ACTIVITIES AT THE GRADUATE CENTER
A lot of seminars are organized at the Graduate Center.
Look at the weekly seminars bulletin that is updated every Tuesday.
Here, you will find the seminars I am involved with, and conferences I have organized 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
Tuesday, 1:00pm3:00pm
CUNY Graduate Center, 365 Fifth Avenue, NYC
Room 5417
One goal of this reading group and seminars is to
introduce some papers that are related to a series of symposium in applied mathematics that are sponsored by the
Initiative for the Theoretical Sciences.
SCHEDULE Fall 2015:

September 15, 2015
Tarek M. Elgindi, Princeton University
Recent results on the transport equation
We discuss several recent results on the well/illposedness of transport equations with singular integral forcing in spaces at the same scaling as $L^\infty$. Such equations arise naturally in the study of fluid equations and other applications. As a byproduct of one of the theorems we will discuss, we prove the strong illposedness of the incompressible Euler equations in the class of C^1 velocity fields. Some of what will be discussed is joint work with N. Masmoudi and F. BernicotS.

September 29, 2015
Tristan Buckmaster, Courant Institute, NYU
Onsager's Conjecture
In 1949, Lars Onsager in his famous note on statistical hydrodynamics conjectured that weak solutions to the Euler equation belonging to Hölder spaces with Hölder exponent greater than 1/3 conserve energy; conversely, he conjectured the existence of solutions belonging to any Hölder space with exponent less than 1/3 which dissipate energy.
The first part of this conjecture has since been confirmed (cf. Eyink 1994, Constantin, E and Titi 1994). During this talk we will discuss recent work by Camillo De Lellis, László Székelyhidi Jr., Philip Isett and myself related to resolving the second component of Onsager's conjecture. In particular, we will discuss the construction of weak nonconservative solutions to the Euler equations whose Hölder $1/3\epsilon$ norm is Lebesgue integrable in time.

October 20, 2015
Jerome Goddard, Auburn University Montgomery
Modeling the effects of habitat fragmentation via reaction diffusion equations
Two important aspects of habitat fragmentation are the size of fragmented patches of preferred habitat and the inferior habitat surrounding the patches, called the matrix. Ecological field studies have indicated that an organism’s survival in a patch is often linked to both the size of the patch and the quality of its surrounding matrix. In this talk, we will focus on modeling the effects of habitat fragmentation via the reaction diffusion framework. First, we will introduce the reaction diffusion framework and a specific reaction diffusion model with logistic growth and Robin boundary condition (which will model the negative effects of the patch matrix). Second, we will explore the dynamics of the model via some methods from nonlinear analysis and ultimately obtain a causal relationship between the size of the patch and the quality of the matrix versus the maximum population density sustainable by that patch.

November 10, 2015
Michael Puls, John Jay College CUNY

November 24, 2015
Mythily Ramaswamy, TATA Institute, Bangalore

December 8, 2015
Fabio Pusateri, Princeton University
SCHEDULE Spring 2015:

February 10, 2015
Luciano Medina, NYU Polytechnic
Vortex Equations Governing the Fractional Quantum Hall Effect
Governed by topological excitations in ChernSimons gauge theories, an existence theory is established for a coupled nonlinear elliptic system describing the fractional quantum Hall effect in 2dimensional doublelayered electron systems. Via variational methods, we prove the existence and uniqueness of multiple vortices over a doubly periodic domain and the full plane. In the doubly periodic situation, explicit sufficient and necessary conditions are obtained that relate the size of the domain and the vortex numbers. For the full plane case, vortex solutions are restricted to satisfy topological boundary conditions and exponential decay estimates are proved. Interestingly, quantization phenomena of the magnetic flux are found in both cases.

