Seminars

Seminars usually take place either at

UPV/EHU, Seminar Room of the Mathematics Department, Facultad de Ciencias, on Thursdays at 12:00, or
BCAM, Seminar Room, on Thursdays at 17:00.

Some seminars were recorded, and the videos can be found together with the description of the seminar on the subpage related to the year the talk happened. You can also find them here.

To subscribe to the seminar mailing list, contact one of the organizers.

As of December 4th, 2025, the count of talks reached 274.

Upcoming Seminars

Seminar

UPV/EHU, Thursday, December 11th, 2025, 12:00 - 13:00

Title: Low regularity well-posedness of nonlocal dispersive perturbations of Burger's equation

Didier Pilot - University of Bergen

Abstract

We show that the Cauchy problem associated with a class of dispersive perturbations of Burgers’ equations is locally well-posed. This class includes the low-dispersion Benjamin–Ono equation, also known as the low-dispersion fractional KdV equation:

∂ₜu − Dₓ^α ∂ₓu = ∂ₓ²(u).

We prove local well-posedness in the Sobolev space H^s(K), where K = ℝ or 𝕋, for s > s_α = 1 − (3α)/4, when 2/3 ≤ α ≤ 1. Moreover, we obtain a priori estimates for solutions at a lower regularity threshold, namely s > s̃_α > 1/2 − α/4. The result also extends to other values of s_α when 0 < α < 2/3. As a consequence of these results, and using the Hamiltonian structure of the equation, we obtain global well-posedness in H^s(K) for s > s_α when α > 2/3, and in the energy space H^{α/2}(K) when α > 4/5.

In the first part of the talk, I introduce the equations, explain their connection to fluid mechanics, and review several existing mathematical results as well as open problems.

In the second part, I give an overview of the proof. The argument combines: an energy method for strongly non-resonant dispersive equations, introduced by Molinet and Vento, refined Strichartz estimates, and modified energy methods.

In addition, we use a full symmetrization of the modified energy both for the a priori estimates and for estimating the difference between two solutions. This symmetrization yields crucial cancellations in the associated symbols, which are essential to close the estimates.

TBA, Thursday, January 29th, 2026, TBD

Title: TBA

Anxo Biasi

Abstract

TBA

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