Mark Gross (mathematician)
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Through Combinatorics
Early life and education
Mark William Gross was born on 30 November 1965 in Ithaca, New York, to Leonard Gross and Grazyna Gross. From 1982, he studied at Cornell University, graduating with a bachelor's degree in 1984. He gained a PhD in 1990 from the University of California, Berkeley, for research supervised by Robin Hartshorne with a thesis on the surfaces in the four-dimensional Grassmannian.
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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 and since 2016, a Fellow of King's College, Cambridge.
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.
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.