Thomas Sinclair

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

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

Teaching

• Fall 2023, Math 353, Linear Algebra II.

Research Interests

• Von Neumann Algebras
• Ergodic Theory
• Geometric Group Theory
• Model Theory of Metric Structures

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

https://orcid.org/0000-0003-0401-7232

Publications

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.

Preprints

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

Expository

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

Notes

• Remark on harmonic functions of almost sublinear growth. pdf.
• A very short proof of the existence of an injective envelope for an operator space. pdf.

Undergraduate Mentees

• Garrett Mulcahy, first position: PhD student in Mathematics, University of Washington, NSF Graduate Research Fellow.
• Colton Griffin, first position: PhD student in Mathematics, University of Pennsylvania, NSF Graduate Research Fellow.
• Aneesh Khilnani, first position: PhD student in Aeronautics, Purdue University.
• Naveen Vivek
• Micky Santiago-Zayas
• Sanchita Chakraborty, first position: master's student in Applied Mathematics, University of Wisconsin
• Yuxiao Wang

PhD Students

• Roy Araiza, PhD, Purdue University, 2021
  Thesis, "On the abstract structure of operator systems and applications to quantum information theory"
  first position: J.L. Doob Research Assistant Professor (ntt), University of Illinois.
• Seongjun (Jun) Choi, PhD, Purdue University, 2022
  Thesis, "Rational growth in torus bundle groups"
  first position: Visiting Assistant Professor, Purdue University.

Postdocs

• Meng-Che (Turbo) Ho, Golomb Visiting Assistant Professor, Purdue, 2017-2020
  first position: Assistant Professor of Mathematics (tt), Cal State University Northridge.
• Krishnendu Khan, Visiting Assistant Professor, Purdue, 2022-present

Upcoming Travel

• August 28 - September 1, 2023, Workshop on Operator Algebras and Applications: Connections with Logic, Fields Institute, University of Toronto.

Conferences and Workshops

• Wabash Seminar.
• Geometry, Groups, and Dynamics Workshops.
• Rolando de Santiago, Krishnendu Khan, and I are organizing the 20th annual East Coast Operator Algebras Symposium, October 21-22, at Purdue.
• Roy Araiza, Marius Junge, Felix Leditzky, and I organized the workshop "QLA meets QIT II" which was held in downtown Chicago, November 3-5, 2022. Check out the conference webpage and poster!
• Turbo Ho, Ben McReynolds, Julia Knight, and I are organized a special session "Group Theory and Logic" at the AMS Central Spring Sectional Meeting, Purdue University, April 4-5, 2020.
• Roy Araiza and I organized the workshop "QLA meets QIT," November 14-16, 2019 at Purdue.
• I co-organized the workshop "Classification of Group von Neumann Algebras" which was held at AIM January 29 - February 2, 2018.

Past Teaching

• Spring 2022, Math 351, Linear Algebra I.
• Spring 2022, Math 490, Collaborative Problem Solving.
• Fall 2021, Math 353, Linear Algebra II.
• Spring 2021, Math 490, Collaborative Problem Solving
• Spring 2021, Math 546, Functional Analysis
• Spring 2021, Math 301, Introduction to Proof Through Real Analysis
• Fall 2020, Math 440, Honors Real Analysis
• Spring 2020, Math 490, Collaborative Problem Solving
• Fall 2019, Math 598, Mathematics of Quantum Information Theory
• Fall 2019, Math 261, Multivariate Calculus
• Spring 2019, Math 341, Foundations of Analysis
• Spring 2019, Math 490, Collaborative Problem Solving
• Fall 2018, Math 261, Multivariate Calculus
• Spring 2018, Math 490, Collaborative Problem Solving
• Spring 2018, Math 546, Functional Analysis
• Fall 2017, Math 351, Linear Algebra
• Spring 2017, Math 693, Introduction to K-Theory
• Fall 2016, Math 341, Foundations of Analysis
• Spring 2016, Von Neumann Algebras
• Fall 2015, Math 266

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

John Wooden's Seven Point Creed

• Be true to yourself.
• Make each day your masterpiece.
• Help others.
• Drink deeply from good books.
• Make friendship a fine art.
• Build a shelter against a rainy day.
• Pray for guidance, and give thanks for your blessings every day.