Universidad Politécnica de Cataluña
Departamento de Matemáticas
Laboratorio de Geometría y Sistemas Dinámicos
EPSEB, Edificio B
Av. Doctor Marañón 44-50
08028, Barcelona
E-Mail: ana.peon [at] upc.edu
Here is a copy of my CV.
Research Interests
Geometry and topology of moduli spaces of Higgs bundles. The Hitchin fibration.
Relation with representation varieties, geometric structures and physics.
Published papers
Fixed point branes, singular loci and mirror symmetry. To appear in Oberwolfach Reports, doi: 10.4171/OWR/2019/23
ArXiv.Moduli spaces of framed G-Higgs bundles and symplectic geometry (with Indranil Biswas and Marina Logares). Comm. Math. Phys. (2019) doi:10.1007/s00220-019-03531-3
ArXiv.Symplectic geometry of a moduli space of framed Higgs bundles (with Indranil Biswas and Marina Logares). International Mathematics Research Notices, rnz016, https://doi.org/10.1093/imrn/rnz016.
ArXiv.Very stable bundles and properness of the Hitchin map (with Christian Pauly). A. Geom Dedicata (2018). https://doi.org/10.1007/s10711-018-0333-6.
ArXiv.Higgs bundles for real groups and the Hitchin-Kostant-Rallis section (with Óscar García-Prada and S. Ramanan). Trans. of the Amer. Math. Soc. 370, 4 (2018), 2907-2953
ArXiv.On σδ-Picard-Vessiot extensions, Communications in Algebra 34, 4 (2011), 1242-1249
Preprints
Unramified covers and branes on the Hitchin system (with Emilio Franco, Peter B. Gothen and André G. Oliveira). arxiv:1802.05237 [math.AG].
The Borel subgroup and branes on the Higgs moduli space (with E. Franco). arxiv:1709.03549[math.AG].
Cameral data for SU(p,p+1)-Higgs bundles. Arxiv
Higgs bundles, abelian gerbes and cameral data. (with Óscar García-Prada). arXiv:1902.06139
Education
PhD, Mathematics, August 2009 - December 2013, Universidad Autónoma de Madrid
Advisors: Luis Álvarez-Cónsul and Óscar García-Prada
Title: Higgs bundles, real forms and the Hitchin fibration
Master 2 Mathématiques Fondamentales, September 2006 - June 2007, Université Paris 7 Denis-Diderot
Thesis Title: Théorie des Modèles et Géométrie Réelle
Advisor: Max Dickmann
Licenciatura en Matemáticas, September 2002 - June 2006, Universidad Autónoma de Madrid
Work Experience
Postdoctoral Researcher (Beatriu de Pinós Fellow), November 2019 - present, Universidad Politécnica de Cataluña, Spain.
Postdoctoral Researcher (Assistante), March 2018 - September 2019, Université de Genève, Switzerland.
Postdoctoral Researcher, January 2014 - December 2016, MATCH, Ruprecht-Karls-Universität Heidelberg, Germany.
Teaching assistant, Universidad Autónoma de Madrid 2011/12, 2012/13.
Monitrice (teaching assistant), Université Paris 7 2007/08, 2008/09.
Teaching: past and new
Problem classes for Analyse complexe 2. 2nd year Bachelor Mathématiques/Physique. Université de Genève 2017/18, 2018/19.
Seminar Lie algebras and representation theory, Winter semester 2014/15.
Algebraic geometry for physicists October 6-10 2014, as part of the Physics graduate days. Notes: Affine varieties, Projective varieties, Schemes, Sheaf cohomology.
Problem classes for Matemáticas I. 1st year Grado en Ingeniería Química. Universidad Autónoma de Madrid 2011/12, 2012/13.
Problem classes for Analyse et Algèbre de base. L1 Physique. Université Paris 7 2007/08, 2008/09.
Invited talks
February 28, 2020. Seminario de Geometría Algebraica, Barcelona. TBA.
February 5-7, 2020. Malaga &Topology Meeting, Málaga. TBA.
December 6th, 2019. Institut de Mathématiques de Jussieu, Séminaire d'algèbre. Fibrés très stables, symétrie miroir et le programme de Langlands géométrique.
October 25th, 2019. Universidade do Porto, Seminario de Geometria. Wobbly and shaky bundles in geometric Langlands.
