The Grothendieck-Teichmüller Theory of Dessins d'Enfants
Organiser
Name | Institution |
---|---|
Jones, Gareth | University of Southampton |
Wolfart, Juergen | Goethe-Universität, Frankfurt |
Dessins d'enfants is a theory, initiated by Grothendieck in 1984, which uses maps on surfaces to create a link between on the one hand the Teichmüller theory of Riemann surfaces, and on the other hand the Galois theory of algebraic number fields and the algebraic curves defined over them. The theory thus provides surprising and powerful connections between such apparently dissimilar fields as algebraic geometry, algebraic number theory, combinatorics, Galois theory, group theory, Teichmüller theory and topology, and provides a fertile ground for collaborations between members of these different disciplines.
The main theme of the meeting will be dessins d'enfants, but this will be interpreted very broadly. The workshop will appeal to participants whose interest in the subject comes from many different areas of mathematics: in particular areas such as algebraic geometry, combinatorics, Galois theory, group theory, Riemann surfaces and Teichmüller theory, with participants who are experts (or in some cases, promising beginners) in the theoretical and practical aspects of these subjects. This workshop will involve younger mathematicians from a wide range of relevant mathematical disciplines, and from further afield, with the emphasis of the workshop being on interactive discussion and collaboration.
Numbers will be limited to a maximum of 35 and there will be a contribution to local costs (including accommodation and subsistence) from awards to ICMS. A Registration Fee of £30 will be payable by all delegates.
Participation is by invitation only: those interested in attending should contact Gareth Jones (g.a.jones@maths.soton.ac.uk).
Arrangements
Participation
Participation is by invitation only. The workshop will begin on Monday 8 September and finish on Friday 12 September 2008.
UK Visas
If you are travelling from overseas you may require an entry visa. A European visa does not guarantee entry to the UK. Please use this link to the UK Visas site to find out if you need a visa and if so how to apply for one. If you do require a visa, ICMS can provide a signed invitation letter.
Venue
The workshop will take place at the head-quarters of ICMS, 14 India Street, Edinburgh. This house is the birthplace of James Clerk Maxwell and is situated in the historic New Town of Edinburgh, near the city centre.
The ICMS travel pages contain advice on how to travel to Edinburgh. For local information the finding ICMS page shows the location of ICMS and contains useful maps of the city centre.
The seminar room at ICMS has four whiteboards, two overhead projectors, a data projector and laptop.
Wireless access is available throughout the ICMS building. There are also three public PCs which may be used at any time for internet access and to check email.
Accommodation
ICMS will arrange single en-suite rooms in local guest houses for those who require it. Accommodation is typically about 15 to 30 minutes walk from ICMS. Participants are also free to make their own arrangements and may claim back the cost, with receipts, up to a maximum of £45.00 per night bed and breakfast. A list of Edinburgh accommodation of various sorts and prices is available here . Sections 1-3 are particularly relevant.
Meals and Refreshments
Buffet lunches will be provided on Monday 8 September and Friday 12 September only. For the remainder of the days, participants are free to go out for lunch and explore the many cafes, restaurants, sandwich shops and bars in the surrounding area. On arrival we will provide you with a ‘welcome’ pack which will contain information about eating places nearby.
Morning and afternoon refreshments will be provided throughout the workshop.
There will be an informal wine reception after the close of lectures on Monday 8 September.
On Tuesday 9 September there will be an informal supper at a local restaurant. The workshop dinner will take place on the evening of Thursday 11 September.
Registration
Registration will take place on Monday 8 September.
Financial Arrangements
Unless otherwise specified in your invitation letter, the workshop grant will cover the cost of your bed and breakfast accommodation, tea/coffee throughout the workshop, lunch on Monday and Friday, the wine reception, the informal supper on Tuesday and the Workshop Dinner on Thursday evening.
If we have agreed to pay some of your travel costs, you will be informed by email. Reimbursement will take place after the workshop. At Registration you will be given an expenses claim form and this should be submitted to ICMS, with receipts and bank details. Please note that we cannot reimburse any item without a receipt.
Under the terms of our EPSRC funding we are required to charge a 30.00 GBP registration fee to cover costs not admissible under the grant. The fee will be payable on arrival at the workshop: payment may be by cash, sterling cheque or credit/debit card. If you anticipate any difficulty covering the fee, please let us know.
