Dr Marina Logares
Lecturer in Pure Mathematics
School of Computing, Electronics and Mathematics (Faculty of Science and Engineering)
Member of the London Mathematical Society
Algebraic and complex geometry and mathematical physics. In particular, I study the geometry and topology of moduli spaces arising in mathematical physics such as moduli spaces of instantons and (parabolic) Higgs bundles.
Research degrees awarded to supervised students
- Centre for Mathematical Sciences (CMS)
On Higgs bundles on nodal curves, arXiv: 1809.06021
A lax monoidal Topological Quantum Field Theory for representation varieties (with A. González-Prieto and V. Muñoz), arXiv: 1709.05724
Symplectic geometry of a moduli space of framed Higgs bundles (with I. Biswas and A. Peón-Nieto), Int. Math. Res. Notices, (2018) pp.1--28, doi:10.1093/imrn/rnz016.
Integrable systems and Torelli theorems for the moduli spaces of parabolic bundles and parabolic Higgs bundles, (with I.Biswas and T. Gómez), Canad. J. Math. 68 (2016), 504--520.
Bohr–Sommerfeld Lagrangians of moduli spaces of Higgs bundles, (with I. Biswas and N.L. Gam-melgaard), J. Geom. Phys. 94, (2015), 179–184.
Hodge polynomials of the SL(2,C)-character variety of an elliptic curve with two marked points (withV. Muñoz), Int. J. Math. 25, No. 14, (2014) 1450–125.
The topology of parabolic character varieties of free groups, (with I. Biswas, C. Florentino and S. Law-ton), Geom. Dedicata Vol. 168, Issue 1, (2014) 143–159.
Hodge polynomials of SL(2,C)-character varieties of surfaces of low genus, (with V. Muñoz and P.Newstead), Rev. Mat. Complut., 26 (2013) 635–703.
On the moduli space of Hitchin pairs, (with I. Biswas and P.B. Gothen), Math. Proc. Cambridge Philos. Soc.151, Issue 03 (2011) 441–457.
Brauer group of moduli spaces of pairs, (with I. Biswas and V. Muñoz), Comm. Alg. 40 Issue 5 (2011)1605–161ó
Connection on parabolic vector bundles over curves, (with I. Biswas), Intern. J. Math. 22, Issue 4 (2011)593–602.
Torelli theorem for the moduli space of parabolic Higgs bundles, (with T. Gómez), Adv. Geom. 11,Issue 3, (2011) 429-444.
Moduli of parabolic Higgs bundles and Atiyah algebroids, (with J. Martens), J. Reine Angew. Math. 649, (2010), 89–116.
Torelli theorem for the Deligne-Hitchin moduli space, (with I. Biswas, T. Gómez and N. Hoffmann), Commun. Math. Phys. 290 (2009) 357–369.
Moduli spaces of parabolic U(p, q)-Higgs bundles, (with O. García-Prada, V. Muñoz), Quart. J. Math.60 (2009) 183–233.
Betti numbers of parabolic U(2, 1)-Higgs bundles moduli spaces, Geom. Dedicata 123 (2006) 187-200.
Peer-reviewed Conference Proceedings
15. Rationality of the moduli space of pairs over a curve, (with I. Biswas and V. Muñoz), Non-linear analysis: Stability, Approximation and Inequalities In honour of Th.M.Rassias in his 60th birthday, SpringerOptimization and Its Applications, Vol. 68, (Eds.) Pardalos, Panos M.; Georgiev, Pando G.; Srivastava, Hari M. (2012) ISBN 978-1-4614-3497-9.
16. Book Review for the EMS Newsletter “Donaldson Type Invariants for Algebraic Surfaces, Transactions on Moduli Stacks, by Takuro Mochizuki. LNM1972 Springer”, no.91 March 2014, European Mathematical Society, 57–58.
17. Book: "Las geometrías y otras revoluciones", Editorial Catarata (CSIC), Madrid, 2018.