Peter Gothen

• Professor Associado, Departamento de Matemática, Faculdade de Ciências, Universidade do Porto.
• Member of Centro de Matemática da Universidade do Porto.

Contact information

E-mail: pbgothen (at) fc.up.pt

Phone: +351 220 402 144

Publications

• My publications on the arxiv.
• My Author Profile on MathSciNet.
• Reviews of my papers on Zentralblatt MATH.

Preprints

1. S. B. Bradlow, O. Garcia-Prada and P. B. Gothen, Higgs bundles for the non-compact dual of the special orthogonal group, arXiv:1303.1058 [math.AG].
2. P. B. Gothen, Representations of surface groups and Higgs bundles, lecture notes from my course in the January 2011 School on Moduli Spaces at the Newton Institute, to appear in the proceedings of the Moduli Spaces Programme, arXiv:1209.0568 [math.AG].
3. S. B. S. D. Castro, S. Dakhlia and P. B. Gothen, From Singularity Theory to Finiteness of Walrasian Equilibria (July 25, 2010). Available at SSRN: http://ssrn.com/abstract=1648426.
4. O. Garcia-Prada, P. B. Gothen and I. Mundet i Riera, The Hitchin-Kobayashi correspondence, Higgs pairs and surface group representations, arXiv:0909.4487 [math.AG] (v3: 15 Aug 2012, significantly improved).

Monographs

1. O. García-Prada, P. B. Gothen and V. Muñoz, Betti numbers of the moduli space of rank 3 parabolic Higgs bundles, Memoirs of the American Mathematical Society 187 (2007) no. 879, viii+80 pp. arXiv:math.AG/0411242.

