Past Events

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

L4F01 and Zoom

Speaker : Professor Neal Bez, Saitama University

Title : The Brascamp-Lieb Inequality


★Please click here to register

[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

L4E48 and Zoom

Speaker: Professor Jana Björn, Linköping University and OIST TSVP Visiting Scholar

Title: The Dirichlet Problem and Boundary Regularity for Nonlinear Parabolic Equations

Abstract: As shown by Serrin in 1964, the growth at an isolated singularity of solutions to the elliptic equation div A(x, ∇u) = 0 in Rn (including p-harmonic functions with p > 1) is exactly determined by the dimension n and the parameter p associated with the equation. In this talk, I will discuss growth and integrability properties for p-harmonic Green functions and their gradients on weighted Rn, with a p-admissible weight, as well as on complete metric spaces equipped with a doubling measure supporting a p-Poincar´e inequality. In these situations, the dimension n is replaced by the local growth of the underlying measure near the isolated singularity, and the obtained growth and integrability exponents are sharp.

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

L4E48 and Zoom

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)

2024-02-21 to 2024-03-01
L4F01 + Zoom

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

Lecture 1 Feb 21, Wednesday  10:00-12:00 L4F01
Lecture 2 Feb 26, Monday 14:00-16:00 L4F01
Lecture 3 Feb 28, Wednesday 14:00-16:00 L4F01
Lecture 4 Mar 1, Friday 10:00-12:00 L4F01





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

L4E01 + Zoom

Different definitions of conformal dimension are (essentially) equal,

Professor Sylvester Eriksson-Bique, University of Jyväskylä


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.

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

2023-08-29 to 2023-09-01
Onsite (see classroom below) + Zoom

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

2023-06-20 to 2023-06-22
L4E48 + Zoom

Title: Lectures on Capacities

Speaker: Professor Daniel Spector, National Taiwan Normal University

Zoom registration:

Lecture 1   Tuesday, June 20    10 am

Title:  Riemann and Lebesgue Integration
Abstract:  The Riemann integral is perfectly suited for consideration of volume, surface area, arc length, and integration of functions in classical analysis - when the sets in question are smooth and the functions in question continuous.  In this talk, we introduce these ideas and explain the progression from Riemann integration to Lebesgue integration, emphasizing in particular the powerful tools one obtains from this construction.

Lecture 2  Wednesday, June 21st 10 am

Title:  Capacitary Integration
Abstract:  The Lebesgue integral provides one with a satisfactory tool for many purposes in mathematical analysis.  Yet in the modeling of natural phenomena, with the introduction of partial differential equations, integrals which are not Lebesgue integral makes a prominent appearance - capacitary integrals.  In this talk we discuss this motivation for capacitary integration, with examples, explain the differences with Lebesgue integration, and show the usefulness of these non-standard objects.

Lecture 3   Thursday, June 22nd 10 am

Title: Capacitary Sobolev Inequalities and Applications
Abstract:  The study of capacities and Capacitary Sobolev Inequalities is now more than half a century old, and yet there are still a number of open research questions to investigate concerning them.  In this talk we discuss in more detail Capacitary Sobolev inequalities with an emphasis on a subject with the most recent activity - Capacitary Sobolev Inequalities around L1.  Open problems will be mentioned.


Zoom link: TBA

[Seminar] Critical Sobolev Spaces and Subspaces of BMO, Professor Daniel Spector, National Taiwan Normal University

L4E48 + Zoom


Abstract: It is well-known that functions in critical Sobolev spaces embed into the space of functions of bounded mean oscillation (BMO) originating in the work of John and Nirenberg. Less well-known is the fact that they actually embed into BMO on subspaces of every smaller dimension. In this talk we introduce a class of spaces which are finer targets of these critical Sobolev embeddings than BMO that capture this phenomena, which we term beta-dimensional BMO. Interestingly, these spaces also gives an answer to the question of which BMO functions admit restrictions in BMO of subspaces. The key tool is a capacitary analogue of the John-Nirenberg inequality for the Hausdorff content, obtained recently in a joint work with You-Wei Chen.


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

2023-05-30 to 2023-06-02
Zoom and OIST Main Campus, Sydney Brenner Lecture Theatre (B250)

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

Online via Zoom

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.