Past Seminars: 2013


  Fall 2013

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

  • October 3, 2013: No Seminar

  • 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.

  • 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.

  • 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.

  • 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.

  • 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.

  • Friday December 13, 2013
    RU-CUNY symposium on Geometric analysis in Room 4102 from 9:30am-4:00pm
    TBA
    Speakers: TBA


  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 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.

  • 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

  • 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)

  • 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 9:30am-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)

  • 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 21-March28, 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 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.

  • April 18, 2013: No Seminar

  • 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)