### Informal Geometric Analysis Archives for Academic Year 2014

#### Analytic test configurations after Ross and Witt-Nystrom (continued)

When: Thu, September 11, 2014 - 4:30pm
Where: Math 3206
Speaker: Tamás Darvas (University of Maryland) -

#### Analytic test configurations after Ross and Witt-Nystrom (continued)

When: Thu, September 18, 2014 - 4:30pm
Where: 2300.0
Speaker: Ryan Hunter (UMD) -

#### The Hele-Shaw flow after Ross and Witt-Nystrom

When: Thu, October 2, 2014 - 4:30pm
Where: MATH2300
Speaker: Matthew Dellatorre (UMD) -

#### The Hele-Shaw flow after Ross and Witt-Nystrom

When: Thu, October 9, 2014 - 4:30pm
Where: MATH2300
Speaker: Matthew Dellatorre (UMD) -

#### Harmonic Discs of Solutions to the Complex Homogeneous Monge-Ampère Equation after Ross and Witt-Nystrom

When: Thu, October 16, 2014 - 4:30pm
Where: MATH2300
Speaker: Ryan Hunter (UMD) -

#### Harmonic Discs of Solutions to the Complex Homogeneous Monge-Ampère Equation after Ross and Witt-Nystrom

When: Thu, October 23, 2014 - 4:30pm
Where: MATH2300
Speaker: Tamás Darvas (UMD) -

#### Dirichlet Duality and the Nonlinear Dirichlet Problem (after Harvey and Lawson)

When: Thu, October 30, 2014 - 4:30pm
Where: Math 2300
Speaker: Yanir Rubinstein (UMD) -

#### The Bremerman-Dirichlet problem for q-plurisubharmonic functions after Slodkowski

When: Thu, November 6, 2014 - 4:30pm
Where: Math 2300
Speaker: Matthew Dellatorre (UMD) -

#### Dirichlet Duality and the Nonlinear Dirichlet Problem continued (after Harvey and Lawson)

When: Thu, November 20, 2014 - 4:30pm
Where: Math 2300
Speaker: Tamas Darvas (UMD) -

#### Dirichlet Duality and the Nonlinear Dirichlet Problem continued (after Harvey and Lawson)

When: Tue, November 25, 2014 - 4:30pm
Where: Math 2300
Speaker: Ryan Hunter (UMD) -

#### The Supremum of L^2 Normalized Random Holomorphic Fields

When: Fri, December 5, 2014 - 3:00pm
Where: MTH 1313
Speaker: Renjie Feng (UMCP) -
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.

#### The unnormalized conical Kahler-Ricci flow

When: Thu, February 5, 2015 - 3:00pm
Where: 3206
Speaker: Liangming Shen (Princeton University) -
Abstract: Conical Kahler metrics have become an interesting topic in Kahler geometry, and played an important role in the solution of Yau-Tian-Donaldson conjecture. In this talk, we make use of approximation method of Guenancia-Paun to extend Tian-Zhang's maximal existence result of Kahler-Ricci flow to conic case. Finally, we can sketch the $C^{2,\alpha}$-estimate for conical Kahler-Ricci flow based on Tian's
master thesis.

#### The space of positive Lagrangians: the Calabi homorphism (after Solomon)

When: Thu, February 12, 2015 - 4:30pm
Where: MATH 2300
Speaker: Ryan Hunter (UMCP) -

#### The geodesic equation in the space of postive Lagrangians

When: Tue, February 17, 2015 - 4:30pm
Where: MATH 2300
Speaker: Yanir Rubinstein (UMD) -

#### The space of positive Lagrangians: the geodesic equation.

When: Thu, March 26, 2015 - 4:30pm
Where: MATH2300
Speaker: Yanir Rubinstein (UMD) -

#### The space of positive Lagrangians: the geodesic equation (continued)

When: Tue, March 31, 2015 - 4:30pm
Where: MATH 2300
Speaker: Yanir Rubinstein (UMCP) -

#### Curvature of the space of positive Lagrangians (after J. Solomon)

When: Thu, April 2, 2015 - 4:30pm
Where: MATH2300
Speaker: Tamas Darvas (UMD) -

#### Curvature of the Space of Postive Lagrangians (after J. Solomon)

When: Thu, April 9, 2015 - 4:30pm
Where: MATH2300
Speaker: Tamas Darvas (UMD) -

#### Introduction to Geometric Microlocal Analysis

When: Thu, April 16, 2015 - 4:30pm
Where: MATH 2300
Speaker: Jesse Gell-Redman (JHU) -
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.

#### The Lagrandian neighborhood theorem

When: Thu, April 23, 2015 - 4:30pm
Where: MATH2300
Speaker: Matthew Dellatorre (UMD) -

#### Introduction to Geometric Microlocal Analysis (part 2)

When: Thu, May 7, 2015 - 4:30pm
Where: MATH2300
Speaker: Jesse Gell-Redman (JHU) -
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.

#### Introduction to Geometric Microlocal Analysis (part 3)

When: Thu, May 14, 2015 - 4:30pm
Where: MATH2300
Speaker: Jesse Gell-Redman (JHU) -