Mark Gross (mathematician)
Mark William Gross (30 November 1965) is an American mathematician, specializing in differential geometry, algebraic geometry, and mirror symmetry.
Mark Gross at the Royal Society admissions day in London, July 2017
Mark William Gross
November 30, 1965
|Awards||Clay Research Award (2016)|
|Thesis||Surfaces in the Four-Dimensional Grassmannian (1990)|
|Doctoral advisor||Robin Hartshorne|
Gross studied from 1982 at Cornell University graduating with a bachelor's degree in 1984 and received in 1990 a PhD from the University of California, Berkeley for research supervised by Robin Hartshorne with a thesis on the Surfaces in the Four-Dimensional Grassmannian.
Research and career
From 1990 to 1993 he was an assistant professor at the University of Michigan and spent the academic year 1992–1993 on leave as a postdoctoral researcher at the Mathematical Sciences Research Institute (MSRI) in Berkeley. He was at Cornell University in 1993–1997 an assistant professor and in 1997–2001 an associate professor and then at University of California, San Diego in 2001–2013 a full professor. At the University of Warwick, he was in the academic year 2002–2003 a visiting professor. Since 2013 he has been a professor at the University of Cambridge and since 2016 a Fellow of King's College, Cambridge. Gross works on complex geometry, algebraic geometry, and mirror symmetry. Gross and Bernd Siebert jointly developed a program (known as the Gross–Siebert Program) for studying mirror symmetry within algebraic geometry.
The Gross–Siebert program builds on an earlier, differential-geometric, proposal of Strominger, Yau, and Zaslow, in which the Calabi–Yau manifold is fibred by special Lagrangian tori, and the mirror by dual tori. The program's central idea is to translate this into an algebro-geometric construction in an appropriate limit, involving combinatorial data associated with a degenerating family of Calabi–Yau manifolds. It draws on many areas of geometry, analysis and combinatorics and has made a deep impact on fields such as tropical and non-archimedean geometry, logarithmic geometry, the calculation of Gromov–Witten invariants, the theory of cluster algebras and combinatorial representation theory.
His previous doctoral students have included Daniel Budreau, Andrei Caldararu, Ricardo Castano-Bernard, Man Wai Cheung, Karl Fredrickson, Michael Kasa, Diego Matessi, Brandon Meredith, Peter Overholser, Simone Pavanelli and Michael Slawinski.
- Topological Mirror Symmetry, Inventiones Mathematicae, vol. 144, 2001, pp. 75–137, arXiv:math/9909015
- with D. Joyce, D. Huybrechts (eds.), Calabi–Yau Manifolds and related Geometries (Nordfjordeid 2001), Springer MR1963559; 2012 reprint
- with B. Siebert: From real affine geometry to complex geometry, Annals of Mathematics, vol. 174, 2011, pp. 1301–1428, arXiv:math/0703822
- with Paul S. Aspinwall, Tom Bridgeland, Alastair Craw, Michael R. Douglas, Anton Kapustin, Gregory W. Moore, Graeme Segal, Balázs Szendrői, and P. M. H. Wilson: Dirichlet branes and Mirror Symmetry, Clay Mathematics Monographs 4, 2009
- Tropical geometry and mirror symmetry, CBMS Regional conference series in Mathematics 114, AMS, 2011 MR2722115
- Mirror Symmetry for and Tropical Geometry, Preprint 2009, arXiv:0903.1378
- The Strominger–Yau–Zaslow conjecture: From torus fibrations to degenerations, AMS Symposium Algebraic Geometry, Seattle 2005, Preprint 2008, arXiv:0802.3407
- Mirror Symmetry and the Strominger–Yau–Zaslow conjecture, Current Developments in Mathematics 2012, arXiv:1212.4220
Awards and honors
Gross was an Invited Speaker, jointly with Siebert, with talk Local mirror symmetry in the tropics at the International Congress of Mathematicians in Seoul 2014. In 2016 Gross and Siebert jointly received the Clay Research Award. Gross was elected a Fellow of the Royal Society in 2017.
- Anon (2017) "Gross, Prof. Mark William". Who's Who. ukwhoswho.com (online Oxford University Press ed.). A & C Black, an imprint of Bloomsbury Publishing plc. doi:10.1093/ww/9780199540884.013.289284. (subscription or UK public library membership required) (subscription required)
- Anon (2017). "Professor Mark Gross FRS". royalsociety.org. London: Royal Society. Archived from the original on 2017-08-15. One or more of the preceding sentences incorporates text from the royalsociety.org website where:
“All text published under the heading 'Biography' on Fellow profile pages is available under Creative Commons Attribution 4.0 International License.” --"Royal Society Terms, conditions and policies". Archived from the original on 2016-11-11. Retrieved 2016-03-09.CS1 maint: BOT: original-url status unknown (link)
- Mark Gross at the Mathematics Genealogy Project
- "Mark Gross". dpmms.cam.ac.uk. Retrieved 21 August 2017.
- ICM2014 VideoSeries IL4.2: Mark Gross, Bernd Siebert on Aug14Thu, 9 August 2015 on YouTube
- Mark Gross – Mirror symmetry, Simons Collaboration on Homological Mirror Symmetry, 26 March 2016 on YouTube
- "2016, C.V. Dr. Mark Gross" (PDF). dpmms.cam.ac.uk. Retrieved 21 August 2017.
- "Mark Gross elected Fellow of Royal Society". kings.cam.ac.uk. Retrieved 21 August 2017.
- Mark Gross publications indexed by the Scopus bibliographic database. (subscription required)
- "2016 Clay Research Awards - Clay Mathematics Institute". claymath.org. Retrieved 21 August 2017.
- Matessi, Diego (2001). Constructions of Calabi Yau metrics and of special Lagrangian submanifolds. users.mat.unimi.it (PhD thesis). University of Warwick. OCLC 59373879. EThOS uk.bl.ethos.246770.
- Thomas, Richard. "Review of Calabi–Yau manifolds and related geometries edited by Mark Gross, Daniel Huybrechts and Dominic Joyce". people.maths.ox.ac.uk. Retrieved 2017-08-21.
- Gross, Mark; Siebert, Bernd (2014). "Local mirror symmetry in the tropics". arXiv:1404.3585.