Analysis, Stochastics, and Dispersive Equations
Hiroshima, 2025
December 15-16, 2025
Higashi Hiroshima Campus
Hiroshima University, Hiroshima, Japan
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10:00 - 10:50 |
Andreia Chapouto (Université de Versailles Saint-Quentin, France) | |
| Title: | Pathwise well-posedness of stochastic nonlinear dispersive equations with multiplicative noises | |
| Abstract: |
Over the last decades, the well-posedness issue of
stochastic dispersive PDEs with multiplicative noises has been
extensively studied. However, this study was done primarily from the
viewpoint of Ito solution theory, and pathwise well-posedness remained
completely open. In this talk, I will present the first pathwise
well-posedness results
for stochastic nonlinear wave equations and stochastic nonlinear
Schrödinger equations with multiplicative
white-in-time/coloured-in-space noise. Here, we combine the
operator-value controlled rough paths adapted to dispersive flows,
together with random tensor estimates, and the Fourier restriction
norm method adapted to controlled rough paths.
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| 10:50 - 11:10 | Short break
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11:10 - 12:00 | Árpád Bényi (Western Washington University, USA) | |
| Title: | Bilinear Hilbert-Carleson operator along curves | |
| Abstract: |
Motivated by a fundamental connection to the trilinear Hilbert transform along curves, we introduce the bilinear Hilbert-Carleson operator in the non-zero curvature setting and discuss its maximal boundedness range (up to end-points). This is joint work with Bingyang Hu (Auburn University) and Victor Lie (Purdue University). | |
| 12:00 - 13:50 | Lunch | |
13:50 - 14:40 | Yoshio Tsutsumi (Kyoto University, Japan) | |
| Title: | Well-posedness of the Cauchy problem in low regularity for kinetic DNLS on the torus | |
| Abstract: |
The kinetic derivative nonlinear Schrodinger equation (KDNLS) is a nonlinear Schrodinger equation with a nonlocal cubic derivative nonlinear term, which has dissipative nature. The gauge transformation is known to be effective for the standard derivative NLS (DNLS) but it does not work for KDNLS as well as DNLS. I will talk about the local well-posedness of the Cauchy problem for KDNLS on 1D torus. Our proof uses the dissipative nature of KDNLS. This is a joint work with Nobu Kishimoto, RIMS, Kyoto University. | |
14:45 - 15:10 | Hiroshi Tsuji (Institute of Science Tokyo, Japan) | |
| Title: | Inverse Brascamp-Lieb type inequality and its application | |
| Abstract: |
The Brascamp-Lieb theory seeks the optimal constant for a multilinear integral functional and has been applied in broad fields such as harmonic analysis, convex geometry, and information theory. In this talk, we focus on the inverse Brascamp-Lieb inequality and construct a variant of the inequality for multiple centered functions. As a corollary, we present a generalization of the Gaussian Correlation Inequality (GCI), originally studied in the contexts of convex geometry, probability, and statistics. Our generalization also provides the characterization for certain two events in probability space being independent. This talk is based on a joint work with Shohei Nakamura (University of Birmingham). | |
| 15:10 - 15:35 | Coffee break | |
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15:35 - 16:25 | Tadahiro Oh (The University of Edinburgh, UK) | |
| Title: | Probabilistic well-posedness of dispersive PDEs beyond variance blowup | |
| Abstract: |
Over the last two decades, there has been significant progress in probabilistic well-posedness theory of nonlinear dispersive PDEs with random initial data. In recent years, several examples of "variance blowup" for equations with quadratic nonlinearities have been observed, where the construction of basic stochastic objects breaks down before reaching the limit of the analytical framework. In the study of stochastic parabolic PDEs, such a variance blowup phenomenon has been observed for the fractional KPZ equation (with a noise rougher than a space-time white noise) and, in a recent work (2025), Hairer introduced a renormalization beyond variance blowup. In this talk, I will talk about a possible extension of probabilistic well-posedness theory of dispersive PDEs beyond variance blowup, taking the Benjamin-Bona-Mahony equation and the quadratic nonlinear wave equation as model examples, and show that these equations with renormalized (rough) Gaussian initial data converge in law to those with stochastic forcings. If time permits, I will discuss what happens in the KdV case. This talk is based on joint works with Andreia Chapouto (Versailles), Guopeng Li (Beijing Institute of Technology), Jiawei Li (Edinburgh), Shao Liu (Bonn), and Nikolay Tzvetkov (ENS Lyon). | |
16:30 - 17:20 | Shinya Kinoshita (Nagoya University, Japan) | |
| Title: | Small data scattering for the 2D cubic Zakharov-Kuznetsov equation | |
| Abstract: |
In this talk, we consider the 2D cubic Zakharov-Kuznetsov equation. This equation is a two-dimensional generalization of the modified KdV equation. Linares and Pastor established the global well-posedness in the energy space when the mass of the initial datum is below the ground state. In this talk, we will show the global well-posedness and scattering for small initial data in a two-parameter anisotropic space. This space is naturally associated with the dispersive effects of the equation. This talk is based on joint work with Simão Correia (Instituto Superior Técnico). |
09:30 - 10:20 |
Justin Forlano (Monash University, Australia) | |
| Title: | The intermediate nonlinear Schrödinger equation | |
| Abstract: |
In this talk, I will discuss recent results regarding the intermediate nonlinear Schrödinger equation (INLS). Analytically speaking, INLS is a one-dimensional completely integrable nonlinear Schrödinger equation with a cubic derivative nonlinearity and is L2-critical. A limiting form of INLS is the continuum Calogero-Moser equation (CCM), which is also completely integrable. Interestingly, CCM keeps the Hardy space L 2 + invariant, and, under this assumption, tools from complete integrability have recently resolved the well-posedness problem for CCM in L 2 + . I will discuss progress on the well-posedness for INLS and CCM (not relying on complete integrability), outside of the Hardy space and in low-regularity. Our approach combines a gauge transformation, bilinear Strichartz estimates and a refined decomposition for smooth solutions. This is based on joint work with A. Chapouto (CNRS, UVSQ) and T. Laurens (UW-Madison). | |
| 10:20 - 10:40 | Short break
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10:40 - 11:05 | Toshiki Kondo (The University of Osaka, Japan) | |
| Title: | Well-posedness of the Cauchy problem for derivative fractional nonlinear Schrödinger equations on torus | |
| Abstract: |
We consider the Cauchy problem for derivative fractional nonlinear Schrödinger equations on the torus. In the case of linear Schrödinger equations, a necessary and sufficient condition for well-posedness of the Cauchy problem is known; this is called the Mizohata condition. In this talk, we prove that a condition analogous to the Mizohata condition is a necessary and sufficient condition for the well-posedness of the Cauchy problem for derivative fractional nonlinear Schrödinger equations. This talk is based on a joint work with Takamori Kato (Saga University) and Mamoru Okamoto (Hiroshima University). | |
11:10 - 12:00 | Leonardo Tolomeo (The University of Edinburgh, UK) | |
| Title: | A statistical version of the soliton resolution conjecture for the focusing nonlinear Schrödinger equation | |
| Abstract: |
In this talk, I will discuss a number of recent results for the Gibbs measure of the focusing, mass-subcritical Schrödinger equation. After reviewing the construction of the measure in finite volume, I will show that in infinite volume, in the correct regime, the measure concentrates around a single soliton over a Gaussian background. This provides a version of the soliton resolution conjecture at equilibrium. This talk is based on joint works with T. Oh (Edinburgh), M. Okamoto (Hiroshima), H. Weber (Münster), J. Forlano (Monash), and F. Höfer (Münster). |
