Organizers: Ricardo Nochetto, Wujun Zhang
When: Wednesdays @ 5pm-6pm, starting the first week of February
Where: room TBA
Subtitle: PDE theory and numerical analysis

Fully nonlinear second order elliptic PDEs arise naturally from differential geometry, stochastic control theory, optimal transport and other fields in science and engineering. In this RIT, we will discuss the concept of viscosity solutions and regularity theory of these PDEs. Some possible topics include:

  • fully nonlinear elliptic equations and viscosity solutions
  • Alexandroff-Bakelman-Pucci estimates
  • Harnack inequality and Hölder regularity
  • Uniqueness of solutions
  • W2,p estimates
  • C1, α estimates
  • C2, α estimates

In contrast to an extensive PDE literature, the numerical approximation reduces to a few papers. We would like to discuss some criteria for designing convergent numerical methods and some tools developed recently which are useful to obtain rates of convergence. Some possible topics include:

  • criterion for convergence of numerical methods
  • discrete version of the Alexandroff-Bakelman-Pucci estimate
  • finite element method for linear elliptic equations in non-divergence form
  • numerical method for Monge-Ampere equations

Archives: 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018

  • Augmented reality in the estimation of small tail probabilitiesmall

    Speaker: Benjamin Kedem (UMD) - https://www.math.umd.edu/~bnk/

    When: Wed, September 5, 2018 - 3:15pm
    Where: Kirwan Hall 3206
  • Aziz Lecture: Smooth random functions and smooth random ODEs

    Speaker: Lloyd N. Trefethan (Oxford University)

    When: Wed, September 12, 2018 - 3:15pm
    Where: Kirwan Hall 3206
  • Dirac operators and Hecke algebras

    Speaker: Dan Ciubotaru (University of Oxford) - https://www.maths.ox.ac.uk/people/dan.ciubotaru

    When: Wed, September 19, 2018 - 3:15pm
    Where: Chemical Engineering Room 2110
  • Scholze's Fields medal

    Speaker: Michael Rapoport (UMD and University of Bonn) - http://www.math.uni-bonn.de/ag/alggeom/rapoport

    When: Wed, September 26, 2018 - 3:15pm
    Where: Kirwan Hall 3206
  • Modeling and Simulation of Asteroid-Generated Tsunamis

    Speaker: Marsha Berger (NYU) - https://cs.nyu.edu/berger/

    When: Wed, October 3, 2018 - 3:15pm
    Where: Kirwan Hall 3206
  • Topics in Markov chains

    Speaker: Alan Frieze (CMU) - https://www.math.cmu.edu/~af1p/

    When: Fri, October 5, 2018 - 11:00am
    Where: CSIC 2117
  • (Special Applied Math Colloquium, Special time): Atomistic Simulation of Crystalline Defects [A Numerical Analysis Perspective]

    Speaker: Christoph Ortner (University of Warwick) - https://warwick.ac.uk/fac/sci/maths/people/staff/christoph_ortner/

    When: Tue, October 9, 2018 - 11:00am
    Where: Kirwan Hall 3206
  • Faculty Promotion Meeting

    Speaker: Department meeting () -

    When: Wed, October 10, 2018 - 3:15pm
    Where: Kirwan Hall 3206
  • Effective stability in quasi-periodic dynamics.

    Speaker: Bassam Fayad (Universite de Paris) - https://webusers.imj-prg.fr/~bassam.fayad/

    When: Fri, October 12, 2018 - 3:15pm
    Where: Kirwan Hall 3206
  • Faculty Promotion Meeting

    Speaker: Department meeting () -

    When: Wed, October 17, 2018 - 3:15pm
    Where: Kirwan Hall 3206
  • On traffic modeling and the Braess paradox

    Speaker: Helge Holden (NTNU (Norwegian University of Science and Technology)) - https://www.ntnu.edu/employees/holden

    When: Fri, October 26, 2018 - 3:15pm
    Where: Kirwan Hall 3206
  • (Special Applied Math Colloquium, Special time): Density fitting: Analysis, algorithm and applications

    Speaker: Jianfeng Lu (Duke University) - https://services.math.duke.edu/~jianfeng/

    When: Tue, October 30, 2018 - 11:00am
    Where: Kirwan Hall 3206
  • Making mathematical videos

    Speaker: Jeff Adams (UMD ) - https://www.math.umd.edu/~jda/

    When: Wed, November 7, 2018 - 3:15pm
    Where: Kirwan Hall 3206
  • -Meeting with the Dean Amitabh Varshney

    Speaker: Department meeting () -

    When: Wed, November 14, 2018 - 3:15pm
    Where: Kirwan Hall 3206
  • Title: Quantitative stochastic homogenization of linear elliptic PDE

    Speaker: Dr. Scott ArmstrongAbstract: I will discuss the large-scale asymptotics of solutions of linear elliptic equations with random coefficients. It is well-known that solutions converge (in the limit of scale separation) to those of a deterministic equation, a kind of law of large numbers result called "homogenization". In recent years obtaining quantitative information about this convergence has attracted a lot of attention. I will give an overview of one such approach to the topic based on variational methods, elliptic regularity, and ``renormalization-group'' arguments.

    When: Wed, November 28, 2018 - 3:15pm
    Where: 3206 William E. Kirwan Hall
  • The multiplicity one conjecture on 3-manifolds

    Speaker: Otis Chodosh (Princeton University) - https://web.math.princeton.edu/~ochodosh/

    When: Wed, December 5, 2018 - 3:15pm
    Where: Kirwan Hall 3206
  • Statistical analysis and spectral methods for signal-plus-noise matrix models

    Speaker: Joshua Cape (Johns Hopkins University) -

    When: Fri, December 14, 2018 - 3:15pm
    Where: Kirwan Hall 3206
  • Spectral Methods and Nonconvex Optimization: A Modern Statistical Perspective

    Speaker: Yiqiao (Joe) Zhong (Princeton University) -

    When: Fri, January 4, 2019 - 3:15pm
    Where: Kirwan Hall 3206
  • Total Variation Regularized Fréchet Regression and Change-Point Modeling for Non-Euclidean Data

    Speaker: Zhenhua Lin (University of California -- Davis) -

    When: Mon, January 7, 2019 - 3:15pm
    Where: Kirwan Hall 3206
  • Analysis of Large Multi-Relational Networks

    Speaker: Xueying Tang (Columbia University) -

    When: Wed, January 9, 2019 - 3:15pm
    Where: Kirwan Hall 3206
  • Shrinking characteristics of precision matrix estimators

    Speaker: Aaron Molstad (Fred Hutchinson Cancer Research Center) -

    When: Mon, January 21, 2019 - 3:15pm
    Where: Kirwan Hall 3206