Weekly bulletin

Find out what's happening this week at MSI.


Low-regularity well-posedness 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 low-regularity well-posedness for the modified KdV equation.  We first review the previous results in Sobolev spaces, Fourier-Lebesgue space, and modulation spaces.  Then we talk about our recent results on the generalized Fourier-Lebesgue space.  We will also talk about our recent results in Fourier-Lebesgue space for Benjamin-Ono type equations.


Generic regularity of the free boundary in the Alt-Caffarelli-Phillips 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 Alt-Caffarelli problem and the Alt-Phillips problem are among the most well-studied 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: 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.