Dr Michel van Garrel BSc MSc PhD

Dr Michel van Garrel

School of Mathematics
Assistant Professor

Contact details

Address
School of Mathematics
Watson Building
University of Birmingham
Edgbaston
Birmingham
B15 2TT
UK

Dr van Garrel is a researcher in algebraic geometry and mirror symmetry. He specialises in enumerative geometry, in particular log Gromov-Witten theory, in birational geometry, especially with regards to rationality questions and in the Gross-Siebert programme as the mechanism that explains mirror symmetry and constructs mirror families.

Among his most important contributions, Dr van Garrel initiated new unexpected correspondences of different enumerative theories in different dimensions, relating log, open and local Gromov-Witten invariants, quiver Donaldson-Thomas invariants as well as sheaf counting invariants of local Calabi-Yau fourfolds. Using the Gross-Siebert programme, he developed new instances of mirror symmetry for log Calabi-Yau surfaces with smooth boundary.

Dr van Garrel has organised 13 conferences that build on the growing research communities around these themes. Besides an online conference, these took place at Cambridge, Imperial, the Mathematical Research Institute of Oberwolfach and the Korea Institute for Advanced Study. In addition, Dr van Garrel is an organiser for the LMS Midlands Regional Meeting 2022 at the University of Birmingham. He has given invited talks in 12 countries on 3 continents. He was an invited speaker at the Algebraic Geometry Session of the British Mathematical Colloquium 2021.

Qualifications

  • PhD in Mathematics, California Institute of Technology, 2013
  • MSc in Mathematics, Swiss Federal Institute of Technology Lausanne, 2008
  • BSc in Mathematics, Swiss Federal Institute of Technology Lausanne, 2006
  • Propedeutique I in Physics, Swiss Federal Institute of Technology Lausanne, 2004

Biography

Dr van Garrel grew up in the German part of Switzerland speaking French at home. He did his undergraduate studies at the Swiss Federal Institute of Technology Lausanne with his Master thesis in number theory done with Prof. Ken Ribet at the University of California Berkeley.

After that he went for his doctoral studies to the California Institute of Technology to work with Prof. Tom Graber, one of the pioneers of Gromov-Witten theory. The completion of his PhD was followed by some postdoctoral positions. For the first he was a member of a thematic program on Calabi-Yau varieties at the Fields Institute in Toronto. Then he was a researcher at the Korea Institute for Advanced Study in Seoul. During that time, partly through the organization of 3 conferences on it, he learned the Gross-Siebert program, which then earned him a post with Prof. Bernd Siebert at the University of Hamburg.

This was followed by an EU Horizon 2020 Marie Curie Fellowship at the University of Warwick with Prof. Miles Reid FRS. After a 4 month visitor stay at the Institute for Theoretical Studies of ETH Zurich visiting the group of Prof. Rahul Pandharipande, he started his current post at the University of Birmingham.

Postgraduate supervision

Dr van Garrel is interested in supervising PhD students in Algebraic Geometry, Mirror Symmetry and Enumerative Geometry.

Research

Research Themes

  • Enumerative Geometry: Log Gromov-Witten theory, how it relates to other curve counting theories and to Mirror Constructions.
  • Birational Geometry: Rationality Questions in Gross-Siebert families.
  • Gross-Siebert programme, Mirror Constructions and Mirror Symmetry Results.

Publications

Recent publications

Article

Choi, J, van Garrel, M, Katz, S & Takahashi, N 2021, 'Log BPS numbers of log Calabi-Yau surfaces', Transactions of the American Mathematical Society, vol. 374, no. 1, pp. 687-732. https://doi.org/10.1090/tran/8234

Bousseau, P, Brini, A & van Garrel, M 2021, 'On the log-local principle for the toric boundary', Bulletin of the London Mathematical Society.

Böhning, C, Graf von Bothmer, H-C & van Garrel, M 2021, 'Prelog Chow groups of self-products of degenerations of cubic threefolds', European Journal of Mathematics. https://doi.org/10.1007/s40879-021-00510-8

Choi, J, van Garrel, M, Katz, S & Takahashi, N 2021, 'Sheaves of maximal intersection and multiplicities of stable log maps', Selecta Mathematica, New Series, vol. 27, no. 4, 61 . https://doi.org/10.1007/s00029-021-00671-0

Bousseau, P, Brini, A & van Garrel, M 2021, 'Stable maps to Looijenga pairs: orbifold examples', Letters in Mathematical Physics, vol. 111, no. 4, 11. https://doi.org/10.1007/s11005-021-01451-9

van Garrel, M, Choi, J, Katz, S & Takahashi, N 2020, 'Local BPS Invariants: Enumerative Aspects and Wall-Crossing', International Mathematics Research Notices, vol. 2020, no. 17. https://doi.org/10.1093/imrn/rny171

van Garrel, M, Ruddat, H & Graber, T 2019, 'Local Gromov-Witten invariants are log invariants', Advances in Mathematics, vol. 350.

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