Weekly bulletin
Find out what's happening this week at MSI.
Lowregularity wellposedness for the modified KdV equation
 Mon, Sep 25 2023, 2  3pm
Hanna Neumann Building 145
Seminar Room 1.33
 Zihua Guo (Monash University)
Abstract: We will talk about the lowregularity wellposedness for the modified KdV equation. We first review the previous results in Sobolev spaces, FourierLebesgue space, and modulation spaces. Then we talk about our recent results on the generalized FourierLebesgue space. We will also talk about our recent results in FourierLebesgue space for BenjaminOno type equations.
Generic regularity of the free boundary in the AltCaffarelliPhillips problem
 Tue, Sep 26 2023, 2  3pm
Hanna Neumann Building 145
Seminar Room 1.33
 Professor Hui Yu, Department of Mathematics, National University of Singapore
Abstract: The AltCaffarelli problem and the AltPhillips problem are among the most wellstudied elliptic free boundary problems. Much effort has been devoted to estimating the size of the singular set on the free boundary, for instance, in terms of its Hausdorff dimension.
An uncertainty principle for operators acting on Fock spaces
 Wed, Sep 27 2023, 10:30  11:30am

145 Hanna Neumann Building, room 1.33
 Professor Sundaram Thangavelu (Indian Institute of Science)
Abstract:
Abstract: For each $ \lambda \in \R $ there is a Hilbert space of entire functions $ \mathcal{F}_\lambda(\C^{2n}) $ known as twisted Fock space. We show that within this space there is an algebra $ \mathcal{A}_\lambda(\C^{2n}) $ which is isometrically isomorphic to $ B(L^2(\R^n)).$ The map $ U $ defined by $ UF(z,w) =F(iz,iw) $ is a unitary operator on $ \mathcal{F}_\lambda(\C^{2n}) .$ We show that for any $ \varphi \in \mathcal{A}_\lambda(\C^{2n}),$ the function $ U\varphi $ can never be in $ \mathcal{A}_\lambda(\C^{2n})$ unless $ \varphi $ is a constant. This has an interpretation as an uncertainty principle for a class of operators of convolution type on the Fock space $\mathcal{F}_\lambda(\C^{2n}).$
This talk is based on my recent joint work with Rahul Garg.
On the decay of Fourier transforms
 Wed, Sep 27 2023, 4  5pm

Seminar Room 1.33, Building 145, Science Road, ANU
 Sundaram Thangavelu from Indian Institute of Science
In 1934, Ingham investigated the best possible decay admissible for the Fourier transforms $ \hat{f} $ of compactly supported functions $ f $ on the real line. More precisely he proved the following: Suppose $ \theta $ is a positive even function on $ \R $ decreasing to zero at infinity. Then there exist compactly supported functions $ f $ for which $ \hat{f}(y) \leq C e^{\theta(y)y} $ if and only if $ \int_1^\infty \theta(t)\, t^{1}\, dt < \infty.$ In recent years there are several works investigating analogues of this theorem for Fourier transforms on Lie groups and Riemannian symmetric spaces. In this talk we plan to describe some of the results.
Afternoon tea will be provided at 3:30pm
MSI Graduate Student Colloquium
 Fri, Sep 1 2023, 3  4pm, Fri, Sep 15 2023, 3  4pm, Fri, Sep 29 2023, 3  4pm, Fri, Oct 13 2023, 3  4pm, Fri, Oct 27 2023, 3  4pm

Seminar Room 1.33
Hanna Neumann Building 145 Science Road
Acton ACT 2601
 Vandit Trivedi
Interested in meeting your fellow graduate students and learning about their research? We’re starting an informal colloquium for graduate HDR students to share interesting topics they’ve come across during their studies.
The aim is to introduce everyone to a topic/problem and then discuss a model problem/example together. The talks will be casual and (if appropriate) provide a platform for further discussion about the model problem/example.