Colloquium: "Irrationality of ζ(3) and Higher Normal Functions"

Matt Kerr, Washington University in Saint Louis

Abstract: Normal functions are certain “well-behaved” sections of bundles of complex tori, first studied by Poincaré and Lefschetz.  They arise in particular from algebraic cycles (formal sums of subvarieties) on families of complex algebraic manifolds.  According to the Hodge Conjecture, one of the seven Millenium Problems, such cycles should be the only source.
A more general notion of cycles, due to Bloch and Beilinson and closely related to algebraic K-theory and motivic cohomology, leads to generalizations called “higher normal functions”.  Normal functions and their higher analogues often show up in unexpected places, explaining and generalizing observed arithmetic and functional properties of periods.
In this talk, we will give a brief tour of these ostensibly “well-behaved” functions' party-crashing exploits, in the context of irrationality proofs and Feynman amplitudes.  No knowledge of algebraic cycles (or algebraic geometry, for that matter) will be assumed.

 

Tea @ 3:45 in room 200