Programme
Monday 08 September
09.00 - 10.00 | Registration and coffee |
10.00 - 11.00 | Juergen Wolfart (Goethe-Universität, Frankfurt) |
11.15 - 11.45 | Milagros Izquierdo Barrios (Linköpings Universitet) |
12.00 - 12.30 | David Singerman (University of Southampton) |
12.30 - 14.15 | Buffet lunch |
14.15 - 15.15 | Robert Silhol (Université Montpellier 2) |
15.30 - 16.00 | Bernhard Koeck (University of Southampton) |
16.00 - 16.30 | Coffee/tea break |
16.30 - 17.00 | Grzegorz Gromadzki (University of Gdansk) |
17.15 - 17.45 | Frank Feierabend (Goethe-University) |
18.00 - 18.45 | Wine Reception in the Exhibition Room at ICMS |
Tuesday 09 September
09.30 - 10.15 | Alexander Mednykh (Sobolev Institute of Mathematics) |
10.15 - 10.45 | Coffee/tea break |
10.45 - 11.30 | Roman Nedela (Slovak Academy of Sciences/Matej Bel University) |
11.45 - 12.15 | Martin Skoviera (Comenius University) |
12.15 - 14.00 | Lunch break |
14.00 - 15.00 | Jan-Cristoph Schlage-Puchta (Universität Freiburg) |
15.15 - 15.45 | Jozef Siran (Open University) |
15.45 - 16.15 | Coffee/tea break |
16.15 - 16.45 | Anthony Weaver (City University of New York) |
17.00 - 17.30 | Aaron Wootton (University of Portland) |
19.00 | Informal evening meal at Athena Greek Restaurant, 89 Hanover Street |
Wednesday 10 September
09.30 - 10.30 | Gabriela Schmithuesen (Universität Karlsruhe (TH)) |
10.30 - 11.00 | Coffee/Tea |
11.00 - 11.30 | Frank Herrlich (Universität Karlsruhe (TH)) |
11.45 - 12.15 | Ernesto Girondo Sirvent (Universidad Autonoma de Madrid) |
12.15 - 14.00 | Lunch break |
14.00 - 15.00 | Pierre Lochak (Institut de Mathématiques de Jussieu) |
15.00 | Free time |
Thursday 11 September
09.30 - 10.30 | Marston Conder (University of Auckland) |
10.30 - 11.00 | Coffee/Tea |
11.00 - 11.30 | Cormac Long (University of Southampton) |
11.45 - 12.15 | Antonio Breda d'Azevedo (Universidade de Aveiro) |
12.15 - 14.00 | Lunch break |
14.00 - 15.00 | Gabino Gonzalez-Diez (Universidad Autonoma de Madrid) |
15.15 - 15.45 | Alexandre Zvonkine (Université Bordeaux I) |
15.45 - 16.15 | Coffee/Tea |
16.15 - 16.45 | George Shabat (Russian State University for the Humanities) |
17.00 - 17.30 | George Shabat delivered on behalf of Vladimir Dremov |
19.00 | Workshop dinner at First Coast Restaurant, 99-101 Dalry Road, Edinburgh |
Friday 12 September
09.00 - 09.30 | Fedor Pakovich (Ben Gurion University of the Negev) |
09.45 - 10.15 | Carlo Hamalainen (Charles University) |
10.15 - 10.45 | Coffee/Tea |
10.45 - 11.15 | Cristina Sarti (Universität Frankfurt) |
11.30 - 12.00 | Daniel Pinto (Universidade de Coimbra) |
12.15 - 13.15 | Gareth Jones (University of Southampton) |
13.15 - 14.15 | Buffet lunch |
Presentations
For two given dessins d'enfants, when do they induce the same complex
structure? We will describe in this talk how hyperbolic geometry might be useful to answer the question for the case of uniform dessins in genus 2. The talk is based in some work actually in progress by the author in collaboration with David Torres (Madrid).
Beauville surfaces were introduced by Catanese in 2000 and then studied by himself jointly with Bauer and Grunewald. I shall attempt to report on the significance of these objects and on some results obtained by these authors as well as on more recent work carried out by Y. Fuertes, A. Jaikin and myself.
over the algebraic numbers if and only if the corresponding
Riemann surface can be uniformized by a subgroup of a Fuchsian
triangle group. Such surfaces are known as Belyi surfaces and an
important class of them consists of Riemann surfaces having
so-called large group of automorphisms. Necessary and sufficient
algebraic conditions for these surfaces to be symmetric
were found by Singerman in the middle of seventies and by a recent result of K"ock and Singerman, these numbers can be chosen to be
real if and only if the respective surface is symmetric. The aim
of this talk is to give, in similar like Singerman's terms, formulas for the
topological type of the corresponding symmetries, to which we refer
as to the title symmetries and which correspond the topological type
to the real forms of initial curve.
this talk I will introduce latin bitrades, their representation as
hypermaps, and pose some open problems relating to Belyi functions.
