Date/Time : 29 Sep 2026 11:00
Venue : S16 #05-18
Speaker : Weihang Zheng, Monash University

In the theory of general relativity, an important heuristic provided by Belinskii-Khalatnikov-Lifshitz (BKL) is that cosmological singularities should be either chaotic and oscillatory or quiescent. While the BKL conjecture has been studied for decades, the behaviour near such singularities remains incompletely understood. There is literature dating back to the last century suggesting some ideas about the Big Bang formation. For the quiescent case, the Kasner family of exact solutions to the Einstein-scalar field equations provides a key model. Recently, a remarkable result was given by Fournodavlos-Rodnianski-Speck where they proved the past nonlinear stability of the Kasner-scalar field solutions of the entire sub-critical regime. In this talk, I will discuss a further result, the localized stability, i.e. the stability on a truncated cone domain. This is joint work in part with Florian Beyer and Todd Oliynyk.

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Date/Time : 21 Sep 2026 15:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Shuang Miao, Wuhan University

Constructing dynamical global-in-time solutions to 3D incompressible Euler equation is in general challenging. Recently Guo-Pausader-Widmayer made a breakthrough in this direction by proving asymptotic stability of a uniform-rotating static solution. Their approach heavily depends on the “uniform-rotating” of the background solution. In this talk I will present some recent progress on asymptotic linear stability of a more general columnar flow with non-uniform rotation. This is a joint work with Siqi Ren and Zhifei Zhang.

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Date/Time : 09 Sep 2026 15:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Beomjun Choi, Korea Advanced Institute of Science & Technology (KAIST)

We will discuss how collective behavior in interacting particle systems can lead to qualitative changes in equilibria, and how these equilibria behave dynamically. The first part concerns long-time convergence for Keller–Segel equation, and more generally McKean–Vlasov equations, in relation to phase transitions and bifurcation. The second part concerns the local stability of mixed Nash equilibria for mean-field Langevin descent–ascent, where exponential convergence can be established despite the non-gradient and non-self-adjoint structure. We will also discuss a corresponding finite-particle stability result.

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Date/Time : 26 Aug 2026 14:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Zach Turner, Duke University

Chemotaxis plays a crucial role in the facilitation of biological and ecological processes, often to significantly improve reaction rates between two or more interacting species. One important example is signaling in the immune system; immune cells release chemokines when they sense invaders, which mediates the chemotaxis of lymphocytes towards the site of infection. Another example is reproduction, in which spermatozoa follow the chemical gradient of a chemoattractant released by oocytes. In this talk reporting on a work in progress, we consider a system of two PDEs which describe the flux-limited chemotaxis of two reacting densities. We build on the results of An et al. J. Math. Biol. 92, 57 (2026)., by treating the three-dimensional case. We argue that whether significant reaction enhancement occurs is largely governed by the spatial scale of the initial concentration of the attracted density, distinguishing it from two-dimensional chemotaxis. In particular, we show that there are reasonable scenarios where three-dimensional chemotaxis could possibly fail to practically improve biological reaction rates.

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Date/Time : 26 Aug 2026 15:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Shi-Zhuo Looi, California Institute of Technology

Dyadic shell models are infinite systems of ODEs that retain the quadratic nonlinearity, energy identity, and scaling of the 3D incompressible Navier-Stokes equations. Such models can be realized as averaged Navier-Stokes equations at the PDE level, and some of them blow up in finite time despite satisfying the energy identity, showing that these features do not preclude singularity formation. Among dyadic models with these features, the Obukhov model is distinguished by its regulated cascade mechanism: the inviscid version is globally regular. However, the inviscid proof relies on exact energy conservation, which viscosity destroys. We prove that the viscous Obukhov model is globally regular for all initial data in the critical Sobolev space and above, obtaining a sharp threshold exponent result. The proof introduces a critical rescaling that shows a viscous activation threshold for each shell, and establishes regularity by showing that two competing scales, viscous damping and nonlinear growth, become incompatible at high frequencies. Time permitting, we discuss a proof of global regularity for the Katz-Pavlovic dyadic model close to the sharp threshold exponent (above which blowup is known).

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Date/Time : 19 Aug 2026 15:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Silu Yin, Hangzhou Normal University

In this talk, I will introduce a Morawetz type estimate for the wave equations in $\R^2$ and develop a non-negative Morawetz type energy. With this estimate in hand, an alternative proof of global existence for the Cauchy problem of quasilinear wave equation with small and compactly supported data is given. What is more, such weighted Morawetz type energy estimate also works for certain wave system with multiple speeds, which can be used to prove global existence of some admissible harmonic elastic wave system in $\R^2$.

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Date/Time : 17 Aug 2026 11:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : In-Jee Jeong, Korea Institute For Advanced Study

For the incompressible Euler equation in vorticity form in two and three dimensions, we consider the initial value problem with data in the critical Sobolev space, W^{d/p,p}(R^d). In the case 1<p<infinity, we give a simple proof of strong illposedness, based on the Hardy inequality and “Key Lemma” of Kiselev and Sverak, using vorticities having the form of “diadic bubbles”. Then, we discuss endpoint cases, namely p = 1 and p = infinity.

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Date/Time : 07 Aug 2026 15:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Zijian Wang, Nankai University and NUS

In this talk, we will present several new results investigating the (in)stability properties of rotating drops and jets. 

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Date/Time : 04 Aug 2026 15:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Giovanni Brigati, Institute of Science and Technology, Austria

In this talk, I am proposing a gradient-flow interpretation for a class of non-linear kinetic Fokker—Planck equation (among which the linear case of the Vlasov—Fokker—Planck). The challenge lies in the fact that such dynamics are driven by an interplay of conservative and dissipative effects. Namely, free transport, and diffusion in the velocity variables only. Thus, we rely on the geometry of “kinetic optimal transport”, which is based on Newton’s equations. In this framework, regular curves of measures can be rewritten as solutions to Vlasov’s equations, for a certain force field.

The first main result of the talk is a chain rule for a family of free energy functionals along Vlasov’s equations, which allows us to compute the slope of the energy. Curves of maximal slope correspond to solutions to the non-linear kinetic Fokker—Planck equation. I will then discuss convergence for JKO-like schemes, and further analytical properties of the non-linear kinetic equations, together with a few open questions. My presentation is based on joint works with Guillaume Carlier, Jean Dolbeault, Jan Maas, and Filippo Quattrocchi.

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