2026-03-17
Dawei Shen
In 1993, the global stability of Minkowski spacetime has been proven in the celebrated work of Christodoulou and Klainerman. In 2003, Klainerman and Nicolo revisited Minkowski stability in the exterior of an outgoing null cone. In 2023, the author extended the results of Christodoulou and Klainerman to minimal decay assumptions. In this paper, we prove that the exterior stability of Minkowski holds with decay which is borderline compared to the minimal decay considered in by the author in 2023.
2026-03-17
Hubert Lacoin, Stefan Junk
We show that if the normalized partition function $W^{\beta}_n$ of the directed polymer model on $\mathbb{Z}^d$ converges to zero, then it does so exponentially fast. This implies that there exists a critical temperature $\beta_c$ such that the renormalized partition function has a non-degenerate limit for all $\beta\in [0,\beta_c]$ -- weak disorder holds -- while for $\beta\in (\beta_c,\infty)$ it converges exponentially fast to zero -- very strong disorder holds. This solves a twenty-years-old conjecture formulated by Comets, Yoshida, Carmona and Hu. Our proof requires a technical assumption on the environment, namely, that it is bounded from above.
2026-03-17
Kevin Coulembier
We initiate the systematic study of modular representations of symmetric groups that arise via the braiding in (symmetric) tensor categories over fields of positive characteristic. We determine what representations appear for certain examples of tensor categories, develop general principles and demonstrate how this question connects with the ongoing study of the structure theory of tensor categories. We also formalise a theory of polynomial functors as functors which act coherently on all tensor categories. We conclude that the classification of such functors is a different way of posing the above question of which representation of symmetric groups appear. Finally, we extend the classical notion of strict polynomial functors from the category of (super) vector spaces to arbitrary tensor categories, and show that this idea is also a different packaging of the same information.
2026-03-11
Robert Schippa, Sebastian Herr, Nikolay Tzvetkov
We extend Bourgain's $L^2$ -wellposedness result for the KP-II equation on $\T^2$ to initial data with negative Sobolev regularity. The key ingredient is a new linear $L^4$ -Strichartz estimate which is effective on frequency-dependent time scales. The $L^4$ -Strichartz estimates follow from combining an $\ell^2$ -decoupling inequality recently proved by Guth--Maldague--Oh with semiclassical Strichartz estimates. Moreover, we rely on a variant of Bourgain's bilinear Strichartz estimate on frequency-dependent times, which is proved via the Córdoba--Fefferman square function estimate.