Igor Rivin

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Igor Rivin
Alma materPrinceton University
University of Toronto
Known forInscribable polyhedra
AwardsWhitehead Prize (1998)
Scientific career
FieldsMathematics, Computer Science, Materials Science
InstitutionsUniversity of St. Andrews
Temple University
University of Warwick
Institute for Advanced Study
Institut des Hautes Études Scientifiques
Doctoral advisorWilliam Thurston
Doctoral studentsMichael 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 was the Regius Professor of Mathematics at the University of St. Andrews from 2015 to 2017, and was the chief research officer at Cryptos Fund until 2019. He is doing research for Edgestream LP, in addition to his academic work.


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. Between 2015 to 2017 he was Regius Professor of Mathematics at the University of St. Andrews.

Major accomplishments[edit]

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.

Igor Rivin is the co-creator, with economist Carlo Scevola, of Cryptocurrencies Index 30 (CCi30),[11] an index of the top 30 cryptocurrencies weighted by market capitalization. CCi30 is sometimes used by academic economists as a market index when comparing the cryptocurrency trading market as a whole with individual currencies.[12][13]



  1. ^ Rivin, Igor (1986). "On geometry of convex polyhedra in hyperbolic 3-space". MR 2635205. {{cite journal}}: Cite journal requires |journal= (help)
  2. ^ Hodgson, C. D.; Rivin, I. (1993). "A characterization of compact convex polyhedra in hyperbolic 3-space". Inventiones Mathematicae. 111: 77–111. Bibcode:1993InMat.111...77H. doi:10.1007/BF01231281. S2CID 123418536.
  3. ^ Rivin, Igor (1994). "Euclidean Structures on Simplicial Surfaces and Hyperbolic Volume". Annals of Mathematics. 139 (3): 553–580. doi:10.2307/2118572. JSTOR 2118572. S2CID 120299702.
  4. ^ Rivin, Igor (1996). "A Characterization of Ideal Polyhedra in Hyperbolic 3-Space". Annals of Mathematics. 143 (1): 51–70. doi:10.2307/2118652. JSTOR 2118652.
  5. ^ Rivin, I. (2003). "Combinatorial optimization in geometry". Advances in Applied Mathematics. 31: 242–271. arXiv:math/9907032. doi:10.1016/S0196-8858(03)00093-9. S2CID 119153365.
  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. ^ Futer, David; Guéritaud, François (2011), "From angled triangulations to hyperbolic structures", Interactions between hyperbolic geometry, quantum topology and number theory, Contemporary Mathematics, vol. 541, Providence, RI, pp. 159–182, arXiv:1004.0440, doi:10.1090/conm/541/10683, MR 2796632, S2CID 29221584
  8. ^ Rivin, I. (2001). "Simple Curves on Surfaces". Geometriae Dedicata. 87: 345–360. arXiv:math/9907041. doi:10.1023/A:1012010721583. S2CID 17338586.
  9. ^ Rivin, I. (2008). "Walks on groups, counting reducible matrices, polynomials, and surface and free group automorphisms". Duke Mathematical Journal. 142 (2): 353–379. arXiv:math/0703532. doi:10.1215/00127094-2008-009. S2CID 10093564.
  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. S2CID 9510842.
  11. ^ "Cryptocurrency Index 30 - CCi30".
  12. ^ Ajaz, Taufeeq; Kumar, Anoop S. (2018-06-01). "Herding in crypto-currency markets". Annals of Financial Economics. 13 (2): 1850006. doi:10.1142/S2010495218500069. ISSN 2010-4952. S2CID 158488687.
  13. ^ Felix, Thomas Heine; von Eije, Henk (2019-04-03). "Underpricing in the cryptocurrency world: evidence from initial coin offerings" (PDF). Managerial Finance. 45 (4): 563–578. doi:10.1108/MF-06-2018-0281. ISSN 0307-4358. S2CID 159119639.
  14. ^ "List of LMS prize winners | London Mathematical Society".
  15. ^ "Archived copy". Archived from the original on 2012-07-19. Retrieved 2012-08-26.{{cite web}}: CS1 maint: archived copy as title (link)
  16. ^ List of Fellows of the American Mathematical Society, retrieved 2014-12-17

External links[edit]