Title: The geometry and topology of lower bounds on scalar curvatureAbstract: In this talk, I will discuss some recent results about controlling the geometry and topology of manifolds from a […]

Title: On isolated singularities and generic regularity of min-max CMC hypersurfacesAbstract: Smooth constant mean curvature (CMC) hypersurfaces serve as effective tools to study the geometry and topology of Riemannian manifolds. […]

Tittle: Partial regularity for Lipschitz solutions to the minimal surface system Abstract: The minimal surface system is the Euler-Lagrange system for the area functional of a high codimension graph and reduces […]

Title: The Lawson-Osserman conjecture for the minimal surface systemAbstract: In their seminal work on the minimal surface system, Lawson and Osserman conjectured that Lipschitz graphs that are critical points of […]

Title: The Nevo-Thangavelu spherical maximal function on two step nilpotent Lie groups.Consider R^d times R^m with the group structure of a 2-step Carnot  Lie group and natural parabolic dilations.  The […]

Title: Optimal observability times for wave and Schrodinger equations on really simple domainsAbstract: Observability for evolution equations asks: if I take a partial measurement in a system, can it “see” […]

Title: Existence of 5 minimal tori in 3-spheres of positive Ricci curvatureAbstract: In 1989, Brian White conjectured that every Riemannian 3-sphere contains at least five embedded minimal tori. The number […]

Title: The Saint Venant inequality and quantitative resolvent estimates for the Dirichlet Laplacian.Abstract: Among all cylindrical beams of a given material, those with circular cross sections are the most resistant […]

Title: Restriction estimates for spectral projectionsAbstract: Restriction estimates for spectral projections have been widely studied since the work of Burq, Gérard, and Tzvetkov as a method for investigating eigenfunction concentration. […]