Papers

1. O. Garcia-Prada, P. B. Gothen and I. Mundet i Riera, Higgs bundles and surface group representations in the real symplectic group, Journal of Topology, First published online: November 27, 2012. doi: 10.1112/jtopol/jts030. arXiv:0809.0576 [math.AG].
2. P. B. Gothen and A. Oliveira, The singular fibre of the Hitchin map, Int. Math. Res. Notices 2013 no. 5 (2013), 1079-1121, doi:10.1093/imrn/rns020. arXiv:1012.5541 [math.AG].
3. S. B. Bradlow, O. Garcia-Prada and P. B. Gothen, Deformations of maximal representations in Sp(4,R), Q. J. Math. 63 (2012), 795-843. doi: 10.1093/qmath/har010. arXiv:0903.5496 [math.AG].
4. P. B. Gothen, Higgs bundles and the real symplectic group, Proceedings of the XIX International Fall Workshop on Geometry and Physics, AIP Conf. Proc. 1360 (2011), 39-50. doi:10.1063/1.3599126. arXiv:1102.4175 [math.DG].
5. P. B. Gothen and A. Oliveira, Rank two quadratic pairs and surface group representations , Geometriae Dedicata 161 (2012), 335-375. doi:10.1007/s10711-012-9709-1. arXiv:1106.1766 [math.AG].
6. I. Biswas, P. B. Gothen and M. Logares, On moduli spaces of Hitchin pairs, Math. Proc. Cambridge Philos. Soc. 151 (2011), 441-457. doi:10.1017/S0305004111000405. arXiv:0912.4615 [math.AG].
7. S. B. S. D. Castro, S. Dakhlia, and P. B. Gothen, Direct Perturbations of Aggregate Excess Demand, Journal of Mathematical Economics 46 (2010), 562-571. doi:10.1016/j.jmateco.2010.03.008. Preprint version available at SSRN: http://ssrn.com/abstract=1156098.
8. S. B. Bradlow, O. Garcia-Prada and P. B. Gothen, Homotopy groups of moduli spaces of representations, Topology 47 (2008), 203-224. doi:10.1016/j.top.2007.06.001. arXiv:math.AG/0506444.
9. S. B. Bradlow, O. García-Prada, and P. B. Gothen, What is a Higgs bundle?, Notices of the AMS 54, no. 8 (2007), 980-981.
10. S. B. Bradlow, O. Garcia-Prada and P. B. Gothen, Maximal surface group representations in isometry groups of classical Hermitian symmetric spaces, Geometriae Dedicata 122 (2006), 185-213 (Oostende Special Issue). doi:10.1007/s10711-007-9127-y. arXiv:math.AG/0511415.
11. P. B. Gothen and A. D. King, Homological algebra of twisted quiver bundles, J. London Math. Soc. 71 (2005), 85-99. doi:10.1112/S0024610704005952. arXiv:math.AG/0202033.
12. S. B. Bradlow, O. Garcia-Prada and P. B. Gothen, Representations of surface groups in the general linear group, Proceedings of the XII Fall Workshop on Geometry and Physics, Coimbra 2003, Publicaciones de la RSME 7 (2004), 83-94. arXiv:math.AG/0401064.
13. S. B. Bradlow, O. Garcia-Prada and P. B. Gothen, Moduli spaces of holomorphic triples over compact Riemann surfaces, Math. Ann. 328 (2004), 299-351. doi:10.1007/s00208-003-0484-z. arXiv:math.AG/0211428.
14. S. B. Bradlow, O. Garcia-Prada and P. B. Gothen, Surface group representations and U(p,q)-Higgs bundles, J. Diff. Geom. 64 (2003), 111-170. arXiv:math.AG/0211431.
15. P. B. Gothen, Topology of U(2,1) representation spaces, Bull. London Math. Soc. 34 (2002), 729-738. doi:10.1112/S0024609302001364. arXiv:math.AG/0012074.
16. S. B. Bradlow, O. Garcia-Prada and P. B. Gothen, Representations of the fundamental group of a surface in PU(p,q) and holomorphic triples, C. R. Acad. Sci. Paris Sér. I Math. 333 (2001), 347-352. doi:10.1016/S0764-4442(01)02069-9. arXiv:math.AG/0107103.
17. P. B. Gothen, Components of spaces of representations and stable triples, Topology 40 (2001), 823-850. doi:10.1016/S0040-9383(99)00086-5. arXiv:math.AG/9904114.
18. P. B. Gothen, The Betti Numbers of the Moduli Space of Rank 3 Higgs Bundles, International Journal of Mathematics 5 (1994), 861-875. doi:10.1142/S0129167X94000449. Preprint version available in pdf, postscript and dvi formats.

Other Stuff

• The Topology of Higgs Bundle Moduli Spaces, Ph.D. thesis, University of Warwick, (1995). Available in pdf, postscript and dvi formats.
• A. C. Ferreira and P. B. Gothen, A cohomological approach to n-gerbes with connection, CMUP preprint 2006-13.
• Surface group representations, Higgs bundles, and holomorphic triples (with S. B. Bradlow and O. García-Prada), preprint, arXiv:math.AG/0206012.
  (Note: this preprint is an earlier version of [5] and [6] above)
• Higgs Bundles, slides from my lectures on Higgs bundles at the International School on Geometry and Physics: moduli spaces in geometry, topology and physics of the Spanish Semester on Moduli Spaces (January-June 2008).

Networks and Projects

• Topological Invariants via Differential Geometry (Principal Investigator).
• Geometria Algébrica em Portugal - Algebraic Geometry in Portugal.
• Interactions of Low-Dimensional Topology and Geometry with Mathematical Physics (member of the steering committee).
• Vector Bundles on Algebraic Curves - an international research group chaired by Peter Newstead.
• GEAR Network (GEometric structures And Representation varieties).

Seminars and Conferences

• IST Courses on Algebraic Geometry: June 25-28, 2013 - Porto, Portugal.
• Seminars of the Centro de Matemática da Universidade do Porto.
• Topological Quantum Field Theory Club (Departamento de Matemática, Instituto Superior Técnico, Lisbon.)
• Oporto Meetings on Geometry, Topology and Physics.

Teaching

• Differentiable Manifolds (1st semester 2012/2013).
• Geometry of Manifolds (2nd semester 2012/2013).