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

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
  No seminar
  
  
  
• September 19, 2019
  Mohameden Ahmedou, Giessen University (Germany)
  Morse theory and the resonant $Q$-curvature problem
  Abstract: The Q-curvature is a scalar quantity which plays a central role in conformal geometry, in particular in the search of high order conformal invariants. 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
  TBA
  
  
• October 24, 2019
  Niclas Linne, Giessen University (Germany)
  The prescribed mean curvature problem on Riemannian manifolds with boundary
  Abstract: 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
  One-day Symposium
  Monica Clapp (Universidad Nacional Autonoma de Mexico), Luca Martinazzi (University of Padua, Italy), Tristan Riviere (ETH Zurich, Swizterland), Yi Wang (Johns Hopkins)
  Schedule
  
  
• November 7, 2019
  Vincent Martinez, CUNY-Hunter College
  Learning Seminar on Incompressible Euler and Navier-Stokes: Issues in Regularity and Well-posedness, Part I
  Abstract: 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
  Abstract: 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
  Abstract: 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
  Abstract: 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.

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