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.


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.



  1. ^ Rivin, Igor (1986). "On geometry of convex polyhedra in hyperbolic 3-space". MR 2635205 
  2. ^ Hodgson, C. D.; Rivin, I. (1993). "A characterization of compact convex polyhedra in hyperbolic 3-space". Inventiones Mathematicae 111: 77. doi:10.1007/BF01231281. 
  3. ^ Rivin, Igor (1994). "Euclidean Structures on Simplicial Surfaces and Hyperbolic Volume". Annals of Mathematics 139 (3): 553–580. doi:10.2307/2118572. 
  4. ^ Rivin, Igor (1996). "A Characterization of Ideal Polyhedra in Hyperbolic 3-Space". Annals of Mathematics 143 (1): 51–70. doi:10.2307/2118652. 
  5. ^ Rivin, I. (2003). "Combinatorial optimization in geometry". Advances in Applied Mathematics 31: 242–201. doi:10.1016/S0196-8858(03)00093-9. 
  6. ^ 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. 
  7. ^ 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. 
  8. ^ Rivin, I. (2001). "Simple Curves on Surfaces". Geometriae Dedicata 87: 345–360. doi:10.1023/A:1012010721583. 
  9. ^ 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. 
  10. ^ 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. 
  11. ^ http://www.lms.ac.uk/content/list-lms-prize-winners#Whitehead_Prize
  12. ^ http://www.math-berlin.de/Guests.html
  13. ^ List of Fellows of the American Mathematical Society, retrieved 2014-12-17