February 24, 2015
Ovidiu Savin, Columbia University
A singular minimizer in the Calculus of Variations in low dimensions
I will discuss about a counterexample to C^1 regularity in the Calculus of Variations. We consider minimizers of smooth convex functionals depending only on the derivative of a map from R^n to R^m. Classical results of Morrey and De GiorgiNash state that such minimizing maps are smooth when $n=2$ or when $m=1$. On the other hand some examples due to Necas and SverakYan show that the regularity of minimizers is not expected in general.
In my talk I will discuss an example of a singular minimizer in the lowest possible dimensions when $n=3$ and $m=2$.

March 10, 2015
Chuan Xue, Ohio State University
Chemotaxis, velocity jump process and the KellerSegel equations
Chemotaxis is the directed movement of cells or organisms towards external chemical signals
in the environment. Chemotaxis of a single bacterium or a eukaryotic cell has been extensively
studied and a great deal is known on the molecular machinery involved in intracellular signaling
and cell movement. However, systematic methods to embed such information into continuum
PDE models for cell population dynamics are still in their infancy. In this talk, I will present our
recent results in this aspect for runandtumble bacteria whose movement, at the single cell
level, is usually modeled by velocity jump processes with internal dynamics. I will show that the
wellknown KellerSegel chemotaxis equation is valid when the external signal changes slowly,
but inadequate when the signal changes fast.

March 31, 2015
Ratnasingham Shivaji, The University of North Carolina Greensboro
Existence Results for Classes of Steady State Reaction Diffusion Equations
Abstract

April 14, 2015
Kyril Tintarev, Uppsala University, Sweden
TBA

May 5, 2015
Xiangwen Zhang, Columbia University
Uniqueness Theorem for convex surfaces
A classical uniqueness problem of Alexandrov says that: a closed strictly convex twice differentiable surface in $R^3$ is uniquely determined to within a parallel translation when one gives a proper function of the principle curvatures. We will talk about a PDE proof for this theorem, by using the maximal principle and weak uniqueness continuation theorem of BersNirenberg. Moreover, a stability result related to the uniqueness problem will be mentioned. This is joint work with P. Guan and Z. Wang.
SCHEDULE Spring 2014:

February 27, 2014
Dongbin Xiu, University of Utah
Multidimensional polynomial interpolation on arbitrary nodes
Abstract:
Polynomial interpolation is well understood on the real line. In multidimensional spaces, one often adopts a wellestablished onedimensional method and fills up the space using certain tensor product rule. Examples like this include full tensor construction and sparse grids construction. This approach typically results in fast growth of the total number of interpolation nodes and certain fixed geometrical structure of the nodal sets. This imposes difficulties for practical applications, where obtaining function values at a large number of nodes is infeasible. Also, one often has function data from nodal locations that are not by "mathematical design" and are ``unstructured''.
In this talk, we present a mathematical framework for conducting polynomial interpolation in multiple dimensions using arbitrary set of unstructured nodes. The resulting method, least orthogonal interpolation, is rigorous and has a straightforward numerical implementation. It can faithfully interpolate any function data on any nodal sets, even on those that are considered degenerate by the traditional methods. We also present a strategy to choose ``optimal'' nodes that result in robust interpolation. The strategy is based on optimization of Lebesgue function and has certain highly desirable mathematical properties.

TUESDAY March 11, 2014, 5:00pm, ROOM 6417 (Note special time, and room!)
Friedemann Schuricht, TUDresden
Nonsmooth variational problems
Abstract:
Several problems arising in physics lead to natural lack of differentiability in the models used to describe them. Appropriate tools are needed to handle the
questions of existence of solutions in such framework. We present some fundamental ideas that allow to treat some convex functional that are not necessarily differentiable.

