Masterclass: Elliptic Motives

Stockholm, May 20–24, 2019
R. Hain, F. Brown

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

One may think of the category of mixed Tate motives as the category of all objects obtained from the motive of P1 by tensor operations, extensions and taking subobjects. If in this definition we replace P1 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.

Senior lecturers:

  • Richard Hain (Duke)

  • Francis Brown (Oxford, IHES)


5 Lectures each by the senior lecturers, some contributed talks by participants. Details t.b.a.

Financial support

We expect to be able to cover, or contribute significantly to, travel and accommodation expenses for junior participants. 


The deadline for registration is 25:th of March if you would like to apply for funding or have us book a hotel room for you.

Register here


The master class is jointly organized by the Stockholm University (SU) and the Royal Institute of Technology (KTH). The funding is made available by the Stockholm Mathematics Centre (SMC).