Peter Gothen

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

Publications

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

Preprints

1. O. Garcia-Prada, P. B. Gothen and I. Mundet i Riera, Representations of surface groups in the real symplectic group, arXiv:0809.0576 [math.AG].
2. 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].
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.

Papers

1. 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.
2. 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.
3. 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.
4. 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.
5. 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.
6. 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.
7. 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.
8. 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.
9. 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.
10. 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.
11. 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.
12. 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.
13. 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].
14. S. B. Bradlow, O. Garcia-Prada and P. B. Gothen, Deformations of maximal representations in Sp(4,R), Q. J. Math., first published online June 21, 2011, doi: 10.1093/qmath/har010. arXiv:0903.5496 [math.AG].
15. 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].
16. P. B. Gothen and A. Oliveira, The singular fibre of the Hitchin map, Int. Math. Res. Notices, first published online: February 17, 2012, doi:10.1093/imrn/rns020. arXiv:1012.5541 [math.AG].
17. P. B. Gothen and A. Oliveira, Rank two quadratic pairs and surface group representations , Geometriae Dedicata, to appear. doi:10.1007/s10711-012-9709-1. arXiv:1106.1766 [math.AG].

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.

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.

Post-doctoral opportunities

• A nine month postdoc position is avaliable within the Topological Invariants via Differential Geometry project starting June 15, 2012. For details see the call for applications.

Seminars and Conferences

• 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 2011/2012).
• Geometria Diferencial (M355) (2nd semester 2011/2012).

Address

E-mail: pbgothen (at) fc.up.pt
Phone: +351 220 402 144