Organizers: Ioakeim Ampatzoglou, Dan Ginsberg, Weilin Li, Vincent Martinez, and Azita Mayeli
Time: Friday, 2:00-4:00pm EST
Location (in-person and hybrid): GC 9116
Zoom: link Passcode: HAPDE2024
Current Schedule (Fall 2025)
January 30
Speaker: Kevin Dembski (Duke)
Title: Singularity Formation in the Incompressible Porous Medium Equation without Boundary Mass
Abstract: In this talk, I will discuss recent work on the problem of singularity formation in the incompressible porous medium (IPM) equation. We construct Lipschitz continuous solutions of the IPM equation which vanish on the boundary of the domain and blow-up in finite time. At the blow-up point, the flow is hyperbolic with points approaching the boundary from the interior and escaping tangent to the boundary.
February 6
Speaker: Genevieve Romanelli (CUNY)
Title: Form Uniqueness for Weakly Spherically Symmetric Graphs
Abstract: Dirichlet forms are generalizations of the Laplacian which are especially useful for studying infinite graphs. Importantly, unlike with traditional graph Laplacians on finite graphs, there may not be a unique operator and Dirichlet form associated to a graph. I will provide two characterizations for uniqueness of the Dirichlet form on graphs satisfying a certain spherical symmetry constraint, one via graph structure and the other via boundary capacity. Time permitting, I will give some stability results. This work was joint with Luis Hernandez, Sean Ku, Jun Masamune, and Radoslaw Wojciechowski.
February 13
Speaker: Han Li (CUNY)
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February 27
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March 13
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March 20
(No seminar) CUNY closed
March 27
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April 3
(No seminar) CUNY closed for spring break
April 10
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