Department of Mathematics

Title: Intermittency and dissipation in fluid turbulenceAbstract: Intermittency is a remarkable and robust feature of three-dimensional turbulence for which we still lack explanation from first principles. It will be shown how a dissipation with a non-trivial lower-dimensional part induces a quantitative intermittent regularity on the weak solution.

Title: On the Yau--Tian--Donaldson conjecture for extremal metricsAbstract: Let X be a compact Kähler manifold. Calabi asked whether a given Kähler class on X contains a "canonical" Kähler metric, such as an extremal metric. Roughly speaking, the Yau-Tian-Donaldson conjecture states that if the Kähler class is the first Chern class of an ample line bundle, then the […]

Title: Hecke algebras, KLR algebras, and James's conjectureAbstract: I will give a brief account of the combinatorial representation theory of type A Iwahori–Hecke algebras, and their realisation as cyclotomic KLR algebras. In this story, I will largely focus on the decomposition number problem as one of the key problems in this field, and James's conjecture, which […]

Title: Counting points without abelian varieties Abstract: Counting mod p points on Shimura varieties has been for a few decades the main avenue for establishing non-abelian reciprocity laws. This began with the work of Deligne and Langlands on the modular curve, continued with that of Kottwitz on PEL type Shimura varieties, and has culminated in recent […]

Title: Immersions of small normal curvature Abstract: Given a closed manifold and a sufficiently large integer N, we study the smallest possible normal curvature, C_N(X), of all immersions of X into the unit ball of the N dimensional Euclidean space. This question was recently initiated by Gromov, who studied the case when X is the […]