Cremona conference- Basel 2016
Basel, Switzerland, September 5-16, 2016,

 A Cremona transformation is a birational transformation of the plane (or more generally of the n-dimensional space). It corresponds to a map given by rational functions that admits an inverse of the same type. These maps have been a subject of study since centuries: the first appearance are in the ancient Greek: inversions and Moebius transformations.
The subject has then been really much developped by the italian school in the nineteenth century and then never ceased to interest mathematicians until now. It has also many applications and relations with other topics of mathematics, like number theory, group theory , dynamical systems or hyperbolic geometry.
The aim of this conference is to bring together a maximum of people having worked on this during the last decade, and to let young people discover it.
Speakers
In the first week (5-9 September 2016), there will be mini-courses introducing the subject, given by
Alberto CALABRI
Serge CANTAT
Igor DOLGACHEV
Stéphane LAMY
Yuri PROKHOROV
Ferrara
Rennes
Ann Arbor
Toulouse
Moscow

In the second week (12-16 September 2016), we will have research talks. Speakers are:
Eric BEDFORD
Ivan CHELTSOV
Ciro CILIBERTO
Julie DESERTI
Jeffrey DILLER
Igor DOLGACHEV
Charles FAVRE
Jean-Philippe FURTER
Marat GIZATULLIN
Massimiliano MELLA
Kenji OGUISO
Ivan PAN
Vladimir POPOV
Yuri PROKHOROV
Francesco RUSSO
Nicholas SHEPHERD-BARRON
Aron SIMIS
Junyi XIE
Indiana
Edinburgh
Roma
Paris
Notre Dame
Ann Arbor
Paris
La Rochelle
Samara
Ferrara
Tokyo
Montevideo
Moscow
Moscow
Catania
London
Recife
Toulouse
We will also have poster sessions and question sessions, in order to encourage discussions between the participants and to promote all recent results on the subject.

Schedule
Talks: In Basel, Alte Universität, Rheinsprung 9 Basel 4051
Monday  
September 5
Tuesday  
September 6
Wednesday  
September 7
Thursday  
September 8
Friday  
September 9
  9h00-10h00 
 Calabri

10h30-11h15 
 Cantat

11h30-12h30 
 Lamy
9h00-10h00 
 Cantat

10h30-11h15 
 Calabri

11h30-12h30 
 Lamy
9h00-10h00 
 Dolgachev

10h30-11h30 
 Lamy

11h45-12h45 
 Prokhorov
9h00-10h00 
 Dolgachev

10h30-11h15 
 Lamy

11h30-12h30 
 Prokhorov
       
13h30 welcome

14h00-15h00 
 Calabri

15h30-16h30 
 Cantat

17h00-18h00 
 exercise session

 Welcome Apéritif




14h00-15h00 
 Calabri

15h30-16h30 
 Cantat

17h00-18h00 
 exercise session

 Poster session


  


 social activities




14h00-14h45 
 Dolgachev

15h00-15h45 
 Prokhorov




 Apéritif





14h00-15h00 
 Dolgachev

15h30-16h30 
 Prokhorov


Monday  
September 12
Tuesday  
September 13
Wednesday  
September 14
Thursday  
September 15
Friday  
September 16
10h30 
welcome 

11h00-12h00 
 talk
9h30-10h30 
 talk

11h00-12h00 
 talk
9h30-10h30 
 talk

11h00-12h00 
 talk
9h30-10h30 
 talk

11h00-12h00 
 talk
9h30-10h30 
 talk

11h00-12h00 
 talk
       
14h00-15h00 
 talk

15h30-16h30 
 talk

17h00-18h00 
 talk

 Welcome
Apéritif
14h00-15h00 
 talk

15h30-16h30 
 talk

17h00-18h00 
 talk

 Poster session


 social activities
14h00-15h00 
 talk

15h30-16h30 
 talk

17h00-18h00 
 talk

 Question session

 Social dinner

Mini-courses - titles and abstracts
Mini-Course 1 - Alberto CALABRI - Introduction to plane Cremona maps
The following subjects will be explained: fundamental points and exceptional curves of a plane Cremona map, examples like quadratic and De Jonquières maps, properties like Noether's equations and inequality, factorization of maps and proofs of Noether-Castelnuovo theorem, Cremona equivalence of plane curves.

 
Mini-Course 2 - Serge CANTAT - Examples of birational transformations
One example of birational transformation will be given at each course. We will look at the dynamics, the sequence of degrees of iterates, the possibility to conjugate it to an automorphism or not,...

