GAPS: Difference between revisions
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|Amelia Stokolosa | |Amelia Stokolosa | ||
|Inverses of product kernels and flag kernels on graded Lie groups | |Inverses of product kernels and flag kernels on graded Lie groups | ||
|1:20-1:50 | |||
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|3/11 | |||
|Allison Byars | |||
|Wave Packets for NLS | |||
|1:55-2:10 | |||
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|3/18 | |3/18 | ||
|Mingfeng Chen | |Mingfeng Chen | ||
|TBD | |TBD | ||
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|4/1 | |4/1 | ||
|Lizhe Wan | |Lizhe Wan | ||
|TBD | |TBD | ||
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|4/8 | |4/8 | ||
|Taylor Tan | |Taylor Tan | ||
|TBD | |TBD | ||
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|4/15 | |4/15 | ||
|Kaiyi Huang | |Kaiyi Huang | ||
|TBD | |TBD | ||
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|4/22 | |4/22 | ||
|Sam Craig | |Sam Craig | ||
|TBD | |TBD | ||
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|4/19 | |4/19 | ||
|Allison Byars | |Allison Byars | ||
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===== '''[https://sites.google.com/wisc.edu/stokolosa/home Amelia Stokolosa]: Inverses of product kernels and flag kernels on graded Lie groups''' ===== | ===== '''[https://sites.google.com/wisc.edu/stokolosa/home 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. | '''''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. | ||
===== '''[https://sites.google.com/wisc.edu/allisonbyars 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. | |||
===== '''[https://sites.google.com/view/chenmingfeng/home Mingfeng Chen]: TBD''' ===== | ===== '''[https://sites.google.com/view/chenmingfeng/home Mingfeng Chen]: TBD''' ===== | ||
Revision as of 00:02, 27 February 2024
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) is 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.