Peter Gothen

• Professor Associado, Departamento de Matemática, Faculdade de Ciências, Universidade do Porto.
• PI of the Geometry Area of the Centro de Matemática da Universidade do Porto.
• Editor-in-Chief of Portugaliae Mathematica.
• Editor of the journal Moduli.

Publications

• My publications on the arxiv.
• My Author Profile on MathSciNet.
• My Author Profile on zbMATH.
• Other identifiers (ORCID, Scopus, etc.) can be found on my official homepage.

Preprints

1. 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).

Books

1. Peter Gothen, António Guedes de Oliveira, Geometria Euclidiana Com Construções Interativas, U.Porto Press, 2021. ISBN-13: 978-989-746-293-1.
2. 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.

Book (editor)

1. Moduli spaces and vector bundles - new trends. Proceedings of the VBAC 2022 Conference, in honor of Peter Newstead's 80th birthday, July 25-29, 2022, University of Warwick, Coventry, United Kingdom. Edited by Peter Gothen, Margarida Melo and Monteserrat Teixidor i Bigas. Contemp. Math., 803 American Mathematical Society 2024. viii+370 pp.

Papers

1. S. Bradlow, B. Collier, O. Garcia-Prada, P. B. Gothen and A. Oliveira, A general Cayley correspondence and higher rank Teichmüller spaces, Annals of Mathematics (2) 200 (2024), no. 3, in press. arXiv:2101.09377 [math.AG].
2. P. M. Silva and P. B. Gothen, The conformal limit and projective structures, International Mathematics Research Notices (2024), no. 16, 11812-11831. doi:10.1093/imrn/rnae142. arXiv:2401.07759 [math.DG].
3. E. Franco, P. B. Gothen, A. Oliveira and A. Peón-Nieto, Narasimhan-Ramanan branes and wobbly Higgs bundles, International Journal of Mathematics 35 (2024), 2441006. doi:10.1142/S0129167X24410064. arXiv:2302.02736 [math.AG].
4. P. B. Gothen, Geometry on Surfaces and Higgs bundles, CIM Bulletin 45 (2023), 25-34. arXiv:2311.12506 [math.AG].
5. G. Barajas, O. García-Prada, P. B. Gothen, I. Mundet i Riera, Non-connected Lie groups, twisted equivariant bundles and coverings, Geometriae Dedicata 217 (2023), Paper No. 27, 41 pp. doi:10.1007/s10711-022-00764-w. arXiv:2208.09022 [math.DG].
6. P. Gothen and A. Guedes de Oliveira, On Euler's rotation theorem, The College Mathematics Journal 54 (2023), 171-175. doi:10.1080/07468342.2022.2015214. arXiv:2012.10757 [math.GM].
7. P. B. Gothen and R. A. Zúñiga-Rojas, Stratifications on the Nilpotent Cone of the moduli space of Hitchin pairs, Revista Matemática Complutense 35 (2022), 311–321. doi:10.1007/s13163-021-00400-3. arXiv:2006.08837 [math.AG].
8. E. Franco, P. B. Gothen, A. Oliveira and A. Peón-Nieto, Torsion line bundles and branes on the Hitchin system, Advances in Mathematics 377 (2021), 107493. doi:j.aim.2020.107493. arXiv:1802.05237 [math.AG].
9. P. Gothen and A. Guedes de Oliveira, On the classification of the rigid motions of the plane, The College Mathematics Journal 53 (2022), 315-317. CMUP preprint (2020).
10. M. Aparicio-Arroyo, S. Bradlow, B. Collier, O. Garcia-Prada, P. B. Gothen and A. Oliveira, SO(p,q)-Higgs bundles and higher Teichmüller components, Inventiones Mathematicae 218 (2019), 197-299. doi:10.1007/s00222-019-00885-2. arXiv:1802.08093 [math.AG].
11. C. Florentino, P. B. Gothen and A. Nozad, Homotopy type of moduli spaces of G-Higgs bundles and reducibility of the nilpotent cone, Bulletin des Sciences Mathématiques 150 (2019), 84-101. doi:10.1016/j.bulsci.2018.10.002. arXiv: 1805.10081[math.AG].
12. P. B. Gothen and A. Oliveira, Topological mirror symmetry for parabolic Higgs bundles, Journal of Geometry and Physics 137 (2019), 7-34. doi:10.1016/j.geomphys.2018.08.020. arXiv:1707.08536 [math.AG].
13. P. B. Gothen and A. Nozad, Quiver Bundles and Wall Crossing for Chains, Geometriae Dedicata 199 (2019), 137-146. doi:10.1007/s10711-018-0341-6. arXiv:1709.09581 [math.AG].
14. M. Aparicio-Arroyo, S. Bradlow, B. Collier, O. Garcia-Prada, P. B. Gothen and A. Oliveira, Exotic components of SO(p,q) surface group representations, and their Higgs bundle avatars, C. R. Acad. Sci. Paris, Ser. I 356 (2018), 666-673. doi:10.1016/j.crma.2018.04.024. arXiv:1801.08561 [math.AG].
15. S. B. Bradlow, O. Garcia-Prada, P. B. Gothen and J. Heinloth, Irreducibility of moduli of semistable Chains and applications to U(p,q)-Higgs bundles, Geometry and Physics: Volume 2, A Festschrift in honour of Nigel Hitchin, Oxford University Press, 2018, pp. 455-470. doi:10.1093/oso/9780198802020.003.0018. arXiv:1703.06168 [math.AG].
16. P. B. Gothen and R. A. Zúñiga-Rojas, Stratifications on the Moduli Space of Higgs Bundles, Portugaliae Mathematica 74 (2017), 127-148. doi:10.4171/PM/1996. arXiv:1511.03985 [math.AG].
17. P. B. Gothen and A. Nozad, Birationality of moduli spaces of twisted U(p,q)-Higgs bundles, Revista Matemática Complutense 30 (2017), 91-128. doi:10.1007/s13163-016-0207-0. arXiv:1602.02712 [math.AG].
18. P. B. Gothen, Hitchin Pairs for non-compact real Lie groups, Travaux Mathématiques 24 (2016), 183-200, Special issue based on School GEOQUANT at the ICMAT Madrid, Spain, September 2015. arXiv:1607.08150 [math.AG].
19. S. B. Bradlow, O. Garcia-Prada and P. B. Gothen, Higgs bundles for the non-compact dual of the special orthogonal group, Geometriae Dedicata 175 (2015), 1-48. doi:10.1007/s10711-014-0026-8. arXiv:1303.1058 [math.AG].
20. P. B. Gothen, Representations of surface groups and Higgs bundles, Moduli Spaces, pp. 151-178. Brambila-Paz L, Newstead P, Thomas RPW, Garcia-Prada O, editors, London Mathematical Society Lecture Note Series (No. 411), Cambridge University Press 2014. doi:10.1017/CBO9781107279544.004. Lecture notes from my course at the Newton Institute Moduli Spaces Programme. arXiv:1209.0568 [math.AG].
21. S. B. S. D. Castro, S. Dakhlia and P. B. Gothen, From Singularity Theory to Finiteness of Walrasian Equilibria Mathematical Social Sciences 66 (2013), 169-175. doi:j.mathsocsci.2013.03.002. Preprint version available at SSRN: http://ssrn.com/abstract=1648426.
22. 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 6 (2013), 64-118. doi: 10.1112/jtopol/jts030. arXiv:0809.0576 [math.AG].
23. 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].
24. 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].
25. 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].
26. 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].
27. 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].
28. 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.
29. 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.
30. S. B. Bradlow, O. Garcia-Prada, and P. B. Gothen, What is a Higgs bundle?, Notices of the AMS 54, no. 8 (2007), 980-981.
31. 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. doi:10.1007/s10711-007-9127-y. arXiv:math.AG/0511415.
32. 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.
33. 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.
34. 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.
35. 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. doi:10.4310/jdg/1090426889. arXiv:math.AG/0211431.
36. 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.
37. 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.
38. 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.
39. 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 was superseded by this paper and the one following it.
• Higgs Bundles, slides from my lectures on Higgs bundles at the International School on Geometry and Physics: moduli spaces in geometry, topology and physics in Castro Urdiales; Spanish Semester on Moduli Spaces (January-June 2008).
• Complementos de Geometria – M3004 (2022, class notes, in Portuguese)

