying them, one of the key issues is that finding the domain on which the fluid equations are posed itself is part of the problem. Thus before we can apply all the standard machinery from PDE and the calculus of variations, we must first translate it to work on changing domains. The aim of this talk will be to explore precisely this. On one hand it will be an introduction into fluid structure interaction highlighting some recent results. On the other hand this will be used as an opportunity to illustrate and discuss several old and new methods on how to deal with Sobolev spaces when the domain itself is not fixed. This talk is based on results obtained with S.Schwarzacher and B.Benešová as well as work with N.Evseev and A.Menovschikov.

Analysis on Metric Spaces Seminar 2025 | Topological regularity of Busemann spaces, Professor Tadashi Fujioka, Kyoto University

Title: Topological regularity of Busemann spaces, Professor Tadashi Fujioka, Kyoto University

Abstract:

We discuss the topological regularity theorem for Busemann spaces of nonpositive curvature, while reviewing the corresponding results for Alexandrov spaces and CAT spaces. All of these are metric spaces with upper or lower curvature bounds in some synthetic senses, and we address the question of when such spaces are topological manifolds. This is joint work with Shijie Gu (Northeastern University, China). Preprint available at arXiv:2504.14455.

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Analysis on Metric Spaces Seminar 2025 | Periodic homogenization for non-local stable-like operators, Professor Takashi Kumagai, Waseda University

Periodic homogenization for non-local stable-like operators

Professor Takashi Kumagai Waseda University

Abstract :

Homogenization has been a very active area of research in both PDE and probability theory for many years. In this talk, we will first review classical results on periodic homogenization for divergence form operators. We will then present our recent results on periodic homogenization for non-local, stable-like operators. Both qualitative and quantitative results will be discussed. Moreover, we will explore quantitative periodic homogenization on bounded domains, where the rate of convergence near the boundary slows down

Analysis on Metric Spaces Seminar 2025 | Recent development in bilinear rough singular integrals, Professor Bae Jun Park Sungkyunkwan University, Suwon, South Korea

Analysis on Metric Spaces Seminar 2025

Speaker: Bae Jun Park, Sungkyunkwan University, Suwon, South Korea

Title: Recent development in bilinear rough singular integrals

Abstract:

In this talk we will study the Lp1 × Lp2 → Lp boundedness for bilinear rough singular
integral operators LΩ associated with Ω ∈ L(log L)α(S2n−1) with mean value zero. We
will first review classical linear singular integrals and then study how the results have been
extended and developed in the bilinear setting, presenting the most recent results. If time
permits, general multilinear problems will be also discussed

【Seminar】 The Brascamp-Lieb inequality | Professor Neal Bez, Saitama University

Speaker : Professor Neal Bez, Saitama University

Title : The Brascamp-Lieb Inequality

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[Seminar] Growth estimates for \(p-\)harmonic Green functions on weighted \(R^n\) and metric spaces | Professor Jana　Björn, Linköping University and OIST TSVP Visiting Scholar

【Seminar】The Dirichlet problem and boundary regularity for nonlinear parabolic equations | Prof. Professor Anders Björn, Linköping University and OIST TSVP Visiting Scholar

Speaker:  Professor Anders Björn, Linkoping University and OIST TSVP Visiting Scholar

Title: The Dirichlet problem and boundary regularity for nonlinear parabolic equations    

Abstract: The p-parabolic equation \[ \partial_t u = \Delta_p u := \dvg(|\nabla u|^{p-2}\nabla u) \] is a nonlinear cousin of the classical heat equation. As such, it offers both difficulties and advantages compared with the heat equation. In the talk, we consider the Perron method for solving the Dirichlet problem for the p-parabolic equation in general bounded domains in $R^{n+1}$. Compared to space-time cylinders, such domains allow the space domain to change in time. Of particular interest will be boundary regularity for such domains, i.e. whether solutions attain their boundary data in a continuous way. Relations between regular boundary points and barriers will be discussed, as well as some peculiar examples and surprising phenomena related to boundary regularity. Towards the end I will discuss the same type of questions for two other nonlinear cousins of the heat equation, the porous medium equation \[ \partial_t u = \dvg(u^m) \] and the so-called normalized p-parabolic equation \[ \partial_t u = |\nabla u|^{2-p}\Delta_p u. \] The talk is based on collaborations with Jana Bj\"orn (Link\"oping), Ugo Gianazza (Pavia), Mikko Parviainen (Jyv\"askyl\"a) and Juhana Siljander (Jyv\"askyl\"a).

[Mini-Course] Metric Embeddings - What, How and Why? Professor Sylvester Eriksson-Bique (University of Jyväskylä)

Title: Metric Embeddings - What, How and Why?
Speaker: Professor Sylvester Eriksson-Bique (University of Jyväskylä)

[Seminar] Different definitions of conformal dimension are (essentially) equal, Professor Sylvester Eriksson-Bique, University of Jyväskylä

Different definitions of conformal dimension are (essentially) equal,

Professor Sylvester Eriksson-Bique, University of Jyväskylä

Abstract:

I want to tell you about something that came out of OIST. Last May OIST hosted a work-
shop in analysis, random walks and potential theory on metric spaces, which showcased
some exciting developments in these areas. I was fortunate to participate, and the topics
of the conference prompted discussions with another participant Mathav Murugan, who
told about an open problem regarding the conformal dimension of the Sierpinski carpet.
The question asks, if different definitions of this notion are equal. Through discussions at
the workshop, I solved this question. I will explain the problem, the notions of conformal
dimension, and the crucial tool: a new notion of discrete modulus. There are roughly two
approaches classically to define discrete modulus, and this new approach lies roughly in
between the two — in such a way, that it can benefit from good estimates in both of the
worlds. The talk will be fairly mathematical, but I will try to give definitions of the main
concepts and some motivation.