Informal Geometric Analysis Seminar

Department of Mathematics

University of Maryland

Fall 2014 - Spring 2015

Date: Thursdays at 4:30pm.
Room: Mathematics Building 2300.

Organized by: T. Darvas, Y.A. Rubinstein.

The aim of this seminar is to attract graduate students to Geometric Analysis, through learning and research talks. All talks should be accessible to beginning graduate students who might have background either in PDE or in geometry, but not necessarily in both.


    Previous years: 2012-2013, 2013-2014.

  • September 4, Tamás Darvas
    Analytic test configurations after Ross and Witt-Nystrom

  • September 11, Tamás Darvas
    Analytic test configurations after Ross and Witt-Nystrom (continued)

  • September 18, Ryan Hunter
    Analytic test configurations after Ross and Witt-Nystrom (continued)

  • October 9, Matthew Dellatorre
    The Hele-Shaw flow after Ross and Witt-Nystrom.

  • October 16, Ryan Hunter
    Harmonic discs of solutions to the homogeneous Monge-Ampere equation after Ross and Witt-Nystrom.

  • October 30, Yanir Rubinstein
    Dirichlet Duality and the Nonlinear Dirichlet Problem after Harvey and Lawson.

  • November 6, Matthew Dellatorre
    The Bremerman-Dirichlet problem for q-plurisubharmonic functions after Slodkowski,

  • November 20, Tamas Darvas
    Dirichlet Duality and the Nonlinear Dirichlet Problem after Harvey and Lawson (continued)

  • November 25, 3PM, Ryan Hunter
    Dirichlet Duality and the Nonlinear Dirichlet Problem after Harvey and Lawson (continued)

  • December 2, 3 PM, Matthew Dellatorre
    Dirichlet Duality and the Nonlinear Dirichlet Problem after Harvey and Lawson (continued)

  • December 5, 3 PM, Renjie Feng,
    Title: The supremum of L^2 normalized random holomorphic fields
    Abstract: In this talk, I will define random polynomials and their generalization to complex manifolds. The main result is regarding the landscape of such random holomorphic fields: I will show that the expected value and median of the supremum of L^2 normalized random holomorphic fields of degree n on m-dimensional Kahler manifolds are asymptotically of order \sqrt{m\log n}. This is the joint work with S. Zelditch.

  • January 15, Tamas Darvas
    Title: The space of positive Lagrangians (after J. Solomon).

  • January 22, Tamas Darvas
    Title: The space of positive Lagrangians (after J. Solomon).

  • January 29, Matthew Dellatorre
    Title: The special Lagrangian equation (after Harvey and Lawson).

  • February 5, Liangming Shen (Princeton University)
    Title: The unnormalized conical Kahler-Ricci flow.

  • February 12, Ryan Hunter
    Title: The space of positive Lagrangians: the Calabi homomorphism (after J. Solomon).

  • March 26, Yanir Rubinstein
    Title: The space of positive Lagrangians: the geodesic equation.

  • April 9, Tamas Darvas
    Title: Curvature of the space of positive Lagrangians (after J. Solomon).

  • April 16, Jesse Gell-Redman
    Title: Introduction to Geometric Microlocal Analysis
    Abstract: We discuss some of the basic structures in the modern perspective on Microlocal Analysis (which we call "geometric") which goes back to Melrose in the early 80's. The original objects of study were linear elliptic operators on non-compact manifolds, their mapping properties, spectral theory, etc. We will focus our discussion on the application of these techniques to certain singular spaces, beginning with manifolds with conic singularities, arriving (hopefully) at a generalizable framework for semilinear elliptic equations on singular spaces. Related work includes that of Jeffers-Mazzeo-Rubinstein on K\"ahler-Einstein metrics, but we will focus on the substantially simpler harmonic map problem. The first lecture will be mostly motivation and technical background, and hopefully the beginning of the discussion of the linear elliptic theory.

  • May 7, Jesse Gell-Redman
    Title: Introduction to Geometric Microlocal Analysis

  • May 14, Jesse Gell-Redman
    Title: Introduction to Geometric Microlocal Analysis