Final Report Summary - SPACE AUT (Birational geometry and polynomial automorphisms of the affine space)
SPACE-AUT - Grant Agreement number: 234954. Birational geometry and polynomial automorphisms of the affine space. The project itself, described in prose, was very successful. Lamy wrote 5 papers, including one that solves a major long-standing problem, attended about 8 conferences, defended his Habilitation (Higher Doctorate), gave a lecture course at Warwick, won a large grant from French ANR for an inter-European research network and won a prestigious full professorship at Univ. of Toulouse. Lamy's publications, preprints and works in progress are available on his website http://www.math.univ-toulouse.fr/~slamy/publi.html
Main research outcomes:
1. Lamy's work in collaboration with Serge Cantat on the non-simplicity of the Cremona group. The research was done in January-April 2010, the paper submitted in July 2010, presented at several conferences and seminars (Edinburgh, Warwick, Toulouse, Paris, Lyon...). The result is a major breakthrough on a long-standing problem. The grant allowed Lamy to spend 15 days in Rennes in January 2010 at the beginning of this project. Serge Cantat and Stéphane Lamy, Normal subgroups in the Cremona group, Acta Mathematica to appear Vol 207, 2012, preprint arXiv: 1007. 0895, 53 pages.
2. Habilitation: Lamy's mémoire was written in March-May 2010, and defended at Lyon in October 2010, with panel consisting of Mikhail Zaidenberg (Grenoble), Etienne Ghys (Lyon), Michel Brion (Grenoble), Miles Reid (Warwick) and Lucy Moser-Jauslin (Dijon). The papers making up the Mémoire d'Habilitation are available on Lamy's website: http://www.math.univ-toulouse.fr/~slamy/publi.html
3. Affine Sarkisov program: Lamy read the preprint of Hacon-McKernan and wrote notes on it. In May 2010 he initiated a collaboration with Jérémy Blanc with the aim of producing some examples of automorphisms on the complement of a smooth cubic surface in PP^3. He gave a series of lectures at a Winter School in Switzerland in Jan 2011 related to this material; the lecture notes are available from Lamy's website. Lamy also collaborated with Dubouloz (Dijon) on the related Sarkisov program in the log category. Adrien Dubouloz and Stéphane Lamy, Variations on Log Sarkisov Program for Surfaces, arXiv: 0802. 2441, 26 pp.
4. Tame Polynomial automorphisms of CC^3: from Aug 2010, Lamy worked on the Kuroda's recent reworking of the proof of the existence of non-tame automorphisms of CC^3. The notes he wrote on this are available from http://www.math.univ-toulouse.fr/~slamy/stock/notes_kuroda.pdf and he reported on this work in a Dijon workshop in November 2010. Lamy initiated a collaboration with Stephan Vénéreau with the aim to extend these results to the case of the automorphisms on the complement of a quadric in P^3. S. Lamy and S. Vénéreau, The tame and the wild automorphisms of an affine quadric threefold, to appear in J. of Japan Math Soc., preprint arXiv: 1103. 4291, 16 pp.
5. Lamy's collaboration with J. Blanc produced an article on Sarkisov link derived from a space curve. Lamy initiated a follow-up project with Ivan Pan during an Apr 2011 visit to Montevideo, Uruguay funded by the grant. Jeremy Blanc and Stephan Lamy, Weak Fano threefolds obtained by blowing-up a space curve and construction of Sarkisov links, preprint arXiv: 1106. 3716, 33 pages.
Other outcomes:
1. Lamy's Habilitation (higher doctorate) qualified to apply for a Professorial position in France from early 2011. Lamy won such a position, and is now full Professor at Univ. of Toulouse.
2. Follow-up grants. Lamy collaborated with Blanc, Cantat, Dubouloz and others in winning a large grant from French ANR for a 4-year inter-European project "Automorphismes polynomiaux et transformations birationnelles". The project continues several strands of Lamy's work at Warwick on his Marie Curie fellowship. The project website is http://birpol.math.cnrs.fr
Main research outcomes:
1. Lamy's work in collaboration with Serge Cantat on the non-simplicity of the Cremona group. The research was done in January-April 2010, the paper submitted in July 2010, presented at several conferences and seminars (Edinburgh, Warwick, Toulouse, Paris, Lyon...). The result is a major breakthrough on a long-standing problem. The grant allowed Lamy to spend 15 days in Rennes in January 2010 at the beginning of this project. Serge Cantat and Stéphane Lamy, Normal subgroups in the Cremona group, Acta Mathematica to appear Vol 207, 2012, preprint arXiv: 1007. 0895, 53 pages.
2. Habilitation: Lamy's mémoire was written in March-May 2010, and defended at Lyon in October 2010, with panel consisting of Mikhail Zaidenberg (Grenoble), Etienne Ghys (Lyon), Michel Brion (Grenoble), Miles Reid (Warwick) and Lucy Moser-Jauslin (Dijon). The papers making up the Mémoire d'Habilitation are available on Lamy's website: http://www.math.univ-toulouse.fr/~slamy/publi.html
3. Affine Sarkisov program: Lamy read the preprint of Hacon-McKernan and wrote notes on it. In May 2010 he initiated a collaboration with Jérémy Blanc with the aim of producing some examples of automorphisms on the complement of a smooth cubic surface in PP^3. He gave a series of lectures at a Winter School in Switzerland in Jan 2011 related to this material; the lecture notes are available from Lamy's website. Lamy also collaborated with Dubouloz (Dijon) on the related Sarkisov program in the log category. Adrien Dubouloz and Stéphane Lamy, Variations on Log Sarkisov Program for Surfaces, arXiv: 0802. 2441, 26 pp.
4. Tame Polynomial automorphisms of CC^3: from Aug 2010, Lamy worked on the Kuroda's recent reworking of the proof of the existence of non-tame automorphisms of CC^3. The notes he wrote on this are available from http://www.math.univ-toulouse.fr/~slamy/stock/notes_kuroda.pdf and he reported on this work in a Dijon workshop in November 2010. Lamy initiated a collaboration with Stephan Vénéreau with the aim to extend these results to the case of the automorphisms on the complement of a quadric in P^3. S. Lamy and S. Vénéreau, The tame and the wild automorphisms of an affine quadric threefold, to appear in J. of Japan Math Soc., preprint arXiv: 1103. 4291, 16 pp.
5. Lamy's collaboration with J. Blanc produced an article on Sarkisov link derived from a space curve. Lamy initiated a follow-up project with Ivan Pan during an Apr 2011 visit to Montevideo, Uruguay funded by the grant. Jeremy Blanc and Stephan Lamy, Weak Fano threefolds obtained by blowing-up a space curve and construction of Sarkisov links, preprint arXiv: 1106. 3716, 33 pages.
Other outcomes:
1. Lamy's Habilitation (higher doctorate) qualified to apply for a Professorial position in France from early 2011. Lamy won such a position, and is now full Professor at Univ. of Toulouse.
2. Follow-up grants. Lamy collaborated with Blanc, Cantat, Dubouloz and others in winning a large grant from French ANR for a 4-year inter-European project "Automorphismes polynomiaux et transformations birationnelles". The project continues several strands of Lamy's work at Warwick on his Marie Curie fellowship. The project website is http://birpol.math.cnrs.fr