Seminar

TY 427

The purpose of this series of talks is to introduce Schwarzschild universe and a non-commutative generalization.  This first talk focuses on the Schwarzschild universe, by which we mean a maximal conformal analytic extension of the static, spherically symmetric space-time vacuum.  We shall discuss the structure of its null geodesics (they are elliptic curves), null geodesic deviation, and the theorem proven jointly by the speaker and George Sparling that every null geodesic in Schwarzschild "feels" the temperature of the singularity (a la Gibbons and Hawking).

Abstract. This is a report on joint work with Dan Ciubotaru.  We consider a cuspidal automorphic representation π of a semisimple group G over a function field K.  When G = PGL(n), the Ramanujan conjecture, which asserts that every local component of π is tempered, was proved in connection with the global Langlands correspondence by L.

Abstract: A basic problem in extremal graph theory is to find large graphs
that contain no copy of a specific subgraph. Surprisingly, in
essentially all the known instances, the best constructions for this
problem come from appropriate varieties. I will present several such
constructions, and give a survey of the area.

This is a the second talk of the series of two talks in which we give a sketch of the main ideas motivating the Langlands Program. These are designed to be pre-talks in preparation for Professor Michael Harris's Michalik Lecture on Sept 30 and his ACoG seminar talk on Sept 29.

Abstract