In the talk I shall also focus on a second relation between origamis and dessins d'enfants, namely a construction which associates a dessin to every cusp of an origami curve.
Motivated by the results obtained for surfaces, it is reasonable to ask whether analogous theorems can be obtained in higher dimensions. In this talk, a brief survey of current work in this area will be presented, together with a look at some specific results in the case of hyperbolic 3-manifolds. Particular attention will be given to the Lanner groups, where a classification of all PSL(2,q) groups arising as quotients of these groups will be given.
"Find the number of non-equivalent n-fold orientable coverings of a given non-orientable manifold with a finitely generated fundamental group."
The main purpose of this report is to give a solution of the Liskovets problem. As an
application, we enumerate reflexible coverings and chiral pairs of coverings of a non-orientable manifold with a finitely generated fundamental group. These results form a background for counting chiral pairs of maps and hypermaps on closed orientable surface. It will be done in a forthcoming paper by A. Breda, R. Nedela and A. Mednykh. The obtained formula for the number of reflexible coverings allows also to count self-dual and Petri-dual maps and other combinatorial objects.
New results are based on systematic use of maps on orbifolds. Both orientable and non-orientable case will be considered.
nonorientable hypermaps of a given genus g and type (l,m,n), when two
of the parameters are equal. The methods used in those constructions are
adapted from the ones previously developed for orientable hypermaps.
projective spaces P^m(F_n). In this context Galois automorphisms of finite fields play a crucial role
Given such an orbit the family it defines can also be described from a hyperbolic point of view (in terms of Fuchsian groups or Fenchel-Nielsen coordinates) and in some cases in terms of equations.
Using these descriptions the natural action of SL2(Z) on such families can be interpreted in terms of the hyperbolic structure and be described as an action on the equations of Galois groups of coverings.
We generalize this covering setting and put it in the context of Culler-Vogtmann's Outer Space, the classifying space of marked metric finite graphs with a fixed fundamental group. The study of origamis in Outer Space enables us to obtain new insights on the classical objects in Teichmüller space.
Participants
Name | Institution |
---|---|
Antonio, Breda d'Azevedo | Universidade de Aveiro |
Marston, Conder | University of Auckland |
Frank, Feierabend | Goethe-University |
Herbert, Gangl | University of Durham |
Ernesto, Girondo Sirvent | Universidad Autonoma de Madrid |
Gabino, Gonzalez-Diez | Universidad Autonoma de Madrid |
Grzegorz, Gromadzki | University of Gdansk |
Carlo, Hamalainen | Charles University |
Frank, Herrlich | Universität Karlsruhe (TH) |
Milagros, Izquierdo Barrios | Linköpings Universitet |
Gareth, Jones | University of Southampton |
Bernhard, Koeck | University of Southampton |
Zoe, Laing | University oF Southampton |
Pierre, Lochak | Université Paris Pierre et Marie Curie |
Cormac, Long | University of Southampton |
Alexander, Mednykh | Sobolev Institute of Mathematics |
Benjamin, Muelhbauer | Goethe-University Frankfurt |
Roman, Nedela | Slovak Academy of Sciences/Matej Bel University |
Fedor, Pakovich | Ben Gurion University of the Negev |
Daniel, Pinto | Universidade de Coimbra |
Cristina, Sarti | Universität Frankfurt |
Robert, Scheichl | University of Bath |
Jan-Cristoph, Schlage-Puchta | Universität Freiburg |
Gabriela, Schmithuesen | Universität Karlsruhe (TH) |
George, Shabat | Russian State University for the Humanities |
David, Singerman | University of Southampton |
Jozef, Siran | Open University |
Martin, Skoviera | Comenius University |
Manfred, Streit | DB Systel |
Anthony, Weaver | City University of New York |
Juergen, Wolfart | Goethe-Universität, Frankfurt |
Aaron, Wootton | University of Portland |
Alexandre, Zvonkine | Université Bordeaux I |