BS, Mathematics, IUPUI, 2006

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.

- Fall 2023, Math 353, Linear Algebra II.

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

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

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

- w/ Roy Araiza and Colton Griffin, An index for inclusions of operator systems, J. Operator Theory, accepted. arXiv.
- 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.
- w/ Roy Araiza, Colton Griffin, and Aneesh Khilnani, Approximating projections by quantum operations, Linear Algebra Appl. 663 (2023), 178-199. arXiv. article.
- w/ Garrett Mulcahy, Malnormal matrices, Proc. Amer. Math. Soc. 150 (2022), no. 7, 2969-2982. arXiv. article.
- w/ Rolando de Santiago, Ben Hayes, and Daniel J. Hoff, Maximal rigid subalgebras of deformations and L
^{2}-cohomology, Anal. PDE. 14 (2021), no. 7, 2269-2306. arXiv. article. - 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.
- w/ Isaac Goldbring, On the axiomatizability of C*-algebras as operator systems, Glasg. Math. J., 61 (2019). arXiv. article.
- w/ Isaac Goldbring, Robinson forcing and the quasidiagonality problem, Internat. J. Math., 28 (2017) Article 175008. arXiv. article.
- CP-stability and the local lifting property, New York J. Math. 23 (2017) 739-747. arXiv. article.
- w/ Isaac Goldbring, Omitting types in operator systems, Indiana Univ. Math. J. 66 (2017) 821-844. arXiv. article.
- 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.
- 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.
- w/ Isaac Goldbring, Games and elementary equivalence of II
_{1}factors, Pacific J. Math. 278 (2015) 103-118. arXiv. article. - w/ Isaac Goldbring, On Kirchberg's embedding problem, J. Funct. Anal. 269 (2015), 155-198 arXiv. article.
- w/ Ionuţ Chifan, On the ergodic theorem for affine actions on Hilbert space, Bull. Belgian Math. Soc. 22 (2015), 429-446.arXiv. article.
- 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.
- w/ Ionuţ Chifan and Bogdan Udrea, On the structural theory of II
_{1}factors of negatively curved groups, II, Adv. Math. 245 (2013), 208-236. arXiv. article. - w/ Ionuţ Chifan, On the structural theory of II
_{1}factors of negatively curved groups, Ann. Sci. Éc. Norm. Supér. 46 (2013), 1-33. arXiv. article. - w/ Jesse Peterson, On cocycle superrigidity for Gaussian actions, Ergodic Theory Dynam. Systems 32 (2012), 249-272. pdf. article.
- 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.

- w/ Isaac Goldbring and Bradd Hart, Correspondences, ultraproducts and model theory, preprint. arXiv.
- 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.

- 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.

- 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

- 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.

- 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

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

- 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.

- 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.