 
Mini-Course 3 - Stéphane LAMY - Polynomial automorphisms
Polynomial automophisms of the affine plane (or space) can be view as birational maps. This subgroup is sufficiently rich to share many properties with the full Cremona group, but at the same time many specific combinatorial tools are available for its study.
In particular in these lectures I plan to cover the following topics:
- Almagamated product structure of Aut(A^2) and action on the related Bass-Serre tree.
- Linearisation of finite subgroups and other consequences (description of algebraic subgroups, Tits alternative...).
- Action on (a subtree of) the tree of valuations (following Jonsson-Favre), comparison with the Bass-serre tree (they are not the same!)
- If time permits, a glimpse at possible generalisations to Tame(A^3) (or even Tame(A^n)...), of both the Bass-Serre point of view, and the valuative point of view.

 
Mini-Course 4 - Igor DOLGACHEV - Dynamical degrees and Salem numbers
I will discuss the notions of topological entropy and the equivalent notion of a dynamical degree of a birational automorphism of an algebraic surface. I will consider examples of computations of the dynamical degrees of automorphisms of Coble rational surfaces:blow-ups of at least ten points in the projective plane with no effective anticanonical divisor but with an effective bi-anticanonical divisor. The automorphism groups of such surfaces realize many interesting infinite discrete subgroups of the plane Cremona group.

 
Mini-Course 5 - Yuri PROKHOROV - Automorphism groups of Fano threefolds
I am going to speak about automorphisms of Fano varieties (with applications to finite subgroups of Cremona groups). I will start with simple examples of "interesting" automorphism groups of Fano varieties in dimension 2 and 3. Then I will explain the classification of smooth Fano 3-folds according to Iskovskikh and Mukai , and outline a recipe of describing automorphisms in terms of Hilbert schemes of lines, conics etc. Finally, if time permits, I can say something about singular Fano 3-folds.
 

Research talks
During the second week, the invited speakers will give research talk of one hour. The title / abstracts will appear some weeks before the conference beginning.

Poster sessions
All participants are welcome to present a poster during the conference. There will be two poster sessions, one in each week with an apéritif. The aim is to present to people the recent work made on Cremona transformations and encourage the discussion around the topic.
The posters have to be on A0-size (841 x 1189 mm), portrait (not landscape) or on A1-size and should not contain too much text (include pictures / diagrams, give space...). If you send us the PDF in advance, we can print it for you. We can also help you by giving advice if you are not used to make posters: email us at cremonaconference gmail if you plan to do a poster or have questions about it.

Participants which have planned to present a poster (the list can of course grow up):
Nasrollah Nejad ABBAS, Fanelli ANDREA, Mohamed BENZERGA, Marcello BERNARDARA, Jérémy BLANC, Alexander DUNCAN, Eric EDO, Ewan JOHNSTONE, Isac HEDÉN, Mattias HEMMIG, Martinez Garcia JESUS, Igor KRYLOV, Stéphane LAMY, Anne LONJOU, Alexandre MARTIN, Alexander PEREPECHKO, Rita RODRÍGUEZ VÁZQUEZ, Immanuel STAMPFLI, Christian URECH, Junyi XIE, Susanna ZIMMERMANN

Literature
People that are interested to read before the conference can have a look at the following surveys on Cremona transformations:
Cremona transformations in plane and space. Hilda. P. Hudson. Cambridge University Press, 1927.
Geometry of the plane Cremona maps Maria Alberich-Carramiñana. Lecture Notes in Mathematics, 1769, Springer-Verlag, Berlin, xvi+257, 2002.
Lectures on Cremona transformations Igor Dolgachev.
(2010-11, updated in 2016)
Some properties of the Cremona group Julie Déserti. Ensaios Matemáticos, 21. Sociedade Brasileira de Matemàtica, Rio de Janeiro, 2012. ii+188 pp.
The Cremona group in two variables Serge Cantat. Proceedings of the sixth European Congress of Math., pages 211-225 (Europ. Math. Soc., 2013)

A list (maybe not exhaustive, but quite large) of articles on Cremona transformations is available on the webpage of Julie Déserti: click here to see the list. Links to the full-text of the articles are given for most of the texts.

