Igor Rivin

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Igor Rivin
Born 1961
Moscow, USSR
Nationality Canadian
Alma mater Princeton University
University of Toronto
Known for Inscribable polyhedra
Awards Whitehead Prize (1998)
Scientific career
Fields Mathematics, Computer Science, Materials Science
Institutions University of St. Andrews
Temple University
University of Warwick
Institute for Advanced Study
Institut des Hautes Études Scientifiques
Doctoral advisor William Thurston
Doctoral students Jean-Christophe Curtillet
Michael Dobbins

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 and the Chief Quantitative Strategist at Accern.[1]


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[edit]

Rivin's PhD thesis[2][3] and a series of extensions[4][5][6] 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,[7] have been used in 3-manifold topology,[8] theoretical physics, computational geometry, and the recently developed field of discrete differential geometry.

Rivin has also made advances in counting geodesics on surfaces,[9] the study of generic elements of discrete subgroups of Lie groups,[10] and in the theory of dynamical systems.[11]

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. ^ https://www.linkedin.com/in/igor-rivin-6616aa4/
  2. ^ Rivin, Igor (1986). "On geometry of convex polyhedra in hyperbolic 3-space". MR 2635205 
  3. ^ Hodgson, C. D.; Rivin, I. (1993). "A characterization of compact convex polyhedra in hyperbolic 3-space". Inventiones Mathematicae. 111: 77. doi:10.1007/BF01231281. 
  4. ^ Rivin, Igor (1994). "Euclidean Structures on Simplicial Surfaces and Hyperbolic Volume". Annals of Mathematics. 139 (3): 553–580. JSTOR 2118572. doi:10.2307/2118572. 
  5. ^ Rivin, Igor (1996). "A Characterization of Ideal Polyhedra in Hyperbolic 3-Space". Annals of Mathematics. 143 (1): 51–70. JSTOR 2118652. doi:10.2307/2118652. 
  6. ^ Rivin, I. (2003). "Combinatorial optimization in geometry". Advances in Applied Mathematics. 31: 242–271. doi:10.1016/S0196-8858(03)00093-9. 
  7. ^ 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. 
  8. ^ David Futer; François Guéritaud (2011). "From angled triangulations to hyperbolic structures". Contemporary Mathematics. Contemporary Mathematics. 541: 159–182. ISBN 9780821849606. arXiv:1004.0440Freely accessible. doi:10.1090/conm/541/10683. 
  9. ^ Rivin, I. (2001). "Simple Curves on Surfaces". Geometriae Dedicata. 87: 345–360. doi:10.1023/A:1012010721583. 
  10. ^ 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. 
  11. ^ 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. 
  12. ^ http://www.lms.ac.uk/content/list-lms-prize-winners#Whitehead_Prize
  13. ^ http://www.math-berlin.de/Guests.html
  14. ^ List of Fellows of the American Mathematical Society, retrieved 2014-12-17

External links[edit]