ACTIVITIES AT THE GRADUATE CENTER
Here is the list of seminars organized at the Graduate Center
weekly seminars bulletin (updated every Tuesday).
Here, you will find the conferences in nonlinear analysis we are organizing at the Graduate Center.
Nonlinear Group Study
This meeting aims to investigate nonlinear problems arising in Differential geometry and mathematical physics.
It gives graduates students the opportunity to be familiar with a wide range of open problems, and learn tools from the calculus of variations
to tackle some of these questions. Our meeting takes place
Nonlinear Analysis and PDEs
CUNY Graduate Center, 365 Fifth Avenue, NYC
Room 6496, 4:15pm--5:15pm
Goals of these seminars is to discuss techniques that are used nonlinear
problems arising in applied mathematics,physics or differential geometry.
These events are sponsored by the
Initiative for the Theoretical Sciences.
Those participating in the Nonlinear Analysis and PDE seminar may
also be interested in the Geometric Analysis Seminar
which meets also on
Thursdays in the same room 6496 starting at 3pm.
SCHEDULE Fall 2019:
September 12, 2019
September 19, 2019
Mohameden Ahmedou, Giessen University (Germany)
Morse theory and the resonant $Q$-curvature problem
The Q-curvature is a scalar quantity which plays a central role in
conformal geometry, in particular in the search of high order
In this talk we address the problem of finding conformal metrics of
prescribed Q-curvature on four riemannian manifolds in the so called
resonant case, that is when the total integral of the
Q-curvature is a multiple of the one of the four-dimensional round
sphere. This geometric problem has a variational structure with a lack
of compactness. Using some topological tools of the theory of
critical points at infinity of Abbas Bahri, combined with a refined
blow-up analysis, we extend the full Morse theory, including Morse
inequalities, to this non-compact geometric variational problem and
derive existence and multiplicity results.
This is a joint work with C.B. Ndiaye (Howard University)
October 3, 2019
October 24, 2019
Niclas Linne, Giessen University (Germany)
The prescribed mean curvature problem on Riemannian manifolds with boundary
I will introduce the prescribed mean curvature problem on Riemannian manifolds with boundary.
This problem is closely related to the constant mean curvature problem and the Yamabe problem, which
have become very famous during the last decades. I will explain the technical problems and present some results.
Finally I will focus on four dimensional manifolds. I will present our results and give some ideas of the proof. We mainly used variational methods, Morse theory and the theory of "critical points at infinity", which goes back to Abbas Bahri.
October 31, 2019
Monica Clapp (Universidad Nacional Autonoma de Mexico),
Luca Martinazzi (University of Padua, Italy),
Tristan Riviere (ETH Zurich, Swizterland),
Yi Wang (Johns Hopkins)
November 7, 2019
Vincent Martinez, CUNY-Hunter College
Learning Seminar on Incompressible Euler and Navier-Stokes: Issues in Regularity and Well-posedness, Part I
We will introduce the incompressible Euler and Navier-Stokes equations over the whole space or periodic domain.
We will discuss weak solutions and in particular focus on distinguishing features between two- and three-dimensions, as it regards the issue of global regularity. The necessary background on functional spaces will be developed as needed.
November 14, 2019
Jinggang Xiong, Beijing Normal University
Optimal boundary regularity for fast diffusion equations in bounded domains
We prove optimal boundary regularity for bounded positive weak solutions of fast diffusion equations in smooth bounded domains.
This solves a problem raised by Berryman and Holland in 1980 for these equations in the subcritical and critical regimes.
Our proof of the a priori estimates uses a geometric type structure of the fast diffusion equations, where an important ingredient
is an evolution equation for a curvature-like quantity. This is a joint work with Tianling Jin.
November 21, 2019
Vincent Martinez, CUNY-Hunter College
Learning Seminar on Incompressible Euler and Navier-Stokes: Issues in Regularity and Well-posedness, Part II
We develop the well-posedness for the 2D and discuss regularity criterion in 3D that ensures continuation of the solution beyond a given time.
Time-permitting, we discuss the celebrated Beale-Kato-Majda criterion, and some cautionary examples in the scale Holder spaces.
December 5, 2019
Aidin Murtha, CUNY-Hunter College
Learning Seminar on Incompressible Euler and Navier-Stokes: Issues in Regularity and Well-posedness, Part III
We discuss a recent paper of J. Bourgain and D. Li, where ill-posedness of the 3D Euler Equations is established in the scale of the critical Sobolev spaces. Here, ill-posedness derives from the instantaneous loss of continuity of the solution operator. We distill the main ideas by considering the 2D case, which was developed in a set of lecture notes by T. Yoneda.