Participants
Nasrollah Nejad ABBAS
Jacques ALEV
Fanelli ANDREA
Dan AVRITZER
Eric BEDFORD
Mohamed BENZERGA
Hannah BERGNER
Marcello BERNARDARA
Rémi BIGNALET-CAZALET
Michel Arthur BIK
Cinzia BISI
Jérémy BLANC
Alberto CALABRI
Jung Kyu CANCI
Serge CANTAT
Ivan CHELTSOV
Ciro CILIBERTO
Nguyen-Bac DANG
Lucas DAS DORES
Matthew DAWES
Julie DESERTI
Gabriel DILL
Jeffrey DILLER
Igor DOLGACHEV
Adrien DUBOULOZ
Alexander DUNCAN
Sara DURIGHETTO
Eric EDO
Ewan JOHNSTONE
Charles FAVRE
Nestor FERNANDEZ VARGAS
Enrica FLORIS
Kento FUJITA
Mihai FULGER
Jean-Philippe FURTER
Maksymilian GRAB
Isac HEDÉN
Mattias HEMMIG
Michel HILSUM
Kyusik HONG
Andrés JARAMILLO PUENTES
Martinez Garcia JESUS
Johannes JOSI
Masayuki KAWAKITA
Igor KRYLOV
Stéphane LAMY
Kwangwoo LEE
Konstantin LOGINOV
Anne LONJOU
Frédéric MANGOLTE
Matilde MANZAROLI
Alexandre MARTIN
Massimiliano MELLA
Grigory MIKHALKIN
Olivier MILA
Dmitry MINEYEV
Filip MISEV
Shoetsu OGATA
Keiji OGUISO
Ashraf OWIS
Karol PALKA
Ivan PAN
Tomasz PEŁKA
Alexander PEREPECHKO
Pierre-Marie POLONI
Vladimir POPOV
Yuri PROKHOROV
Alexandre RAMOS PEON
Andriy REGETA
Rita RODRÍGUEZ VÁZQUEZ
Matteo RUGGIERO
Russo RUSSO
Julia SCHNEIDER
Nicholas SHEPHERD-BARRON
Constantin SHRAMOV
Aron SIMIS
Immanuel STAMPFLI
Ronan TERPEREAU
Mahdi TEYMURI GARAKANI
Takato UEHARA
Christian URECH
Anna USS
Francesco VENEZIANO
Alessandro VERRA
Alex WRIGHT
Junyi XIE
Yahor YASINSKI
Mikhail ZAIDENBERG
Susanna ZIMMERMANN
Zanjan
Reims
Basel/Düsseldorf
Belo Horizonte
Indiana
Angers
Freiburg in Brisgau
Toulouse
Dijon
Bern
Ferrara
Basel
Ferrara
Basel
Rennes
Edinburgh
Roma
Paris
Liverpool
Bath
Paris
Basel
Notre Dame
Michigan
Dijon
S. Carolina
Ferrara
Nouméa
Liverpool
Paris
Rennes
Bonn/ Basel
Kyoto
EPFL
La Rochelle
Warsaw
Kyoto
Basel
Paris
Seoul
Paris
Bonn
Geneva
Kyoto
Edinburgh
Toulouse
Seoul
Moscow
Toulouse
Angers
Paris
Vienna
Ferrara
Geneva
Bern
Moscow
Bern
Tohoku
Tokyo
Cairo
Warsaw
Montevideo
Warsaw
Moscow
Bern
Moscow
Moscow
Bern
Grenoble
Paris
Paris
Catania
Basel
London
Moscow
Recife
Hamburg
Bonn
Tehran
Saga
Basel
Warsaw
Basel
Roma
Stanford
Toulouse
Moscow
Grenoble
Basel
1-2
1-2
1-2
2
2
1-2
1-2
2
1-2
1-2
1-2
1-2
1-2
1-2
1
2
2
1-2
1-2
1
1-2
1
2
1-2
2
2
1
1-2
1
2
1-2
1-2
1-2
2
1-2
1
1-2
1-2
1
1-2
1-2
1-2
1
1-2
1-2
1-2
1
1-2
1-2
2
1
1
2
1
1
1-2
1
2
2
1-2
1-2
1-2
1
1-2
1-2
2
1-2
1
1-2
2
1-2
2
1-2
2
1-2
2
1-2
1
1-2
2
1-2
1
1-2
2
1
1-2
1-2
2
1-2

(the third column is 1-2 if the participant come on both weeks, or 1, respectively 2, if he/she comes the first, respectively the second week)
We had some partial support for the lodging, available until 1st of June.
You can still register by clicking here, but should preferably ask us if you do not have your own funding.
Participants of the swiss doctoral program in mathematics will be anyway supported, but please register not too late, if you want us to book the hotel for you.
Send an email to cremonaconference gmail com if you have questions regarding the conference.

Organisers
Jérémy Blanc, Mattias Hemmig, Christian Urech, Susanna Zimmermann

Financial support
We gratefully acknowledge support from:
University of Basel
Swiss doctoral program in mathematics