Tuesday, October 31, 2023
10/31/2023 - 3:00pm
Abstract: Borel--Laplace summation is a classical summability method that associates an analytic function to a divergent power series. Divergent power series often appear in mathematics and physics: solving ODEs with irregular singularities, computing asymptotics, computing perturbative expansions in QFT, in complex Chern--Simons, etc. One special feature of the Borel--Laplace sum is that it works well for integrals over Lefschetz thimbles (thimble integrals). Indeed, the Borel--Laplace sum of the asymptotics of a thimble integral is the thimble integral itself. This is part of a joint project with A. Fenyes.
10/31/2023 - 4:00pm
We discussed some properties of a family of symmetric spaces, namely SL(n,R)/SO(n,R) =: P(n), where we replace the Riemannian metric on P(n) with a premetric suggested by Selberg. These include intersecting criteria of Selberg's bisectors, the shape of Dirichlet-Selberg domains, and angle-like functions between Selberg's bisectors. These properties are generalizations of properties on the hyperbolic spaces H^n related to Poincaré's fundamental polyhedron theorem.