PAST Activities of the nonlinear analysis group
Fall 2012:

September 20, 2012
Friedemann Schuricht, Dresden University of Technology
Nonsmooth analysis in PDE problems
Abstract:
We consider nonlinear PDEproblems that are related to variational problems
that do not have the usual differentiability properties.
It turns out that nonsmooth
analytical tools developed in optimization theory can be used for a successful
treatment. After some introductory examples we discuss basic ideas of convex
analysis and some nonconvex extensions. Here we are led to completely new
phenomena that are relevant in the applications.

September 27, 2012
Jorge Basilio, CUNY Graduate Center
Introduction to BVfunctions
Abstract:

October 4, 2012
Sajjad Lakzian, CUNY Graduate Center
Ricci Flow Through Singularities
Abstract:
We will give a brief review of key facts about Ricci Flow and in particular
Ricci Flow neckpinch singularity. We will explain and build on the work of
AngenentCaputoKnopf on the smooth forward evolution of Ricci Flow and will
explore two ways towards defining a weak Ricci Flow through singularities.

October 11, 2012
Deane Yang, NYUPoly
Sobolev via Shannon
Abstract:
I will describe how sharp Sobolev inequalities on R^n can be derived
using information theoretic invariants and inequalities.

October 18, 2012
Luca Martinazzi, Rutgers University
The MoserTrudinger equation on a disk: sharp blowup behavior
and nonexistence
Abstract:
We study the MoserTrudinger equation Delta u = lambda u Exp(u^2),
lambda>0 on a 2dimensional disk, arising from the MoserTrudinger
sharp embedding of H^1_0(Disk) into the Orlicz space of functions u
with Exp(u^2) integrable. We answer some long standing open questions:
a) The weak limit of a blowingup sequence of solutions to the
MoserTrudinger equation on a disk is 0
b) The Dirichlet energy of a blowingup sequence of solutions on a
disk converges to 4pi.
c) For L large enough, the MoserTrudinger equation on a disk admits
no solution with Dirichlet energy larger than L.
This work is joint project with Andrea Malchiodi (SISSA  Trieste)

October 25, 2012
No Seminar: Lawson's birthday conference at Stony Brook this week

November 1, 2012 (Canceled)
Michael Kiessling, Rutgers University
Statistical mechanics of point vortices: The Onsager legacy
Abstract:
In 1949 Lars Onsager wrote a milestone paper where he predicted
the quantization of vorticity in superfluids (in a footnote!), observed
that the nondissipative Euler equations can have dissipative solutions
(more than 10 years before Harold Grad rediscovered that idea for ideal
magnetofluid dynamics), and for the first time ever applied classical
equilibrium statistical mechanics to the Hamiltonian point vortex system,
predicting negative vortex "gas" temperatures (7 years before Ramsey
rediscovered that idea for spin systems). In my talk I survey the
developments since Onsager's paper in regard to the statistical mechanics
of point vortices.

November 8, 2012
One day symposium in Room 4102 from 9:30am4:00pm
Recent Progress in General Relativity
Speakers:
Carla Cederbaum,
Gerhard Huisken,
Shadi TahvildarZadeh,
MuTao Wang
For more details,
click here
An event sponsored by the Initiative for the Theoretical Sciences at CUNY
(ITS)

November 15, 2012
No Seminar

November 22, 2012
Thanksgiving, No Meeting today

November 29, 2012
Po Lam Yung, Rutgers University
Two nonlinear wave equations with conformal invariance
Abstract:
In this talk, we will look at two nonlinear wave equations in 2+1 dimensions, whose elliptic parts exhibit conformal invariance. These equations have their origins in prescribing the Gaussian and mean curvatures respectively, and the goal is to understand wellposedness, blowup and bubbling for these equations. This is joint work with Sagun Chanillo.

December 6, 2012
One day symposium in Room 4102 from 9:30am4:00pm
Harmonic Maps
Speakers:
John Bolton, Fanghua Lin, Tristan Riviere, J.C. Wood
Poster and schedule,
[abstract]
An event sponsored by the Initiative for the Theoretical Sciences at CUNY
(ITS)

December 13, 2012
Michael Kiessling, Rutgers University
Statistical mechanics of point vortices: The Onsager legacy
Abstract:
In 1949 Lars Onsager wrote a milestone paper where he predicted
the quantization of vorticity in superfluids (in a footnote!), observed
that the nondissipative Euler equations can have dissipative solutions
(more than 10 years before Harold Grad rediscovered that idea for ideal
magnetofluid dynamics), and for the first time ever applied classical
equilibrium statistical mechanics to the Hamiltonian point vortex system,
predicting negative vortex "gas" temperatures (7 years before Ramsey
rediscovered that idea for spin systems). In my talk I survey the
developments since Onsager's paper in regard to the statistical mechanics
of point vortices.
In Spring 2011, we focused on "minimal surfaces" (reading a survey paper by Meeks and Perez), and mathematical questions related
to the ChernSimons theory.

