Thomas Sinclair

PhD, Mathematics, Vanderbilt University, 2011
BS, Mathematics, IUPUI, 2006

Associate Professor | Mathematics Department | Purdue University | West Lafayette, IN
MATH 744 | tsincla @ | 7654941901 (math main office) | 7654940548 (fax)

My math genealogy. Family photos. Random botanizing. My pages on MathSciNet and Google Scholar.


Research Interests

My research is currently supported by NSF grant DMS-2055155.

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You can find all of my publications/preprints in their current versions on the arXiv.

  1. w/ Roy Araiza and Colton Griffin, An index for inclusions of operator systems, J. Operator Theory, accepted. arXiv.
  2. w/ Bruno de Mendonça Braga and Javier Alejandro Chávez-Domínguez, Lipschitz geometry of operator spaces and Lipschitz-free operator spaces, Math. Ann., accepted. arXiv. article. view only.
  3. w/ Roy Araiza, Colton Griffin, and Aneesh Khilnani, Approximating projections by quantum operations, Linear Algebra Appl. 663 (2023), 178-199. arXiv. article.
  4. w/ Garrett Mulcahy, Malnormal matrices, Proc. Amer. Math. Soc. 150 (2022), no. 7, 2969-2982. arXiv. article.
  5. w/ Rolando de Santiago, Ben Hayes, and Daniel J. Hoff, Maximal rigid subalgebras of deformations and L2-cohomology, Anal. PDE. 14 (2021), no. 7, 2269-2306. arXiv. article.
  6. w/ Ben Hayes, David Jekel, and Brent Nelson, A random matrix approach to absorption in free products, IMRN (2021), no. 3, 1919-1979. arXiv. article.
  7. w/ Isaac Goldbring, On the axiomatizability of C*-algebras as operator systems, Glasg. Math. J., 61 (2019). arXiv. article.
  8. w/ Isaac Goldbring, Robinson forcing and the quasidiagonality problem, Internat. J. Math., 28 (2017) Article 175008. arXiv. article.
  9. CP-stability and the local lifting property, New York J. Math. 23 (2017) 739-747. arXiv. article.
  10. w/ Isaac Goldbring, Omitting types in operator systems, Indiana Univ. Math. J. 66 (2017) 821-844. arXiv. article.
  11. w/ Rolando de Santiago and Ionuţ Chifan, W*-rigidity for von Neumann algebras of products of hyperbolic groups, Geom. Funct. Anal. 26 (2016) 136-159. arXiv. article.
  12. w/ Ionuţ Chifan and Bogdan Udrea, Inner amenability for groups and central sequences in factors, Ergodic Theory Dynam. Systems, 36 (2016) 1106-1129. arXiv. article.
  13. w/ Isaac Goldbring, Games and elementary equivalence of II1 factors, Pacific J. Math. 278 (2015) 103-118. arXiv. article.
  14. w/ Isaac Goldbring, On Kirchberg's embedding problem, J. Funct. Anal. 269 (2015), 155-198 arXiv. article.
  15. w/ Ionuţ Chifan, On the ergodic theorem for affine actions on Hilbert space, Bull. Belgian Math. Soc. 22 (2015), 429-446.arXiv. article.
  16. w/ Isaac Goldbring and Bradd Hart, The theory of tracial von Neumann algebras does not have a model companion, J. Symbolic Logic 78 (2013), 1000-1004. arXiv. article.
  17. w/ Ionuţ Chifan and Bogdan Udrea, On the structural theory of II1 factors of negatively curved groups, II, Adv. Math. 245 (2013), 208-236. arXiv. article.
  18. w/ Ionuţ Chifan, On the structural theory of II1 factors of negatively curved groups, Ann. Sci. Éc. Norm. Supér. 46 (2013), 1-33. arXiv. article.
  19. w/ Jesse Peterson, On cocycle superrigidity for Gaussian actions, Ergodic Theory Dynam. Systems 32 (2012), 249-272. pdf. article.
  20. Strong solidity of group factors from lattices in SO(n,1) and SU(n,1), J. Funct. Anal. 260 (2011), no. 11, 3209-3221. article.


  1. w/ Isaac Goldbring and Bradd Hart, Correspondences, ultraproducts and model theory, preprint. arXiv.
  2. w/ Naveen Vivek, Remarks on the Grothendieck norm. arXiv.

"[E]ach bringing/ From the water in which he believed and out of desire/ Things made by mid-terrestrial, mid-human/ Makers without knowing, or intending, uses."
---Wallace Stevens, from A Completely New Set of Objects


Model Theory of Operator Systems and C*-Algebras. Contribution to the volume "Model Theory of Operator Algebras." arXiv.


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Good advice from fellow Hoosier, Bruin, and Boilermaker, John Wooden:

John Wooden's Seven Point Creed