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Seminars and short courses RSS feed

Seminars, for informal dissemination of research results, exploratory work by research teams, outreach activities, etc., constitute the simplest form of meetings at a Mathematics research centre.

CAMGSD has recorded the calendar of its seminars for a long time, this page serving both as a means of public announcement of forthcoming activities but also as a historic record.

For a full search interface see the Mathematics Department seminar page.

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Room P3.10, Mathematics Building Instituto Superior Técnico https://tecnico.ulisboa.pt

Lisbon WADE — Webinar in Analysis and Differential Equations

Justin Forlano, Monash University.

In this talk, I will discuss recent results regarding the intermediate nonlinear Schrödinger equation (INLS). Analytically, INLS is a one-dimensional completely integrable nonlinear Schrödinger equation with a cubic derivative nonlinearity and is $L^2$-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, Monash) and T. Laurens (UW-Madison).