February 2: Jim Portegies (Courant Institute), Minimal Surface I

February 9:
Bora Ferlengez (CUNY),
Minimal Surfaces II, Application of Weierstrass representation

February 16:
Sajjad Lakzian (CUNY),
Minimal Surfaces III

February 22 at 2:30PM:
Related Special Event at College of Staten Island
Frank Morgan, Williams College,
[Soap bubbles and mathematics],
[Information]
An event sponsored by the Simons Foundation

February 23:
Meeting in Room 4102 from 9:30am4:00pm
One day symposium:
Recent developments in minimal surfaces

March 1:
Brian Sulkow (CUNY),
Minimal surfaces of finite total curvature

March 8:
Brian Sulkow (CUNY),
Minimal surfaces of finite total curvature

March 15:
Yunpeng Wang (Rutgers),
Pohozaev identity on manifolds

March 22:
Meeting in Room 4102 from 9:30am4:00pm
One day symposium:
Aggregation models in biology

March 29:
Xiaosen Han
(NYU Poly and Henan University),
Some Existence Results on Abelian and NonAbelian Vortices

April 5: No Meeting in the morning (See Seminar below at 1:15pm)

April 19: Xiaosen Han (NYU Poly and Henan University),
NonAbelian ChernSimons models

April 26:
Meeting in Room 4102 from 9:30am4:00pm
One day symposium:
Hyperbolic Conservation Laws

May 1, 2012 (Tuesday)
Meeting in Room 4102 from 9:30am5:00pm
HunterGC Joint Mathematics Day
[poster],
[abstracts]

May 3: No Meeting (HunterGC Mathematics Day on May 1st)

May 10: Longzhi Lin (Rutgers University),
Weakly Harmonic maps
In Fall 2011, we studied the Yamabe problem, and the problem of prescribing scalar curvature on a compact manifold.

September 8:
Sajjad Lakzian, Introduction to the Yamabe problem.

September 15:
Brian Sulkow, An Introduction to Morse theory.

September 22: Oneday symposium.

September 29:
Brian Sulkow, The Morse Lemma.

October 6: Victor Reyes, De Giorgi conjecture in dimension two.

October 13:
Brian Sulkow, The Cell decomposition.

October 20:
Victor Reyes,
The Yamabe functional: The subcritical approximation.

October 27:
Oneday symposium.

November 3:
Victor Reyes,
The gap in the Yamabe argument.

November 10:
Sajjad Lakzian,
Some results for the critical case.

November 17:
Sajjad Lakzian,
The Yamabe problem on the sphere.

November 24:
Thanksgiving.

December 1: TBA.

December 8: TBA.
Spring 2012 Seminars:

February 23, 2012
One day symposium in Room 4102 from 9:30am4:00pm
Recent developments in minimal surfaces
[abstracts],
[poster]
An event sponsored by the Initiative for the Theoretical Sciences at CUNY
(ITS)
and planned by members of the
CIAMCS

March 1, 2012 at 12:15pm
No seminar

March 8, 2012 at 12:15pm
Florin Catrina, St. John's University
Pohozaev Identity for Semilinear Elliptic PDEs
Abstract:
In this talk we show how Pohozaev type identities are used to prove global nonexistence results.
Also, we indicate how local versions can be employed to obtain useful information,
such as to prove nonexistence of families of solutions with bounded energy concentrating at a finite number of points.

March 15, 2012 at 12:15pm
Silvius Klein, Medgar Evers College of CUNY
Spectral Problems for Discrete QuasiPeriodic Schrodinger Operators
Abstract:
I will describe the discrete quasiperiodic Schrodinger operator and some of its expected spectral properties. These operators are used in solid state physics to model disordered systems such as alloys and quasicrystals. I will mention some of the known results for such operators with real analytic potential functions, focusing more on the positivity of the Lyapunov exponent. Then, I will discuss my own results and research projects for more general (rougher) potential functions.

March 22, 2012
One day symposium in Room 4102 from 9:30am4:00pm
Aggregation models in biology
[abstracts],
[poster]
An event sponsored by the Initiative for the Theoretical Sciences at CUNY
(ITS)
and planned by members of the
CIAMCS

March 29, 2012
No seminar

April 5, 2012 at 1:15PM (Note Special Time)
Luis Fernandez, Bronx Community College (CUNY)
Minimal immersions in spheres
Abstract: TBA

April 12, 2012
No seminar, Spring Break

April 19, 2012 at 12:15pm
Timur Milgrom, Drexel University
Temporal boundary value problems in interfacial fluid dynamics
Abstract:
We will develop existence and uniqueness theory for a type of
boundary value problems, where the boundary data is specified at two
different times. The framework developed will consider problems on a
real line and problems which are spatially periodic. The general theory
will be applied to two problems from interfacial fluid dynamics: a
family of the Boussinesq equations developed by Bona, Chen and Saut, and
a vortex sheet.

