Week of Events
Analysis seminar: Vlad Vicol (NYU)
Title: On Putative Self-Similarity for Incompressible 3D EulerDescription: We study hypothetical finite-time self-similar blow-up solutions to the 3D incompressible Euler equations. We prove that finite kinetic energy of the initial data implies the similarity exponent γ satisfies γ > 2/5. If a smooth globally self-similar blow-up profile exists and satisfies an outgoing condition, then γ ≥ 1/2. […]
Algebraic Geometry Seminar: Kimoi Kemboi (Princeton)
Title: The Fano of lines and the Kuznetsov component of cubic fourfoldsAbstract: A smooth cubic fourfold gives rise to two kinds of hyperkähler fourfolds: one is classical --the variety of lines on the cubic; and the other is "non-commutative" --arising from the symmetric square of the Kuznetsov component. Galkin conjectured that these two objects should be derived […]
Number Theory Seminar: Vaughan McDonald (Stanford University)
Title: Eigenvarieties over CM fields and Galois representationsAbstract: Eigenvarieties are parameter spaces for certain p-adic automorphic forms of varying weight. These objects have become increasingly popular for studying the Fontaine—Mazur conjecture, which leads us to ask what kinds of Galois representations appear on eigenvarieties. Our main result shows that for eigenvarieties for the group GL_n […]
Geometric analysis seminar: Arjun Sobnack
Title: The Harnack inequality without convexity for the Curve Shortening Flow Abstract: Everything I will discuss is joint work with P. M. Topping. In 1995, Hamilton introduced a Harnack inequality for convex solutions of the Mean Curvature Flow. Hamilton’s Harnack Inequality has played an important role in the theory of the Curve Shortening Flow (CSF), for […]