Mark Gross

FRS
Gross in 2017
Born (1965-11-30) November 30, 1965
Ithaca, New York, U.S.
Alma mater
AwardsClay Research Award (2016)[1]
Scientific career
Institutions
ThesisSurfaces in the Four-Dimensional Grassmannian (1990)
Doctoral advisorRobin Hartshorne[2]
Websitedpmms.cam.ac.uk/people/mg475/
www.dpmms.cam.ac.uk/~mg475/

Mark William Gross FRS[1] (born 30 November 1965)[3] is an American mathematician, specializing in differential geometry, algebraic geometry, and mirror symmetry.[4][5][6]

Early life and education

Mark William Gross was born on 30 November 1965 in Ithaca, New York, to Leonard Gross and Grazyna Gross.[3] From 1982, he studied at Cornell University, graduating with a bachelor's degree in 1984.[3] He gained a PhD in 1990 from the University of California, Berkeley,[3] for research supervised by Robin Hartshorne[1][2] with a thesis on the surfaces in the four-dimensional Grassmannian.[2]

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. He was a visiting professor at the University of Warwick in the academic year 2002–2003. Since 2013, he has been a professor at the University of Cambridge[7] and since 2016, a Fellow of King's College, Cambridge.[8]

Research

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.[1][9]

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.[10]

Selected publications

  • Topological Mirror Symmetry, Inventiones Mathematicae, vol. 144, 2001, pp. 75–137, arXiv:math/9909015 Free access icon
  • with D. Joyce, D. Huybrechts (eds.), Calabi–Yau Manifolds and related Geometries (Nordfjordeid 2001), Springer MR1963559;[11] 2012 reprint
  • with B. Siebert: From real affine geometry to complex geometry, Annals of Mathematics, vol. 174, 2011, pp. 1301–1428, arXiv:math/0703822 Free access icon
  • 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 Free access icon
  • The Strominger–Yau–Zaslow conjecture: From torus fibrations to degenerations, AMS Symposium Algebraic Geometry, Seattle 2005, Preprint 2008, arXiv:0802.3407 Free access icon
  • Mirror Symmetry and the Strominger–Yau–Zaslow conjecture, Current Developments in Mathematics 2012, arXiv:1212.4220 Free access icon

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.[12] In 2016 Gross and Siebert jointly received the Clay Research Award.[10] Gross was elected a Fellow of the Royal Society in 2017.[1][8]

References

  1. 1 2 3 4 5 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.{{cite web}}: CS1 maint: bot: original URL status unknown (link)
  2. 1 2 3 Mark Gross at the Mathematics Genealogy Project
  3. 1 2 3 4 "Gross, Prof. Mark William". Who's Who. A & C Black. doi:10.1093/ww/9780199540884.013.U289284. (Subscription or UK public library membership required.)
  4. ↑ "Mark Gross". dpmms.cam.ac.uk. Retrieved 21 August 2017.
  5. ↑ ICM2014 VideoSeries IL4.2: Mark Gross, Bernd Siebert on Aug14Thu, 9 August 2015 on YouTube
  6. ↑ Mark Gross – Mirror symmetry, Simons Collaboration on Homological Mirror Symmetry, 26 March 2016 on YouTube
  7. ↑ "2016, C.V. Dr. Mark Gross" (PDF). dpmms.cam.ac.uk. Retrieved 21 August 2017.
  8. 1 2 "Mark Gross elected Fellow of Royal Society". kings.cam.ac.uk. Retrieved 21 August 2017.
  9. ↑ Mark Gross publications indexed by the Scopus bibliographic database. (subscription required)
  10. 1 2 "2016 Clay Research Awards - Clay Mathematics Institute". claymath.org. Retrieved 21 August 2017.
  11. ↑ 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.
  12. ↑ Gross, Mark; Siebert, Bernd (2014). "Local mirror symmetry in the tropics". arXiv:1404.3585 [math.AG].
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