Author Archives: mihaela

Mihai Putinar (University of California at Santa Barbara)

The Analysis and PDE Seminar will take place on Monday, October 24th, in room 740, Evans Hall, from 4:10-5:00 pm.


Title: The essential spectrum of the Neumann-Poincare operator

Using an idea of Poincare one can realize the Neumann-Poincare operator on a space of square integrable fields. In two variables this leads to a precise estimate of the essential spectrum, for domains with corners.

Marcelo Disconzi (Vanderbilt University)

The Analysis and PDE Seminar will take place on Monday, September 19, in room 740, Evans Hall, from 4:10-5:00 pm.

Speaker: Marcelo Disconzi

Title: The three-dimensional free boundary Euler equations with surface tension.
Abstract: We study the free boundary Euler equations with surface tension in three spatial dimensions, showing that the equations are well-posed if the coefficient of surface tension is positive. Then we prove that under natural assumptions, the solutions of the free boundary motion converge to solutions of the Euler equations in a domain with fixed boundary when the coefficient of surface tension tends to infinity. This is a joint work with David G. Ebin.


Mihai Tohaneanu (Kentucky University)

Same room, 891, Evans Hall, from 4:10-5:00pm.

Speaker: Mihai Tohaneanu

Title: Global existence for quasilinear wave equations close to Schwarzschild

Abstract: We study the quasilinear wave equation $\Box_{g} u = 0$, where the metric $g$ depends on $u$ and equals the Schwarzschild metric when u is identically 0. Under a couple of extra assumptions on the metric $g$ near the trapped set and the light cone, we prove global existence of solutions. This is joint work with Hans Lindblad.

Daniel Tataru (UC Berkeley)

The Analysis and PDE Seminar will take place on Monday, March 28, 2016 from 4:10-5:00 pm in Evans Hall, room 891.
Speaker: Daniel Tataru

Title: Integrable systems, inverse scattering and conservation laws


Abstract: One common property of classical integrable systems (e.g. NLS, KdV) is that they have an infinite number of conservation laws, associated to the Sobolev spaces $H^n$. In this talk I will describe joint work with Herbert Koch aimed at finding a continuum of conservation laws for such systems.

Jeremy Marzuola (UNC)

The Analysis and PDE Seminar will take place on Monday on November 22nd 2015 from 4:10-5:00pm in Evans Hall, room 740.

Speaker: Jeremy Marzuola (UNC)

Title: Euler Equations on Rotating Surfaces

Abstract: In an appendix to a recent paper by Michael Taylor, he and I explored various questions related to stability of striated patterns for fluids on rotating spheres.  I will discuss these results and some open problems related to this study.

See you all there!

Marina Iliopoulou (University of Birmingham)-Nov 16th


Analysis and PDE seminar which will take place in 740 Evans Hall on Nov 16th

Speaker: Marina Iliopoulou (University of Birmingham)

Title: Algebraic aspects of harmonic analysis

Abstract: When we want to understand a geometric picture, finding the zero set of a polynomial hiding in it can be very helpful: it can reveal structure and allow computations. Polynomial partitioning, developed by Guth and Katz, is a technique to find such a nice algebraic hypersurface. Polynomial partitioning has revolutionised discrete incidence geometry in the recent years, thanks to the fact that interaction of lines with algebraic hypersurfaces is well-understood. Recently, however, Guth discovered agreeable interaction between tubes and algebraic hypersurfaces, and thus used polynomial partitioning to improve on the 3-dim restriction problem. In this talk, we will present polynomial partitioning via a discrete analogue of the Kakeya problem, and discuss its potential to be extensively used in harmonic analysis.

Baoping Liu

Monday, Nov 9th 2015

Evans Hall, Room 740


Speaker: Baoping Liu, (Peking University)

Titile: Long time dynamics for wave equation with potential
Abstract: We consider the long time dynamics of radial solutions to the defocusing energy critical wave equation with radial potential in 3+1 dimensions. For general potential, the equation can have a unique positive ground state and a number of excited states. In this talk, we show that for generic potential, generic radial solutions scatter to one of the stable steady states and each unstable excited state attracts a finite co-dimensional manifold of solutions. This gives affirmative answer to the soliton resolution conjecture for this particular model.
This talk is based on joint works with Hao Jia, Wilhelm Schlag and Guixiang Xu.

Richard Melrose (MIT)

Place & Time : Evans Hall, room 740, Nov 2nd 2015, 4:10-5:00 pm.

Speaker: Richard B. Melrose (MIT)

Title: Differential operators undergoing adiabatic transitions

Abstract: I will describe a geometric type of degeneration of differential operators, which includes semiclassical and adiabatic limits. The most basic result  for elliptic operators of this type is the inheritance of invertibility from the limiting operators. I will discuss this and applications of it, in particular in differential topology.

Organizers: Mihaela and Peter

Mohammad Reza Pakzad (University of Pittsburgh )


Speaker: Mohammad Reza Pakzad

Title: Rigidity of weak solutions to Monge-Ampere equations

Abstract: In this talk, we will explore rigidity of the weak solutions to the Monge-Amp\`ere equation, by replacing the Hessian determinant by other weaker variants, without any a priori convexity assumptions. Some past and recent results and their proofs concerning rigid behaviour (e.g. convexity or developabilty) of Sobolev solutions in two and higher dimensions will be discussed. We will also study the rigidity of solutions with H\”older continuous derivatives. We will contrast these results with some some non-rigidity statements recently proved by the speaker and M. Lewicka using convex integration.

Vedran Sohinger (ETH Zurich)


Speaker: Vedran Sohinger (ETH Zurich)

Title: The Gross-Pitaevskii hierarchy on periodic domains

Abstract: The Gross-Pitavskii hierarchy is a system of infinitely many linear PDEs which occurs in the derivation of the nonlinear Schrodinger equation from the dynamics of many-body quantum systems. We will study this problem in the periodic setting. Even though the hierarchy is linear, it is non closed, in the sense that the equation for the k-th density matrix in the system depends on the (k+1)-st density matrix. This structure poses its challenges in the study of the problem, in particular in the understanding of uniqueness of solutions. Moreover, by randomizing in the collision operator, it is possible to use probabilistic techniques in order to study related hierarchies at low regularities. I will present some recent results obtained on these problems, partly in joint work with Philip Gressman, Sebastian Herr, and Gigliola Staffilani.