Dr Andrea Brini PhD

Dr Andrea Brini

School of Mathematics
Senior Lecturer in Mathematics

Contact details

Address
University of Birmingham
Edgbaston
Birmingham
B15 2TT
UK

Andrea Brini is a Senior Lecturer within the Geometry and Mathematical Physics group at the School of Mathematics.
His research field lies at the intersection of Algebraic Geometry, Integrable Systems and High Energy Physics. Andrea works on the Geometry of String Theory and its interface with other areas of Mathematics. His main research topic is the theory of topological strings and Gromov-Witten invariants, with emphasis on its connections with gauge theory, matrix models, integrable systems, and other moduli space problems. His research has been funded by the European Commission, the French Centre National de la Recherche Scientifique, and more recently by a research fellowship of the Engineering and Physical Sciences Research Council.

Qualifications

  • CNRS Admission (Chargé de Recherches), 2012; promotion to 1st class, 2017
  • Anile Prize for the best PhD thesis in Mathematics and applications at an Italian University, 2011
  • PhD, Mathematical Physics, SISSA Trieste, 2009
  • MSc, cum laude, Theoretical Physics, University of Milan-Bicocca, 2005
  • BSc, cum laude, Physics, University of Milan-Bicocca, 2003

Biography

Andrea Brini graduated with a BSc in Physics (2003) and a MSc in Theoretical Physics (2005), both cum laude, from the University of Milan-Bicocca. He went on to study for a PhD in Mathematical Physics at the International School for Advanced Studies (SISSA/ISAS) in Trieste, graduating in 2009. After a postdoctoral stint at the University of Geneva, he obtained a Marie Curie Fellowship of the European Commission in 2011, followed by a permanent research post at the French Centre National de la Recherche Scientifique (CNRS) in 2013, based at the University of Montpellier. After holding visiting research positions at Imperial College London (2016-18) and MSRI Berkeley (2018, research member), he was appointed a Senior Lecturer at the School of Mathematics in September 2018, and has held a 5-year EPSRC Early Career Fellowship since October 2018.

Research

Andrea is a mathematical physicist with broad interests in Geometry (particularly Algebraic Geometry), Topology and Mathematical Physics. The primary objects of concern in his research are curve counting invariants: these record the number of curves of given genus and degree which meet a prescribed collection of cycles in a given algebraic variety (or symplectic manifold) X. Their systematic study has been the subject of an explosion of activity in the last two decades, as a startling range of fundamental questions, both within and outside geometry, receive a complete answer through their calculation:

  • In algebraic geometry, they codify enumerative information about the geometry of X, and provide the solution to a wide range of classical and modern enumerative-geometric problems;
  • In symplectic geometry and topology, they supply a sophisticated, infinite set of invariants of the symplectic isotopy class of X;
  • In high energy mathematical physics, they capture exact information about symmetry-protected observables of an important class of quantum gauge and string theories;
  • Generating functions of the invariants often satisfy an infinite-dimensional group of symmetry constraints given by the flows of a classical integrable hierarchy: a very special non-linear partial differential equation possessing infinitely many commuting conserved currents.

Within the polarised relationship between geometers and mathematical physicists of his research field-at-large, Andrea has consistently strived to keep a dual-loyalty profile: his research has straddled the border between the two subjects, with research outputs in both Algebraic Geometry and Mathematical Physics, and he devotes most of his time figuring out ways to create, transfer and convert ideas and methods from one field to the other. One big pay-off is that hard questions in one subject can sometimes be tackled with unexpected and powerful tools inspired by a priori distant areas of Mathematics. His work in particular has explored and revealed new connections between Gromov-Witten theory and integrable systems, open Gromov-Witten theory and birational geometry, and quantum topology, enumerative geometry, and matrix models.

Publications

Selected publications:

  • Rational reductions of the 2D-Toda hierarchy and mirror symmetry, with G. Carlet, S. Romano and P. Rossi, J. Eur. Math. Soc. 19 (2017), 835-880, DOI 10.4171/JEMS/681
  • Crepant resolutions and open strings, with R. Cavalieri and D. Ross, J. Reine. Angew. Math. (Crelle’s journal), DOI:10.1515/crelle-2017-0011 (2017)
  • Torus knots and mirror symmetry, with B. Eynard and M. Mariño, Annales Henri Poincaré (2012), DOI: 10.1007/s00023-012-0171-2
  • Open topological strings and integrable hierarchies: Remodeling the A-model, Commun. Math. Phys Vol. 312, Issue 3 (2012), 735-780
  • Open orbifold Gromov-Witten invariants of [C 3 /Z n ]: mirror symmetry and localization, with R. Cavalieri, Selecta Math., Volume 17, Number 4 (2011), 879-933, doi:10.1007/s00029-011-0060-4
  • The local Gromov-Witten theory of CP1 and integrable hierarchies, Commun. Math. Phys Vol. 313 (2012) 571-605

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