Past Seminars: 2013
  Fall 2013
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September 5, 2013
Ratnasingham Shivaji, University of North Carolina
Uniqueness of Nonnegative Radial Solutions for Semipositone Problems on Exterior Domains
Abstract
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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
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September 19, 2013:
No seminar
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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 self-adjointness as well as estimating the bottom of the spectrum from above by the volume growth and from below by a Cheeger-type constant. This is joint work with several groups of authors.
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October 3, 2013:
No Seminar
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October 10, 2013
Hui Wang, Rutgers University
A semilinear singular Sturm-Liouville equation involving measure data
Abstract:
We consider a semilinear singular Sturm-Liouville 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 right-hand side. We answer the questions of the existence, nonexistence, uniqueness, and non-uniqueness of the solution(s). We also classify the isolated singularity at 0.
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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., distance-preserving
homeomorphisms) of an equiregular subRiemannian manifold is a
finite-dimensional 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.
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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 Gauss-Bonnet 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.
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October 31, 2013
Meijun Zhu, University of Oklahoma
Reversed Hardy-Littlewood-Sobolev inequality
Abstract:
For the classically defined integral operator $I_\alpha f$, we establish the reversed Hardy-Littlewood-Sobolev 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.
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November 7, 2013:
No Seminar
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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.
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Friday December 13, 2013
RU-CUNY symposium on Geometric analysis
in Room 4102 from 9:30am-4:00pm
TBA
Speakers:
TBA
  Spring 2013
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February 7, 2013:
No Seminar
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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
reaction-diffusion 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 King-Yeung Lam, Mathematical Biosciences Institute.
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February 21, 2013
Mikhail Shklyar, Graduate Center (CUNY)
Minimizers for a Moser-Trudinger type functional
Abstract:
We summarize some known results that ensure existence of minimizers for a functional that is related to the two-dimensional Moser-Trudinger inequality
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February 28, 2013
One day symposium in Room 4102 from 9:30am-4:00pm
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)
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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.
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March 14, 2013
One day symposium in Room 4102 from 9:30am-4:00pm
Pi-Day with Chern-Simons Theory
Speakers:
Zheng-Chao Han (Rutgers University), Jyotsna Prajapat (PI-Institue, 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)
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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)
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March 21-March28, 2013:
No Seminar (Spring Break)
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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 diï¬erential equations.
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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 Allen-Cahn
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 Allen-Cahn 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.
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April 18, 2013:
No Seminar
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April 25, 2013
One day symposium in Room 4102 from 9:30am-4:00pm
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)