GAPS

The Graduate Analysis and PDEs Seminar (GAPS) is intended to build community for graduate students in the different subfields of analysis and PDEs. The goal is to give accessible talks about your current research projects, papers you found interesting on the arXiv, or even just a theorem/result that you use and think is really cool!

We currently meet Mondays, 1:20pm-2:10pm, in Van Vleck 901. Oreos and apple juice (from concentrate) are provided. If you have any questions, please email the organizers: Summer Al Hamdani (alhamdani (at) wisc.edu) and Allison Byars (abyars (at) wisc.edu)

Spring 2024

Date	Speaker	Title	Comments
2/26	Organizational Meeting
3/4	skip-bc of PLANT
3/11	Amelia Stokolosa	Inverses of product kernels and flag kernels on graded Lie groups	1:20-1:50
3/11	Allison Byars	Wave Packets for NLS	1:55-2:10
3/18	Mingfeng Chen	TBD
4/1	Lizhe Wan	TBD
4/8	Taylor Tan	TBD
4/15	Kaiyi Huang	TBD
4/22	Sam Craig	TBD
4/19	Allison Byars	TBD

Spring 2024 Abstracts

Amelia Stokolosa: Inverses of product kernels and flag kernels on graded Lie groups

Abstract. Consider the following problem solved in the late 80s by Christ and Geller: Let $Tf = f*K$ where $K$ is a homogeneous distribution on a graded Lie group. Suppose $T$ is $L^2$ invertible. Is $T^{-1}$ also a translation-invariant operator given by convolution with a homogeneous kernel? Christ and Geller proved that the answer is yes. Extending the above problem to the multi-parameter setting, consider the operator $Tf = f*K$, where $K$ is a product or a flag kernel on a graded Lie group $G$. Suppose $T$ is $L^2$ invertible. Is $T^{-1}$ also given by group convolution with a product or flag kernel accordingly? We prove that the answer is again yes. In the non-commutative setting, one cannot make use of the Fourier transform to answer this question. Instead, the key construction is an a priori estimate.

Allison Byars: Wave Packets for NLS

Abstract. Well-posedness for the NLS equation has been established for some time. In 2014, Ifrim and Tataru provided a simpler proof of this well-posedness, introducing the idea of wave packets. The idea of wave packets is to find an approximate solution to the equation which is localized in both space and frequency. This method can be used in many situations. In this talk, we will learn how they can be used to prove dispersive estimates.

Mingfeng Chen: TBD

Abstract.

Lizhe Wan: TBD

Abstract.

Taylor Tan: TBD

Abstract.

Kaiyi Huang: TBD

Abstract.

Sam Craig: TBD

Abstract.

Allison Byars: TBD

Abstract.