# Masterclass: Elliptic Motives

The goal of this masterclass is to give two courses on the mathematics surrounding elliptic motives.

**Time: **
Mon 2019-05-20 09.30 - Fri 2019-05-24 12.00

**Lecturer: **
Richard Hain (Duke) and Francis Brown (Oxford, IHES)

**Location: ** E3 at KTH and room 14 at SU

One may think of the category of *mixed Tate motives* as the category of all objects obtained from the motive of P^{1} by tensor operations, extensions and taking subobjects. If in this definition we replace P^{1} by any fixed elliptic curve E we obtain instead a category of *elliptic motives*; this is a "genus-one" analogue of the theory of mixed Tate motives. Varying the elliptic curve E gives a "local system" of categories of mixed elliptic motives over the stack of elliptic curves, whose degeneration along the Tate curve at infinity may be used to study the structure of mixed Tate motives.

Several different stories come together via elliptic motives: elliptic polylogarithms, the Beilinson symbol, Manin's iterated Shimura integrals, the elliptic Knizhnik-Zamolodchikov-Bernard equation; it is a theory at the interface of algebraic K-theory, arithmetic geometry and algebraic topology. In this masterclass we hope to bring together participants from various backgrounds and give a useful introduction to aspects of this developing theory.

Target group: primarily, but not exclusively, PhD students and postdocs.

For more information see web page .