March 13, 2014
Edger Sterjo, Graduate Center at CUNY
An introduction to Morse Theory and its applications
Abstract:
Given a function f defined on a manifold M, both sufficiently differentiable, what is the topological significance of the critical points of f? In one dimension, for example, the level sets of the parabola f(x) = x^2 all have 2 components, except at the critical value y=0, at which the level set is a point.
Similarly on R^2, the function f(x,y) = x^2  y^2 has level sets which are hyperbolas, except at the critical value z=0, where the level set is the union of
two diagonals. The idea of Morse theory is to relate the critical point structure of f to the topological characteristics of it's (sub)level sets.
In all of this compactness properties play a big role. However, in the infinite dimensional setting, where our manifold is no longer locally compact,
we must make up for this lack of compactness by imposing a further condition on our function.

March 20, 2014
Alessandro Ottazzi, CIRM, Bruno Kessler Foundation, Trento, Italy
Maps on stratified Lie groups
Abstract:
In this talk I discuss some new results concerning the study of special maps
on CarnotCarathéodory spaces, obtained in different collaborations.
I shall begin with the definition of CarnotCarathéodory space and that of
Carnot group. Then I describe the classes of maps in which I am interested: isometries, conformal maps, quasiconformal maps. Finally, I will briefly comment on the techniques
that are used in the proofs, with particular attention on Tanaka prolongation theory.

March 27, 2014
Cyril Joël Batkam, University of Sherbrooke (Canada)
Multiple solutions to some differential systems with strongly indefinite variational structure
Abstract:
Abstract

April 10, 2014
Michael McCourt, University of Colorado, Denver
Positive Definite Kernels, Opportunities and Challenges
Abstract:
Scattered data approximation, the process of fitting a function to given data, is an important tool in applications including spatial statistics, econometrics, machine learning, computer graphics and others. In one dimension, polynomials and splines are often used; however, when higher dimensions are considered, possibly with oddlyshaped domains, polynomials and splines can prove problematic.
Positive definite kernels (sometimes called radial basis functions) provide a mechanism for conducting mesh free approximation in higher dimensions and complicated domains without the fear of nonuniqueness that accompanies polynomials. In this talk we will introduce positive definite kernels and focus on the properties of the Gaussian, long the preferred kernel of many applications because of its spectrally accurate convergence properties. We will explain how interpolation with a Gaussian basis has the potential to outperform polynomial interpolation, even in one dimension, and also show how numerical instabilities can sabotage this superior performance. We will then describe a new technique to stably evaluate Gaussian interpolants, allowing for their theoretically optimal behavior to emerge.

April 24, 2014
Dhanya Rajendran, Tata Institute, Bangalore (India)
Critical growth elliptic problem with singular discontinuous nonlinearity in R2
Abstract:
Elliptic problems with discontinuous nonlinearity has its own
difficulties due to the nondifferentiability of the associated
functional. Hence, a generalized gradient approach developed by Chang has
been used to solve such problems if the associated functional is known to
be Lipchitz continuous. In this talk, we will consider critical elliptic
problem in a bounded domain in R^2 with the simultaneous
presence of a Heaviside type discontinuity and a powerlaw type
singularity and investigate the existence of multiple positive solutions.
Here discontinuity coupled with singularity does not fit into any of the
known framework and we will discuss our approach employed to obtain
multiple positive solutions.

May 1, 2014
One day symposium in Room 4102 from 9:30am4:00pm
Hyperbolic Conservation Laws: Recent Progress
Speakers:
Alberto Bressan, Geng Chen, Sebastian Noelle, Ronghua Pan
An event sponsored by the Initiative for the Theoretical Sciences at CUNY
(ITS)

May 8, 2014
No seminar: Undergraduate Lecture at CSI

May 15, 2014 (!! Meeting at 3:00pm !!)
Abbas Bahri, Rutgers University
Periodic orbits of Reeb vector fields in dimension three
Abstract:

May 22, 2014
Mythily Ramaswamy, Tata Institute, Bangalore
Control aspects of NavierStokes equations
Abstract:
We recall the concepts of contrability and stabilization for PDEs'
and apply it for the compressible NavierStokes system in one dimension.
SCHEDULE Fall 2013:

