Dr Ana Peón-Nieto PhD

Dr Ana Peón-Nieto

School of Mathematics
Lecturer (Assistant Professor)

Contact details

Address
University of Birmingham
Edgbaston
Birmingham
B15 2TT
UK

Dr. Peón-Nieto’s work focuses on Higgs bundles. These objects appeared as solutions to differential equations motivated by physics; they are to monopoles what the latter are to instantons. Several approaches allow to tackle Higgs bundles, be it from the differential, symplectic or algebraic geometric point of view. This richness has led to connections with many subjects in mathematics and physics, such as integrable systems, mirror symmetry, geometric structures, gauge theory, S-duality, the geometric Langlands programme,… most of which appear either directly or as a motivation in Dr. Peón-Nieto’s research.

As a postdoc, Dr. Peón-Nieto was awarded several post-doctoral fellowships, including a Marie Sklodowska-Curie European Individual Fellowship (2020-2022), Juan de la Cierva Incorporación Fellowship (2020-2023) and Beatriu de Pinós-Marie Curie COFUND Fellowship (2019).

Qualifications

  • Acreditación Profesora Ayudante Doctor (Spanish qualification to apply for Lectureships), 2020.
  • PhD Mathematics, Universidad Autónoma de Madrid, 2013.
  • Master 2 in Pure Mathematics (equivalent to MPhil), University Paris 7 Denis-Diderot, 2007.
  • Licenciatura in Mathematics (equivalent to MSci), Universidad Autónoma de Madrid, 2006.
  • Imperial College International Diploma (BSc level qualification awarded to international students), 2005.

Biography

Dr. Peón-Nieto obtained her PhD from Universidad Autónoma de Madrid in 2013. Her thesis, performed under the supervision of Dr. Álvarez-Cónsul and Prof. García-Prada, studies the Hitchin system for Higgs bundles associated to real forms (closely related to geometric structures for real Lie groups).  Prior to that she got a “Licenciatura” (MSci) in Mathematics from Universidad Autónoma de and a Master II (MPhil) in Pure Mathematics in Paris 7.

Ana’s years as a postdoc brought her to Heidelberg (2014-2016), Nice (2017), Geneva (2018-19), Barcelona (2019) and back to Nice (2020). During these years, she evolved towards the study of (Higgs) bundles on non-smooth surfaces, the connections with character varieties, mirror symmetry and more fundamental aspects of moduli spaces of bundles.

Since 2020, Dr. Peón-Nieto is a Lecturer in the Geometry and Mathematical Physics group of the University of Birmingham.

Publications

  • E. Franco, P.B. Gothen and A.G. Oliveira and A. Peón-Nieto, Unramified covers and branes on the Hitchin system, to appear in Adv. Math, arXiv:1802.05237 [math.AG]
  • I. Biswas, M. Logares and A. Peón-Nieto, Symplectic geometry of a moduli space of framed Higgs bundles.
    Int. Math. Res. Notices (2019).
  • I. Biswas, M. Logares and A. Peón-Nieto, Moduli spaces of framed G–Higgs bundles and symplectic geometry. Commun. Math. Phys (2019), https://doi.org/10.1007/s00220-019-03531-3.
  • A.Peón-Nieto, Fixed bundles, singular loci and mirror symmetry. To appear in Oberwolfah Reports (EMS, DOI: 10.4171/OWR). Preprint: arXiv:1907.04903.
  • C. Pauly and A. Peón-Nieto, Very stable bundles and properness of the Hitchin map.  A. Geom. Dedicata (2018). DOI: 10.1007/s10711-018-0333-6.
  • O. García-Prada, A. Peón-Nieto and S.Ramanan Higgs bundles for real groups and the Hitchin–Kostant–Rallis section. Trans. Amer. Math. Soc. 370, (4), 2907–2953 (2018).
  • A. Peón-Nieto, On σδ Picard–Vessiot extensions, Communications in Algebra 34, 4 (2011), 1242–1249.

Preprints

  • A. Peón-Nieto, Wobbly and shaky bundles and resolution of rational maps. arXiv: 2007.13447 [math.AG].
  • O. García-Prada  and A. Peón-Nieto, Higgs bundles, abelian gerbes and cameral data, arXiv:1902.06139.
  • E. Franco, P.B. Gothen and A.G. Oliveira and A. Peón-Nieto, Unramified covers and branes on the Hitchin system, arXiv:1802.05237 [math.AG]
  • E. Franco  and A. Peón-Nieto, The Borel subgroup and branes on the Higgs moduli space, arXiv:1709.03549v2 [math.AG]
  • A. Peón-Nieto, Cameral data for SU(p,p+1)-Higgs bundles, arXiv:1506.01318.

View all publications in research portal