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.

Summer 2022 research opportunity for undergraduates. Contact me if you are interested!


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/ Garrett Mulcahy, Malnormal matrices, Proc. Amer. Math. Soc. 150 (2022), no. 7, 2969-2982. arXiv.
  2. 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.
  3. 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.
  4. w/ Isaac Goldbring, On the axiomatizability of C*-algebras as operator systems, Glasg. Math. J., 61 (2019). arXiv. article.
  5. w/ Isaac Goldbring, Robinson forcing and the quasidiagonality problem, Internat. J. Math., 28 (2017) Article 175008. arXiv. article.
  6. CP-stability and the local lifting property, New York J. Math. 23 (2017) 739-747. arXiv. article.
  7. w/ Isaac Goldbring, Omitting types in operator systems, Indiana Univ. Math. J. 66 (2017) 821-844. arXiv. article.
  8. 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.
  9. 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.
  10. w/ Isaac Goldbring, Games and elementary equivalence of II1 factors, Pacific J. Math. 278 (2015) 103-118. arXiv. article.
  11. w/ Isaac Goldbring, On Kirchberg's embedding problem, J. Funct. Anal. 269 (2015), 155-198 arXiv. article.
  12. w/ Ionuţ Chifan, On the ergodic theorem for affine actions on Hilbert space, Bull. Belgian Math. Soc. 22 (2015), 429-446.arXiv.
  13. 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.
  14. 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.
  15. 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.
  16. w/ Jesse Peterson, On cocycle superrigidity for Gaussian actions, Ergodic Theory Dynam. Systems 32 (2012), 249-272. pdf. article.
  17. 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/ Bruno de Mendonça Braga and Javier Alejandro Chávez-Domínguez, Lipschitz geometry of operator spaces and Lipschitz-free operator spaces, arXiv.
  3. w/ Roy Araiza, Colton Griffin, and Aneesh Khilnani, Approximating projections by quantum operations. arXiv.
  4. w/ Roy Araiza and Colton Griffin, An index for inclusions of operator systems. 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


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Past Teaching


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

John Wooden's Seven Point Creed