July 30, 2019. ISAAC 2019, special session on complex geometry, Aveiro. Mirror symmetry on some non generic loci of the Hitchin system.
June 13, 2019. Universidad de Santiago de Compostela. Geometría del sistema de Hitchin.
May 14, 2019. Geometry and Physics of Higgs Bundles, MFO. Fixed point branes, singular loci and mirror symmetry.
April 12, 2019. Harmonic maps and Rigidity, Sisteron. Arithmetic lattices.
February 18, 2019. Women at the intersection of geometry and high energy physics, Université de Genève. Geometry and physics of Hitchin systems.
December, 2018. Université de Fribourg. A criterion for very stability via the Hitchin map.
November, 2018. New trends in Higgs bundle theory, ICMAT. Branes on the Hitchin system from torsion line bundles.
April, 2018. Université de Genève. Mirror symmetry and branes on the singular locus of the Hitchin system.
February 13, 2018. Université d'Orsay. Topological mirror symmetry and branes.
January 11, 2018. Universidad de Salamanca. Topological mirror symmetry and branes.
October 19, 2017. Université de Nice. Parabolic subgroups and mirror symmetry on the singular locus of the Hithin system.
April 1, 2016. Universidad Central de Barcelona. Mirror symmetry for Cartan branes.
March 11, 2016. Universidade do Porto. Mirror symmetry for Cartan branes.
February 29-March 3, 2016. Higgs Bundles in Geometry and Physics, IWH Heidelberg. Mirror symmetry for Cartan branes.
February 2, 2016. Goethe Universitaet Frankfurt. SU(p,p+1)-Higgs bundles and the Hitchin map.
January 11-15, 2016. Higgs bundles and Hitchin system - VBAC2016, CIB Lausanne. A cameral construction for Higgs bundles for quasi-split real forms.
December 10, 2015. Université de Rennes 1. Une construction camérale pour des fibrés de Higgs pour des groupes algébriques réels quasi-déployés.
October 5-16, 2015. 50 years of the Narasimhan-Seshadri theorem, Chennai Mathematical Institute. Cameral covers, real forms and the Hitchin map.
September 29-27, 2015. Current trends on spectral data for Higgs bundles. Cameral covers and quasi-split forms
June 9-12, 2015. Joint meeting AMS/EMS/SPM, Special session on Higgs bundles and character varieties, Oporto. Slides.
April 14, 2015. Université de Lille. Fibrés de Higgs, groupes réels et le systèsme de Hitchin.
March 16, 2015. Université de Marseille. Fibrés de Higgs, groupes réels et le systèsme de Hitchin.
March 12, 2015. Université de Nice. Fibrés de Higgs, groupes réels et le systèsme de Hitchin.
November 24, 2014. Université de Strasbourg. Fibrés de Higgs, formes reélles et la section de Hitchin--Kostant--Rallis.
November 10-14 2014. Conference Geometric Structures and representation varieties, KIAS, Seoul. Minicourse " Connected components of representation varieties. A view through Higgs bundles. "
June 2014 Workshop on the Geometry and Physics of Moduli Spaces, Miraflores de la Sierra (Madrid, Spain). " Higgs bundles and abelianization "
April 2014, Center for symmetry and representations, University of Copenhagen (Denmark). " Abelianization of Higgs bundles "
December 2013, Geometry seminar, Universidad complutense de Madrid (Spain). " Higgs bundles, real forms and gerbes "
July 2013, Geometry seminar, Ruprecht-Karls Universität, Heidelberg (Germany). " Higgs bundles, real forms and cameral covers"
March 2013, Hitchin Lab workshop, Miraflores de la Sierra (Spain). " The Hitchin fibration for real forms through cameral covers. "
February 2013, Math-Physics seminar, University of Pennsylvania, Philadelphia (USA). " Higgs bundles, real forms and cameral covers"
Other math stuff
Click here for the poster " Higgs bundles and abelianization " that I presented at the Second Gear Retreat, University of Maryland, (USA).
Slides of the talk " Higgs bundles and abelianization " (May 2014 Second Junior Gear Retreat, Ann Arbor).
Some latex tricks: how to cite authors with multiple surnames (very useful for Spaniards...)
last updated: January 8, 2020