September 5, 2013
Ratnasingham Shivaji, University of North Carolina
Uniqueness of Nonnegative Radial Solutions for Semipositone Problems on Exterior Domains
Abstract:
Abstract

September 13, 2013 (Friday instead of Thursday)
R. Prashanth, Tata Institute, Bangalore (India)
Simplicity for Rayleigh quotient
Abstract:
In this talk I will explain some results on the simplicity of minimisers for Rayleigh quotient given in a very general form

September 19, 2013
No seminar

September 26, 2013 (at 2:45pm !!)
Radoslaw Wojciechowski, York College at CUNY
Spectral properties and intrinsic metrics on infinite graphs
Abstract:
I will introduce the concept of an intrinsic metric on an infinite weighted graph and study applications to spectral properties of the Laplacian. In particular, I will address issues of selfadjointness as well as estimating the bottom of the spectrum from above by the volume growth and from below by a Cheegertype constant. This is joint work with several groups of authors.

October 3, 2013
No Seminar

October 10, 2013
Hui Wang, Rutgers University
A semilinear singular SturmLiouville equation involving measure data
Abstract:
We consider a semilinear singular SturmLiouville equation involving measure data. More precisely, it is a second order ODE on the interval (1,1) in the divergence form, with the leading coefficient taking zero value at the origin, with a power nonlinearity and with a bounded Radon measure as the righthand side. We answer the questions of the existence, nonexistence, uniqueness, and nonuniqueness of the solution(s). We also classify the isolated singularity at 0.

October 17, 2013
Luca Capogna, Worcester Polytechnic Institute
Smoothness of isometries between subRiemannian manifolds
Abstract:
In a joint work with Enrico Le Donne (Jyvaskyla, Finland)
we show that the group of isometries (i.e., distancepreserving
homeomorphisms) of an equiregular subRiemannian manifold is a
finitedimensional Lie group of
smooth transformations. The proof is based on a new PDE argument, in the
spirit of harmonic coordinates, establishing that in an arbitrary
subRiemannian
manifold there exists
an open dense subset where all isometries are smooth.

October 24, 2013
Meijun Zhu, University of Oklahoma
Sharp Sobolev inequalities in global analysis
Abstract:
In this talk, I shall explain how PDEs can be used for the study of global analysis problems, in particular the essential roles that certain sharp Sobolev inequalities play: From the uniformization Theorem, one can obtain GaussBonnet formula; From the sharp Sobolev inequality, one can solve the Yamabe problem under the energy condition; Using the fact that Liouville energy is bounded from below, one can reprove the uniformization theorem via Ricci flow on a topological sphere. Sharp Soboleb inequality with negative power will also be discussed.

October 31, 2013
Meijun Zhu, University of Oklahoma
Reversed HardyLittlewoodSobolev inequality
Abstract:
For the classically defined integral operator $I_\alpha f$, we establish the reversed HardyLittlewoodSobolev inequality for $\alpha>n$. In conformal case, we also prove the sharp inequality. The motivation, as well as possible applications of such inequality, in particular its relation to the sharp Sobolev inequality with negative power will be discussed.

November 7, 2013
No Seminar

November 14, 2013
Ran Ji, CUNY Graduate Center
The asymptotic Dirichlet problems on manifolds with negative curvature
Abstract:
Elton P. Hsu used probabilistic method to show that the asymptotic
Dirichlet problem is uniquely solvable under the curvature conditions
$C e^{2\eta}r(x) \leq K_M(x)\leq 1$ with $\eta>0$. We give an analytical proof of the same statement by a modification of an argument due to M. T. Anderson and R. Schoen. With this method we are able to construct a Harnack type inequality and use it to study the Martin boundary.