Networks and Projects

Current

• Vector Bundles on Algebraic Curves (Vice-Chair of the Scientific Committee) - an international research group founded by Peter Newstead.
• The Hitchin-Ngô Lab - ICMAT Madrid.

Past (non-exhaustive)

• Mirror symmetry on Higgs bundles moduli spaces (EXPL/MAT-PUR/1162/2021, PI: André Oliveira).
• GEAR Network (GEometric structures And Representation varieties).
• Geometry of Algebraic Varieties (Principal Investigator).
• Topological Invariants via Differential Geometry (Principal Investigator).
• Interactions of Low-Dimensional Topology and Geometry with Mathematical Physics (member of the steering committee).

Conferences, workshops and schools

• Research Programme on Moduli Spaces and geometric structures, ICMAT (Madrid), April 1 - June 30, 2023.
• Workshop on Moduli Spaces and Vertex Algebras, University of Auckland, 21-23 February 2023.
• Moduli spaces and geometric structures, Conference in honour of Oscar García-Prada on the occasion of his 60th birthday ICMAT (Madrid), 12-16 September 2022.
• VBAC 2022: Moduli Spaces and Vector Bundles — New Trends, On the occasion of Peter Newstead’s 80th birthday, University of Warwick, 25-29 July, 2022.
• Algebraic Analysis and Geometry with a view on Higgs bundles and D-modules. Porto, June 3 to 7, 2019.
• Geometry and Physics of Augmented Bundles, A celebration of Steve Bradlow’s 60th birthday, May 5-7, Allerton Center, Illinois, USA.
• Hitchin 70, 5-16 September 2016, Aarhus, Oxford and Madrid.
• Higgs Bundles and Character Varieties, a satellite GEAR workshop and Special Session of the Joint International Meeting of the AMS, EMS and SPM, Porto, June 2015.
• IST Courses on Algebraic Geometry: June 25-28, 2013 - Porto, Portugal.

Seminars

• VBAC Webinars.
• CMUP Seminars.

Outreach activity

• Kolam, April to July 2018.

Photo

Geometria Projetiva - EVMAT 2016 / 2018

• Apontamentos de aulas (versão de 2018).
• Ilustração do Teorema de Desargues.
• Construção de uma cónica por cinco pontos em GeoGebra usando o Teorema de Pascal.

Contact information

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

Phone: +351 220 402 144