本年（2025年）度のセミナーの記録
- 4 月 11 日
- Kiyeon Lee 氏 （KAIST）
- 4 月 18 日
- Anthony Gauvan 氏 （埼玉大学） Anthony Gauvan (Saitama University)
● 2025 年 4 月 11 日 (Fri) 16:00 〜 17:00
- 講演者
- Kiyeon Lee 氏 （Korea Advanced Institute of Science and Technology (KAIST)）
- 講演題目
- Modified scattering phenomena of nonlinear dispersive equations
- 講演要旨
-
In this talk, we will discuss the modified scattering phenomena of nonlinear dispersive equations.
The modified scattering phenomenon is one of the crucial features of dispersive equations in which the dispersive effect is strong.
We first introduce the decay properties of some generic dispersive equations to establish the context for scattering results.
We also classify the short- and long-range nonlinearities depending on these decay bounds and introduce the asymptotic behavior of long-range nonlinearity, called the modified scattering.
Additionally, we describe the space-time resonance method which will play a key role in proving the modified scattering phenomena.
● 2025 年 4 月 18 日 (Fri) 16:00 〜 17:00
- 講演者
- Anthony Gauvan 氏 （埼玉大学）
Anthony Gauvan (Saitama University)
- 講演題目
- On the ubiquity of geometric Brascamp-Lieb data
- 講演要旨
-
The Brascamp-Lieb inequality unifies several important inequalities.
A particularly important special case is the geometric Brascamp-Lieb inequality.
This inequality goes back to pioneering work of Keith Ball in the 1980s in convex geometry, and it turns out to play a fundamental role in the general theory of the Brascamp-Lieb inequality.
For instance, it was shown by Bennett, Carbery, Christ and Tao that a Brascamp-Lieb inequality which possesses maximizers is equivalent to a geometric Brascamp-Lieb inequality.
Relying heavily on work of Garg, Gurvits, Oliveira and Wigderson, here we present another sense in which the class of geometric Brascamp-Lieb data may be considered large.
This addresses a question of Bennett and Tao in their recent work on the adjoint Brascamp-Lieb inequality.
Joint work with Neal Bez and Hiroshi Tsuji.
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