Martí Lahoz




Current Position

Maître de Conférences (MdC) of the UFR en Mathématiques of the Université Paris Diderot - Paris 7.
I am member of the project "Topologie et géométrie algébrique" (TGA) of the "Institut de Mathematiques de Jussieu - Paris Rive Gauche" (IMJ-PRG – UMR7586).

Research lines

My field of research is Algebraic Geometry. Especially I focus on the applications of abstract homological algebra constructions to the geometry of complex projective varieties.

Current Teaching / Enseignement

Cours+TD (1er semestre): MM1 - Algèbre et analyse élémentaires I - Mathématiques et informatique - Université Paris Diderot - Paris 7.
TD (1er semestre) : AG1 - Algèbre et et Géométrie I - U1MC35 - cours: Patrick Le Meur. [webpage]
Cours+TD (2ème semestre): MMAL2 - Algèbre élémentaire II - Mathématiques - Université Paris Diderot - Paris 7.


Publications & Preprints

  1. O. Debarre, Z. Jiang, and M. Lahoz, with an Appendix by W. Sawin Rational cohomology tori. To appear in Geom. Topol. [arXiv]
  2. M. Gulbrandsen and M. Lahoz, Schottky via the punctual Hilbert scheme. To appear in Tohoku Math. J. [arXiv].
  3. M. Lahoz, E. Macrì, and P. Stellari, Arithmetically Cohen–Macaulay bundles on cubic fourfolds containing a plane.
    To appear in the Proceedings of the AIM workshop "Brauer groups and obstruction problems: moduli spaces and arithmetic" (Palo Alto, 2013). [arXiv]
  4. M. Lahoz, E. Macrì, and P. Stellari, Arithmetically Cohen–Macaulay bundles on cubic threefolds. Algebraic Geometry 2 (2015), no. 2, 231–269. [Journal] [arXiv]
  5. Z. Jiang, M. Lahoz, and S. Tirabassi, Characterization of products of theta divisors. Compos. Math. 150 (2014), no. 8, 1384–1412. [Journal] [arXiv]
  6. Z. Jiang, M. Lahoz, and S. Tirabassi, On the Iitaka fibration of varieties of maximal Albanese dimension. Int. Math. Res. Not. 2013 (2013), no. 13, 2984–3005. [Journal] [arXiv]
  7. M. Lahoz and J.C. Naranjo, Theta-duality on Prym varieties and a Torelli theorem. Trans. Amer. Math. Soc. 365 (2013), no. 10, 5051–5069. [Journal] [arXiv]
  8. M. Lahoz, Generic vanishing index and the birationality of the bicanonical map of irregular varieties. Math. Z., 272, (2012), no. 3-4, 1075–1086. [Journal] [arXiv]
  9. M.A. Barja, M. Lahoz, J.C. Naranjo, and G. Pareschi, On the bicanonical map of irregular varieties. J. Algebraic Geom. 21 (2012), no.3, 445–471. [Journal] [arXiv]
  10. M. Gulbrandsen and M. Lahoz, Finite subschemes of abelian varieties and the Schottky problem. Ann. Inst. Fourier, 61 (2011), no. 5, 2039–2064. [Journal] [arXiv]
  11. S. Casalaina-Martin, M. Lahoz, and F. Viviani, Cohomological support loci for Abel-Prym curves. Matematiche 63 (2008), no. 1, 205–222. [Journal] [arXiv]

Events Co-organized

June 2016
Summer School and Conference New Methods in Birational Geometry. [webpage] Toulouse, France.
June 2016
Nordfjordeid Summer School Stability conditions on triangulated categories and geometric applications. [webpage] Sophus Lie Conference Center, Nordfjordeid, Norway.
September 2015
Workshop Derived Categories and Moduli Spaces. [webpage] Stavanger, Norway.
May 2013
Summer School Compactifying Moduli Spaces. [webpage] Barcelona, Spain.
Notes by Valery Alexeev: Moduli of Weighted Hyperplane Arrangements, Birkhäuser, 2015.
Notes by Paul Hacking, Radu Laza and Dragos Oprea: Compactifying Moduli Spaces, Birkhäuser, 2016.
July 2012
Short Summer School The derived category of cubic hypersurfaces. [webpage] Barcelona, Spain.




Previous Positions

2012 - 2013
Sophie Germain postdoc at the AGA research group of the "Département de Mathématiques d'Orsay" (UMR8628) of the Université Paris Sud 11.
2010 - 2012
SFB TR 45 postdoc at the "Mathematisches Institut" of the Universität Bonn.
2008 - 2010
Professor ajudant at the "Departament d'Àlgebra i Geometria" of the Universitat de Barcelona.
2005 - 2008
Becario FPU at the "Departament de Matemàtica Aplicada 1" of the Universitat Politècnica de Catalunya.





Previous Teaching

2014-2015
Cours+TD: MM1 - Algèbre et analyse élémentaires I - Mathématiques et informatique - Université Paris Diderot - Paris 7. [webpage]
TD: AG1 - Algèbre et et Géométrie I - U1MC35 - cours: Patrick Le Meur. [webpage]
2013-2014
Cours+TD. MM1 - Algèbre et analyse élémentaires I - Informatique - Université Paris Diderot - Paris 7. [webpage]
TD : MM2 - Algèbre et analyse élémentaires II - MASS - cours: Frédéric Han. [webpage de TD]
2012-2013
Tutoring sessions for the M2 course of Algebraic Geometry at the Université Paris Sud 11. Fall 2012. [webpage]
2008-2010
Teaching Assistant, Universitat de Barcelona, Barcelona (Spain).
Differential Geometry of Curves and Surfaces for second year bachelor's degree students in Mathematics, Fall 2008, Spring and Fall 2009.
2007-2008
Teaching Assistant, Universitat Politècnica de Catalunya, Barcelona (Spain).
Topology for second year bachelor's degree students in Mathematics, Spring 2007 and 2008.
Geometry for first year bachelor's degree students in Industrial Engineering, Spring 2007 and 2008.








Long Research Visits

Apr - May 2015
IMPA, Rio de Janeiro (Brasil). 5 weeks.
Special Thematic Program on Algebraic Geometry
Feb - Mar 2012
The Ohio State University, Columbus, Ohio (USA). 4 weeks.
Host: E. Macrì. Related topic: Derived category of cubic hypersurfaces.
Sept - Dec 2007
Università degli Studi di Roma, "Tor Vergata", Roma (Italy). 17 weeks.
Tutor: G. Pareschi. Related topic: Bicanonical Map on Irregular Varieties.
Oct - Dec 2006
Università degli Studi di Roma, "Tor Vergata", Roma (Italy). 10 weeks.
Tutor: G. Pareschi. Related topic: Castelnuovo Theory on Abelian Varieties.






Education

May 2010
Doctor (PhD) in Mathematics, algebraic geometry (UPC).
Title dissertation: Theta-duality in Abelian Varieties and the Bicanonical Map of Irregular Varieties.
Doctorate Extraordinary Award.
1999-2004
Llicenciatura (BSc) in Mathematics (UPC).