MIT PDE/Analysis Seminar
Fall 2025
Organizers: Aleksandr Logunov, Christoph Kehle, and Larry Guth
Sep 9 | Michal Shavit (NYU Courant Institute of Mathematical Sciences) |
Signatures of space-time resonances in the spatiotemporal spectrum of nonlinear waves Abstract:In weakly nonlinear dispersive wave systems, long-time dynamics are typically governed by time resonances, where wave phases evolve coherently due to exact frequency matching. Recent advances in measuring the spatio-temporal spectrum, however, reveal prominent excitations beyond those predicted by time resonances. In this talk, I will present an alternative mechanism: space resonances. These occur when wave packets share the same group velocity and remain co-located, producing long-lived interactions. I will illustrate these ideas in the context of surface gravity waves, where triadic interactions occur without exact three-wave time resonances. This talk is based on collaborations with Fabio Pusateri, Jalal Shatah, Yulin Pan, Miguel Onorato, Tristan Backmaster and Yongji Wang. |
Sep 16 Room 2-136 |
Ziad Musslimani (Florida State University) |
Space-time nonlocal integrable systems: Part 1 Abstract: In this talk we will review past and recent results pertaining to the emerging field of integrable space-time nonlocal nonlinear evolution equations. In particular, we will discuss blow-up in finite time of soliton solutions as well as the physical derivations of many integrable nonlocal systems. |
Sep 18 Room 2-361 |
Ziad Musslimani (Florida State University) |
Space-time nonlocal integrable systems: Part 2 Abstract: In this talk we will review past and recent results pertaining to the emerging field of integrable space-time nonlocal nonlinear evolution equations. In particular, we will discuss blow-up in finite time of soliton solutions as well as the physical derivations of many integrable nonlocal systems. |
Sep 23 | Serban Cicortas (Princeton) |
Scattering Theory for Asymptotically de Sitter Vacuum Solutions Abstract: We will talk about recent work establishing a quantitative nonlinear scattering theory for asymptotically de Sitter solutions of the Einstein vacuum equations in $(n+1)$ dimensions with $n\geq4$ even, which are determined by small scattering data at future infinity and past infinity. We will also explain why the case of even spatial dimension $n$ poses significant challenges compared to its odd counterpart and was left open by the previous works in the literature. |
Sep 30 | Michal Wojciechowski (Institute of Mathematics of the Polish Academy of Sciences) |
Singular measure with tiny Fourier spectrum on three dimensional sphere Abstract: I will present a construction of a singular measure on three dimensional sphere $S^3$ whose non-zero components in spherical harmonic decomposition are concentrated around lines $y=ax$ and $x=ay$. This could be seen as a generalization of Aleksandrov's singular pluriharmonic measure or an inverse to the Brummelhuis condition of absolute continuity. The main ingredient is a construction of bounded spherical harmonics with small, localized Fourier spectra. |
Oct 7 | Andreas Wieser (IAS) |
Effective equidistribution of periodic orbits of semisimple groups Abstract: Qualitatively, actions of unipotent groups on homogeneous spaces are very well understood after breakthrough works of Ratner from the 90's. The past two decades have seen dramatic progress in providing rates in these results. In this talk, we will be interested in the distributional properties of periodic orbits of semisimple groups. Here, the desire is to show that such a periodic orbit 'approximates' a periodic orbit of a larger group with a rate that is polynomial in the volume. |
Oct 14 | Mikhail Sodin (Tel Aviv University) |
A curious Lagrange-Ivanov-Yomdin-type lemma Abstract: Suppose $f$ is an $m$-smooth function on the unit ball that is small (for instance, vanishes) on an epsilon-net $E$ for a sufficiently small epsilon. Then the maximum of $f$ is controlled by the $L^1$-norm of its $m-th$ derivative and its uniform norm on $E$. This estimate is dimensionless. The proof is not long and uses only undergraduate analysis. |
Oct 28 | Lior Alon (MIT) |
Periodic Hypersurfaces, Lighthouse Measures, and Lee-Yang Polynomials Abstract: There is a hierarchy of regularity for continuous $\mathbb{Z}^n$-periodic
functions in $\mathbb{R}^n$, $C^0\supset C^1\supset \cdots \supset C^\infty \supset$ analytic $\supset$ trigonometric polynomial, and the decay of the Fourier coefficients pre-
cisely reflects this regularity. In particular, the support supp(f̂)
is finite if and only if $f$ is a trigonometric polynomial. Periodic
hypersurfaces in $\mathbb{R}^n$ exhibit a similar regularity hierarchy, but
there is no analogous Fourier description. |
Nov 4 | Joris Roos (UMass, Lowell) | |
Nov 25 | Yvonne Bronsard Alama (MIT) | |
Dec 9 3:00pm-4:00pm |
Osama Khalil (University of Illinois Chicago) | |
Dec 9 4:15pm-5:15pm |
Erwan Faou (INRIA Bretagne Atlantique & IRMAR) |