Applied mathematics

Our subject spans a huge range, from proving theorems to making policy. Over the course of 2011-12, we will try to represent the diverse interests of our community in a series of workshops.  In addition, we will have a working group on nonlinear problems, meeting every Thursday in Room 5417 at 2 PM during the term. A seminar series also takes place in Room 3209 on Fridays from 4 PM to 5 PM (see below for featured talks this fall). 

All workshops will be held in the Science Center, Room 4102. Events are open to the scientific community, but we ask that you email to register, so that we can provide the right amount of food and coffee (!).

Some funds are available to facilitate the participation of students and postdoctoral fellows from around the New York metropolitan area.  Please email if you would like to take advantage of this opportunity.


Thursday, 25 April, 2013, 9:00 AM 'til 3:00 PM
Topics in Numerical Analysis

Thursday, 02 May, 2013, 9:00 AM 'til 5:00 PM
Finite-time blow-up vs. global regularity for equations of fluid motion

9.30-10.00 AM: Bagels & Coffee

10.00-10.55 AM: Alexis Vasseur (U of Texas - Austin) "Relative entropy applied to the stability of shocks for compressible fluids, and applications to asymptotic analysis"

11.00-11.55 AM: Maria Schonbek (U of California - Santa Cruz) "Asymptotic stability of mild solutions to the Navier-Stokes equations"

12.00-12.55 PM: Isabelle Gallagher (Université Paris - Diderot) "Profile decompositions and the Navier-Stokes equations"

1.00-2.00 PM: Lunch

2.00-2.55: Pierre Germain (Courant Institute NYU) "Water waves and time-space resonances"  

3.00-3.55:  Edriss S. Titi (Weizmann Institute) "Global well-posedness of an inviscid three-dimensional Pseudo-Hasegawa-Mima-Charney-Obukhov Model"

4.00-4.55 Peter Constantin (Princeton) "Long-time behavior in forced critical Surface Quasi-Geostrophic Equation (SQG)"


Thursday, 28 February, 2013, 9:00 AM 'til 3:00 PM 
Perspective of the Ricci flow
Problems in combinatorial and numerical Ricci flow
David Glickenstein, University of Arizona
Type II singularities of Ricci flow
Dan Knopf,  University of Texas at Austin
Kahler-Ricci flow and birational surgery
Jian Song,  Rutgers University
On normalized Ricci flow and smooth structures on 4-manifolds
Ioana Suvaina,  Vanderbilt University

Thursday, 14 March, 2013, 9:00 AM 'til 3:00 PM 
Pi-Day with Chern-Simons Theory
Asymptotic behavior of solutions to the sigma_k-Yamabe
equation near isolated singularities
Zheng-Chao Han, Rutgers University
Uniqueness of topological solutions for a Chern-Simons model with two Higgs fields and two Gauge fields on a Torus 
Jyotshana Prajapat, Petroleum Institute, Abu-Dhabi 
Vortices in the Maxwell-Chern-Simons-Higgs Equations
Daniel Spirn,  University of Minnessota
Gabriella Tarantello, University of Rome II

FALL 2012
Thursday, 6 December, 2012, 9:00 AM 'til 3:00 PM 
Symposium on Harmonic maps
Almost complex surfaces in the product of two 3-spheres
 John Bolton, Durham University, UK
A Harmonic Map Problem with Partial Free Boundary conditions.
Fang-Hua Lin, Courant Institute (NYU), New-York
The analysis if conformal-minimal surfaces
 Tristan Riviere, ETH, Switzerland
Harmonic maps into exceptional symmetric spaces
 John C. Wood, University of Leeds, UK 

Thursday, 8 November, 2012, 9:00 AM 'til 3:00 PM 
Recent Progress in General Relativity
The Geometry of Statics Spacetimes
 Carla Cederbaum, Duke University
An isoperimetric concept for quasilocal mass
 Gerhard Huisken, Max-Planck Institute for Gravitational Physics, Potsdam
 Shadi Tahvildar-Zadeh, Rutgers University
Sharp Minkowski type inequality in the AdS-Schwarzschild space and the Penrose inequality for collapsing shells
 Mu-Tao Wang, Columbia University, New-York

Thursday, 26 April, 2012, 9:00 AM 'til 6:00 PM 
Hyperbolic conservation laws and applications
Nash equilibria for traffic flow on networks
 Alberto Bressan, Penn State University
TVD fields for pairs of conservation laws and the p-system
 Kris Jenssen, Penn State University
Using geometric singular perturbation theory to understand singular shocks
 Barbara Lee Keyfitz, The Ohio State University
Existence results for the Euler equations of compressible fluids in one space dimension
 Philippe G. LeFloch, Universite 
Paris VI (
Pierre et Marie Curie), and CNRS
A partial hodograph transform at a sonic curve for the Euler system
 Yuxi Zheng, Yeshiva University