November 21, 2013
TBA
TBA
Abstract:

Friday December 13, 2013
RUCUNY symposium on Geometric analysis
in Room 4102 from 9:30am4:00pm
TBA
Speakers:
TBA
SCHEDULE Spring 2013:

February 7, 2013
No Seminar

February 14, 2013
Yuan Lou, The Ohio State University
Asymptotic behavior of the principal eigenvalue for cooperative elliptic operators and applications
Abstract:
I will discuss the asymptotic behavior of the principal eigenvalue for general
linear cooperative elliptic systems with sufficiently small diffusion rates.
As an application, we show that if a cooperative system of ordinary differential equations
has a unique positive steady state which is globally asymptotically stable, then the corresponding
reactiondiffusion system with either the Neumann boundary condition alsohas a unique positive
steady state which is globally asymptotically stable, provided that the diffusion coefficients are small.
This is a joint work with KingYeung Lam, Mathematical Biosciences Institute.

February 21, 2013
Mikhail Shklyar, Graduate Center (CUNY)
Minimizers for a MoserTrudinger type functional
Abstract:
We summarize some known results that ensure existence of minimizers for a functional that is related to the twodimensional MoserTrudinger inequality

February 28, 2013
One day symposium in Room 4102 from 9:30am4:00pm
Perspectives on Ricci Flow
Speakers:
David Glickenstein, Dan Knopf, Jian Song, Ioana Suvaina
An event sponsored by the Initiative for the Theoretical Sciences at CUNY
(ITS)

March 7, 2013
Costante Bellettini, Princeton University and Institute for Advanced Study
Regularity issues for Calibrated Currents
Abstract:
Calibrated currents provide interesting explicit examples of solutions
to Plateau's problem. Their role goes however much beyond that: they
naturally appear when dealing with several geometric questions, some
aspects of which require a deep understanding of regularity properties
of calibrated currents. After this introduction I will present an
"infinitesimal regularity" result, namely on the uniqueness of tangent
cones for pseudo holomorphic currents.

March 14, 2013
One day symposium in Room 4102 from 9:30am4:00pm
PiDay with ChernSimons Theory
Speakers:
ZhengChao Han (Rutgers University), Jyotsna Prajapat (PIInstitue, Abu Dhabi), Daniel Spirn (University of Minnesota),
Gabriella Tarantello (Rome University II)
Schedule, abstract
and
Poster
An event sponsored by the Initiative for the Theoretical Sciences at CUNY
(ITS)

Friday March 15, 2013
Research group discussion with
Prof. Fridemann Schuricht (Dresden University)
and Prof Shivaji Ratnasingham (University of North Carolina)
on analytic technics in nonlinear analysis and nonsmooth analysis.
Meeting takes place in the Room 4412 (ITS Room)

March 21March28, 2013
No Seminar (Spring Break)

April 4, 2013
Marco Squassina, University of Verona
Symmetry in variational principles and applications
Abstract:
We formulate symmetric versions of classical variational principles in the
framework of smooth and nonsmooth critical point theory. Then, we discuss
their applications to nonlinear partial diﬀerential equations.

April 11, 2013
Changfeng Gui, University of Connecticut
Traveling wave solutions to reaction diffusion equations
with fractional Laplacians
Abstract:
In this talk, I will discuss the existence and asymptotic behavior of traveling wave solutions to AllenCahn
equation with fractional Laplacians where the double well potential has unequal depths.
A key ingredient is the estimate of the speed of the traveling wave in terms of the potential, which seems new even for the classical AllenCahn equation. I will also discuss nonexistence of traveling wave solutions to a nonlocal combustion model. The talk is based on recent results obtained jointly with Tingting Huan and with Mingfeng Zhao respectively.

April 18, 2013
No Seminar

April 25, 2013
One day symposium in Room 4102 from 9:30am4:00pm
Topics in Numerical Analysis
Speakers:
Yves Bourgault (University of Ottawa, Canada), David Dritschel (St Andrews University, UK),
Tim Kelley (North Carolina), Jie Shen (Purdue University)
Schedule, abstract
and
Poster
An event sponsored by the Initiative for the Theoretical Sciences at CUNY
(ITS)
PAST ACTIVITIES
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