**Igor Rivin** (born 1961 in Moscow, USSR) is a Russian-Canadian mathematician, working in various fields of pure and applied mathematics, computer science, and materials science. He is the Regius Professor of Mathematics at the University of St. Andrews.

## Career

He received his B.Sc (Hon) in Mathematics from the University of Toronto in 1981, and his Ph.D in 1986 from Princeton University under the direction of William Thurston. Following his doctorate, Rivin directed development of QLISP and the Mathematica kernel, before returning to academia in 1992, where he held positions at the Institut des Hautes Études Scientifiques, the Institute for Advanced Study, the University of Melbourne, Warwick, and Caltech. Since 1999, Rivin has been professor of mathematics at Temple University. In 2015, he was appointed Regius Professor of Mathematics at the University of St. Andrews.

## Major accomplishments

Rivin's PhD thesis^{[1]}^{[2]} and a series of extensions^{[3]}^{[4]}^{[5]} characterized hyperbolic 3-dimensional polyhedra in terms of their dihedral angles, resolving a long-standing open question of Jakob Steiner on the inscribable combinatorial types. These, and some related results in convex geometry,^{[6]} have been used in 3-manifold topology,^{[7]} theoretical physics, computational geometry, and the recently developed field of discrete differential geometry.

Rivin has also made advances in counting geodesics on surfaces,^{[8]} the study of generic elements of discrete subgroups of Lie groups,^{[9]} and in the theory of dynamical systems.^{[10]}

Rivin is also active in applied areas, having written large parts of the Mathematica 2.0 kernel, and he developed a database of hypothetical zeolites in collaboration with M. M. J. Treacy.

Rivin is a frequent contributor to MathOverflow.

## Honors

- First prize, Canadian Mathematical Olympiad, 1977
- Whitehead prize of the London Mathematical Society, 1998
^{[11]} - Advanced Research Fellowship of the EPSRC, 1998
- Lady Davis Fellowship at the Hebrew University, 2006
- Berlin Mathematical School Professorship, 2011.
^{[12]} - Fellow of the American Mathematical Society, 2014.
^{[13]}

## References

**^**Rivin, Igor (1986). "On geometry of convex polyhedra in hyperbolic 3-space". MR 2635205**^**Hodgson, C. D.; Rivin, I. (1993). "A characterization of compact convex polyhedra in hyperbolic 3-space".*Inventiones Mathematicae***111**: 77. doi:10.1007/BF01231281.**^**Rivin, Igor (1994). "Euclidean Structures on Simplicial Surfaces and Hyperbolic Volume".*Annals of Mathematics***139**(3): 553–580. doi:10.2307/2118572.**^**Rivin, Igor (1996). "A Characterization of Ideal Polyhedra in Hyperbolic 3-Space".*Annals of Mathematics***143**(1): 51–70. doi:10.2307/2118652.**^**Rivin, I. (2003). "Combinatorial optimization in geometry".*Advances in Applied Mathematics***31**: 242–201. doi:10.1016/S0196-8858(03)00093-9.**^**Rivin, I. (2009). "Asymptotics of convex sets in Euclidean and hyperbolic spaces".*Advances in Mathematics***220**(4): 1297–2013. doi:10.1016/j.aim.2008.11.014.**^**David Futer; François Guéritaud (2011). "From angled triangulations to hyperbolic structures".*Contemporary Mathematics*. Contemporary Mathematics**541**: 159–182. arXiv:1004.0440. doi:10.1090/conm/541/10683. ISBN 9780821849606.**^**Rivin, I. (2001). "Simple Curves on Surfaces".*Geometriae Dedicata***87**: 345–360. doi:10.1023/A:1012010721583.**^**Rivin, I. (2008). "Walks on groups, counting reducible matrices, polynomials, and surface and free group automorphisms".*Duke Mathematical Journal***142**(2): 353. doi:10.1215/00127094-2008-009.**^**Rivin, I. (2005). "On Some Mean Matrix Inequalites of Dynamical Interest".*Communications in Mathematical Physics***254**(3): 651–658. Bibcode:2005CMaPh.254..651R. doi:10.1007/s00220-004-1282-5.**^**http://www.lms.ac.uk/content/list-lms-prize-winners#Whitehead_Prize**^**http://www.math-berlin.de/Guests.html**^**List of Fellows of the American Mathematical Society, retrieved 2014-12-17