April 26, 2012
One day symposium in Room 4102 from 9:30am4:00pm
Hyperbolic conservation laws
[abstracts],
[poster]
An event sponsored by the Initiative for the Theoretical Sciences at CUNY
(ITS)
and planned by members of the
CIAMCS

May 1, 2012 (Tuesday)
Meeting in Room 4102 from 9:30am5:00pm
HunterGC Joint Mathematics Day
[poster],
[abstracts]

May 3, 2012
No seminar
(Graduate and undegraduate conference on May 1st in Science Center)

May 10, 2012 at 12:15pm
LongZhi Lin, Rutgers University
On the uniqueness of weakly harmonic maps and a global estimate for
the energy density
Abstract:
In this talk we shall report a recent joint work with Tobias Lamm on a global estimate (in the local Hardy space)
on the energy density of critical points of a class of conformally invariant variational problems with small energy on the unit
2disc, using Riviere's gauge decomposition technique and Wente type estimates. As a corollary we obtain a new proof of
the energy convexity and uniqueness result for weakly harmonic maps with small energy on the unit 2disc.
Fall 2011 Seminars:

September 22, 2011
Oneday Symposium, in Room 4102 from 9:30am4:00pm
Recent trends in nonlinear PDEs
[abstracts].
An event sponsored by the Initiative for the Theoretical Sciences at CUNY
(ITS)
and planned by members of the
CIAMCS

October 27, 2011
Oneday symposium, in Room 4102 from 9:30am4:00pm
Recent advances in 3D Euler and
NavierStokes equations
[abstracts].
An event sponsored by the Initiative for the Theoretical Sciences at CUNY
(ITS)
and planned by members of the
CIAMCS

November 3, 2011 at 11:00am, Room 4419
Henrik Shahgholian,
The Royal Institute of Technology, Sweden
Quadrature Domains and related topics
[abstract].

November 10, 2011 at 12:15pm,
Room 4419
Ray Yang, Courant Institute NYU,
Optimal regularity and nondegeneracy for minimizers of an
energy
arising from the fractional Laplacian
[abstract].

November 17, 2011 at 12:15pm,
Room 4419
Tianling Jin, Rutgers University,
On a fractional Nirenberg problem: existence and compactness
of solutions
[abstract].

November 24, 2011
Thanksgiving, No Meeting.

December 1, 2011,
No Seminar Today

December 8, 2011 at 12:15pm, Room 4419
M.W. Wong, York University (Toronto),
The Spectral Theory and Number Theory of a Twisted BiLaplacian
[abstract].
In Fall 2010, we studied the Bernstein Theorem,
and questions related to minimal varieties.
In Spring 2011, we first discussed a conjecture
proposed by De Giorgi, which is very similar to
Bernstein's Theorem. These questions have been extended further by studying nonlinear equations
arising in the study of surface
of constant mean curvature in the Euclidean space.
Differential Geometry Seminar
Every Tuesday from 3:004:00pm, I am involved in the Differential geometry seminar with
Zheng Huang
and
Dan Lee.
To see the abstracts and list of speakers planned at this seminar, click
here.
Applied Mathematics Seminar
Here are some past seminars organized in the "applied Mathematics" seminar at
the Graduate Center.
 04/08/2011: Ratnasingham Shivaji, Mississipi State University,
Positive Solutions for Nonlinear Elliptic Systems with Combined Nonlinear Effects
[abstract].
 03/11/2011: Friedemann Schuricht, Dresden University of Technology,
Eigenvalue problem of the 1Laplace operator
[abstract].
 04/16/2010: Peter Gordon, New Jersey Institute of Technology,
Thermal explosion in porous media as a blow up problem.
 04/12/2010: ZhongWei Tang, Beijing Normal University,
Multibump solutions of nonlinear Schrödinger equations with indefinite potential.
 04/05/2010: Florin Catrina, St. John University,
An energy balance identity and radial solutions for elliptical PDE's.
 02/19/2010: Sasha Stoikov, Cornell University,
A stochastic model for order book dynamics.
 12/18/2009: Vitaly Moroz, Swansea University,
Existence and concentration for nonlinear Schrödinger equations with fast decaying.
 12/04/2009: Maria Psarelli, Bronx CC  CUNY,
Time decay properties of nonlinear MaxwellDirac equations in 4dimensional Minkowski spacetime.
 11/13/2009: Carlo Lancellotti, College of Staten Island  CUNY,
The Master Equation Approach in Kinetic Theory.
 03/14/2008: Enea Parini, University of Cologne,
Some results about Cheeger sets: uniqueness and nonuniqueness.
 03/14/2008: Bernd Kawohl, University of Cologne,
Variational versus PDEbased Approaches in Mathematical Image Processing.
 02/15/2008: Cyrill Muratov, New Jersey Institute of Technology,
Selfinduced stochastic resonance: How new nonrandom behaviors can arise from the action of noise.
Special events organized at the Graduate Center