Thursday, 22 March, 2012, 9:00 AM 'til 4:00 PM 
Aggregation models in biology
Blowup in multidimensional aggregation equations
 José Antonio Carrillo de la Plata, Universitat Autònoma de Barcelona
Nonlocal equations
 Peter Constantin, Princeton University
Dispersal in Heterogeneous Landscapes
 Yuan Lou, Ohio State University
Measured valued solutions for the Keller-Segel system
 Juan J.L. Velázquez, Hausdorff Center for Mathematics, Bonn

Thursday, 23 February, 2012, 9:00 AM 'til 4:00 PM 
Recent developments in minimal surfaces
Constant mean curvature spheres in homogeneous three dimensional manifolds
    William Meeks, University of Massachusetts

Dynamics and singularities of mean curvature flow

    William Minicozzi, Johns Hopkins University
Maximal surfaces in the anti-de Sitter space and the universal Teichmüller space
    Jean-Marc Schlenker, Universite Toulouse III
Polynomial Pick forms for affine spheres over the complex plane
    Michael Wolf, Rice University

FALL 2011
Thursday, 27 October, 2011, 9:00 AM 'til 3:00 PM 
Recent advances in 3D Euler and Navier-Stokes equations
The interplay between computation and analysis in the study of 3D incompressible flows
    Tom Hou, California Institute of Technology
An alternative approach to regularity for the Navier-Stokes equations in critical spaces
    Gabriel Koch, University of Sussex
Inviscid limit of the free boundary Navier-Stokes system
    Nader Masmoudi, Courant Institute NYU
Drift diffusion equations with fractional diffusion and the surface quasi-geostrophic equation
    Alexis Vasseur, University of Texas at Austin

Thursday, 22 September, 2011, 9:00 AM 'til 3:00 PM 
Recent trends in nonlinear PDEs
Saddle-shaped solutions to the scalar Ginzburg-Landau equations
    Xavier Cabre, ICREA & Universitat Politecnica de Catalunya
Uniqueness and nondegeneracy of ground states for non-local equations in dimension one
    Rupert Franck, Princeton University
Entire solutions of the Allen-Cahn equation
    Changfeng Gui, University of Connecticut
An optimal partition problem for the Dirichlet eigenvalues
    Fang-Hua Lin, Courant Institute NYU

Thursday, March 31, 2011, 9:00 AM 'til 4:00 PM 
Vortex dynamics & non-Equilibrium statistical mechanics
    Michael Kiessling (Rutgers University), David Dritschel (Univ. St. Andrews), Jeffrey Weiss (Univ. Colorado) 


Spring 2011:
Feb 17: Xing Zhong (New Jersey Institute Technology, New Jersey)
Threshold Phenomena for Symmetric Decreasing Solutions of Reaction-Diffusion Equations

Abstract: We study the Cauchy problem for nonlinear reaction-diffusion equation (u_t = u_xx + f(u), u(x,0) = \phi (x), x \in R, t > 0), with different nonlinearities. By using energy functional and exponentially weighted functional, for symmetric decreasing initial conditions, we prove one-to-one relation between long time behavior of solution and limit value of energy. Then we study the threshold phenomena. This is a joint work with Cyrill Muratov.

Mar 09: Keith Promislow (Michigan State University, East Lansing, MI)
Network Formation and Ion Conduction in Ionomer Membranes

Abstract: Many important processes in the physical world can be described as a gradient (overdamped) flow of a variational energy.  We present a broad formalism for the generation of new classes of  higher-order variational energies with a physically motivated structure. In particular we reformulate the Cahn-Hilliard energy, which is well know to describe the surface area of mixtures, into a higher-order model of interfacial energy for mixtures of charged polymers (ionomers) with solvent. These materials are important as selectively conductive membrane separators in a wide variety of energy conversion devices, including polymer electrolyte membrane fuel cells, Lithium ion batteries, and dye sensitized solar cells. Our reformulated energy, called the Functionalized Cahn-Hilliard (FCH) energy, captures elastrostatic interactions between the charged groups and the complex entropic effects generated by solvent-ion interactions, and allows us to unfold the bilayer and pore networks formed by the solvent phase imbibed into the polymer matrix.  We discuss sharp interface reductions of the FCH energy, its gradient flows, and sharp interface reductions of the gradient flows that give rise to higher-order curvature driven flows. We also describe extensions to models that couple to ionic transport and as well as to multiphase models suitable to describe a wide range of membrane casting processes.

Fall 2011:
Undercompressible shocks and moving phase boundaries
Philippe LeFloch, Universite Paris VI - Pierre et Marie Curie 

Complex (wormlike micellar) fluids: Shear banding and inertial effects
 Pam Cook, University of Delaware (with Lin Zhou, New York City College of Technology and Gareth McKinley, Massachusetts Institute of Technology)