Categorical actions in geometry and representation theory
Clemens Koppensteiner
Member, School of Mathematics
September 29, 2017
This paper proves the first super-logarithmic lower bounds on the cell-probe complexity of dynamic boolean (a.k.a. decision) data structure problems, a long-standing milestone in data structure lower bounds.
According to Langlands, pure motives are related to a certain class of automorphic representations.
Can one see mixed motives in the automorphic set-up? For examples, can one see periods of mixed motives in entirely automorphic terms? The goal of this and the next lecture is to supply some examples.
We define motivic correlators describing the structure of the motivic fundamental group $\pi_1^{\mathcal M}(X)$ of a curve. Their relevance to the questions raised above is explained by the following examples.