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Master Class: 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)


Here is a detailed plan for the main lectures .

  Monday 20 Tuesday 21 Wednesday 22 Thursday 23 Friday 24
9:15 Welcome        
9:30 Brown Brown Brown Brown

Gonzales 9:30-10:15

Matthes 10:20-11:05

10:30 Coffee Coffee Coffee Coffee
11:00 Alm (45') Luo (45') Hain Corwin (45') Coffee
11:30 Hain
12:00 Lunch break Lunch break   Lunch break
13:00 Excursion
13:30 Hain
14:00 Hain Hain
14:30 Fika
15:00 Fika Schlotterer (45') Fika
15:30 Saad (45') Brown
16:00 Panzer (45')
Evening       Dinner

Contributed talks:

J. Alm
The Grothendieck-Teichmueller Lie algebra and Brown's dihedral moduli spaces

A. Saad
Multiple zeta values and modular forms

M. Luo
Extensions of motives from fundamental groups

O. Schlotterer
Elliptic multiple zeta values and modular forms in string amplitudes

E. Panzer
Integration of single-valued real-analytic multiple elliptic polylogarithms on M_{1,n}.

D. Corwin
Elliptic explicit motivic Chabauty-Kim theory

M. Gonzales
The universal twisted elliptic KZB connection and elliptic MZVs at torsion points, part I

N. Matthes
The universal twisted elliptic KZB connection and elliptic MZVs at torsion points, part II

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.

Practical information

Venue: The Master Class will take place at KTH Royal Institute of Technology on Monday and Thursday (lecture room E3 ) and at the University of Stockholm on Tuesday, Wednesday, and Friday (lecture room 14, house 5 ). The two places are within walking distance of each other. The nearest local transport stops are Albano for the University and Tekniska Högskolan / Stockholms Östra for KTH. The conference hotel ( Best Western Time Hotel ) is within a 20 minute walking distance of both. 

Travel: From the airport (Arlanda, ARN) to the hotel, take the airport bus ( flygbussarna ) to Stockholm City and get off at Norra Stationsgatan. The hotel is 700 meters from the bus stop. Tickets can be bought on the bus or in advance on the web site. The buses run very frequently during the day. Avoid the train, which is more expensive and takes longer.


On Wednesday afternoon, you have the choice of a shorter hike around lake Brunnsviken  with the possibility to have tea at Koppartälten  or Gamla orangeriet . If you are interested in a longer walk, we will walk part of Roslagsleden from Täby Kyrkby to Örsta (about 3 hours). There will be some rune stones on the way. For this walk, we leave from the restaurant Kräftan at 1pm sharp.


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).