Thomas Koberda

Associate Professor of Mathematics, University of Virginia

Email: firstname.lastname at gmail dot com, or firstname.lastname at virginia dot edu

Office: Kerchof 304

Mailing Address:

Department of Mathematics

University of Virginia

P. O. Box 400137

Charlottesville, VA 22904-4137 USA



In the spring semester of 2021 I will teach Math 3315 (Advanced Calculus and Linear Algebra). All course materials/syllabi can be found on the relevant collab sites.

In 2013 I taught a course on right-angled Artin groups at Yale. Here are some notes, which will eventually become a book. pdf


My research is best described as geometric group theory. I am especially interested in mapping class groups of surfaces, right-angled Artin groups, and one-dimensional dynamics. I am also interested in the geometry and topology of 3-manifolds, and have become interested in the topology of arrangements and in model theory.

Here is my Google Scholar profile, and my MathSciNet profile.

Here are my research papers, in the (reverse) order that they were written. In an effort to spam the arXiv as little as possible, the pdf versions on this site (when available) are more up-to-date than the arXiv versions.

50. "Structure and regularity of group actions on one-manifolds." Book joint with Sang-hyun Kim. (To appear in the series Springer Monographs in Mathematics). pdf

49. "Virtual critical regularity of mapping class group actions on the circle." Joint with Sang-hyun Kim and Cristóbal Rivas. (To appear in Transformation Groups). pdf

48. "Geometry and combinatorics via right-angled Artin groups." (To appear in In the tradition of Thurston, vol. 2, K. Ohshika and A. Papadopoulos eds.). pdf

47. "Hamiltonicity via cohomology of right-angled Artin groups." Joint with Ramón Flores and Delaram Kahrobaei. (Linear Algebra Appl. 631 (2021), 94-110). pdf

46. "Direct products, overlapping actions, and critical regularity." Joint with Sang-hyun Kim and Cristóbal Rivas. (J. Mod. Dyn. 17 (2021), 285-304). pdf

45. "Shapes of hyperbolic triangles and once-punctured torus groups." Joint with Sang-hyun Kim, Jaejeong Lee, Ken'ichi Ohshika, and Ser Peow Tan, with an appendix by Xinghua Gao. (Math. Z. 299 (2021), no. 3-4, 2103-2130). pdf

44. "Expanders and right-angled Artin groups." Joint with Ramón Flores and Delaram Kahrobaei. (To appear in J. Topol. Anal.). pdf

43. "Model theory of the curve graph." Joint with Valentina Disarlo and Javier de la Nuez González. (Preprint). pdf

42. "An algebraic characterization of k-colorability." Joint with Ramón Flores and Delaram Kahrobaei. (Proc. Amer. Math. Soc. 149 (2021), no. 5, 2249-2255). pdf

41. "Small C1 actions of semidirect products on compact manifolds." Joint with Christian Bonatti, Sang-hyun Kim, and Michele Triestino. (Algebr. Geom. Topol. 20 (2020), 3183-3203). pdf journal

40. "Integrability of moduli and regularity of Denjoy counterexamples." Joint with Sang-hyun Kim. (Discr. Contin. Dynam. Syst. 40 (2020), no. 10, 6061-6088). pdf

39. "A cryptographic application of the Thurston norm." Joint with Ramón Flores and Delaram Kahrobaei. (International Journal of Computer Mathematics: Computer Systems Theory 5 (2020), no. 1, 15-24.) pdf

38. "Commensurators of thin normal subgroups and abelian quotients." Joint with Mahan Mj. (Submitted) pdf

37. "Algebraic Structure of Diffeomorphism Groups of One-Manifolds." Joint with Jaewon Chang and Sang-hyun Kim. (To appear in Proceedings of the Jean-Morlet Semester, Spring 2018, Springer) pdf

36. "An effective Lie-Kolchin theorem for quasi-unipotent matrices." Joint with Feng Luo and Hongbin Sun. (Linear Algebra Appl. 581 (2019) 304-323) pdf

35. "Non-freeness of groups generated by two parabolic elements with small rational parameters." Joint with Sang-hyun Kim. (To appear in Michigan Math. Journal) pdf ancillary file

34. "Commutators, commensurators, and PSL2(Z)." Joint with Mahan Mj. (J. Topol. 14 (2021), no. 3, 861-876) pdf

33. "Algorithmic Problems in right-angled Artin groups: Complexity and Applications." Joint with Ramón Flores and Delaram Kahrobaei. (J. Algebra 519 (2019), 111-129) pdf

32. "Diffeomorphism groups of critical regularity." Joint with Sang-hyun Kim. (Invent. Math. 221 (2020), no. 2, 421-501.) pdf journal

31. "What is... an acylindrical group action?" (Not. Amer. Math. Soc. 65 (2018), no. 1, 31-34.) pdf

30. "Free products and the algebraic structure of diffeomorphism groups." Joint with Sang-hyun Kim. (J. Topol. 11 (2018), 1053-1075) pdf

29. "Actions of right-angled Artin groups in low dimensions." (Handbook of Group Actions (Vol. V) ALM 48, Ch. 6, pp. 227-260) pdf

28. "Two-chains and square roots of Thompson's group F." Joint with Yash Lodha. (Ergodic Theory Dynam. Systems 40 (2020), no. 9, 2515-2532) pdf

27. "Representations of surface groups with finite mapping class group orbits." Joint with Indranil Biwas, Mahan Mj, and Ramanujan Santharoubane. (New York J. Math. 24 (2018), 241-250) pdf journal

26. "Irreducibility of quantum representations of mapping class groups with boundary." Joint with Ramanujan Santharoubane. (Quantum Topology 9 (2018), no. 4, 633-641) pdf

25. "Chain groups of homeomorphisms of the interval." Joint with Sang-hyun Kim and Yash Lodha. (Ann. Sci. de l'ENS (4) 52 (2019), no. 4, 797-820) pdf-long


24. "Flexibility of group actions on the circle." Joint with Sang-hyun Kim and Mahan Mj. (Lecture Notes in Mathematics, 2231. Springer, Cham, 2019) pdf

23. "Residually finite rationally p groups." Joint with Alexander I. Suciu. (Comm. Contemp. Math. 22 (2020), no. 3, 1950016, 44 pp.) pdf

22. "A representation theoretic characterization of simple closed curves on a surface." Joint with Ramanujan Santharoubane. (Math. Res. Lett. 25, No. 5 (2018), 1485-1496) pdf

21. "Unsmoothable group actions on compact one-manifolds." Joint with Hyungryul Baik and Sang-hyun Kim. (J. Eur. Math. Soc. 21 (2019), no. 8, 2333-2353) pdf

20. "Quotients of surface groups and homology of finite covers via quantum representations." Joint with Ramanujan Santharoubane. (Invent. Math. 206 (2016), 269-292) pdf

19. "The geometry of purely loxodromic subgroups of right-angled Artin groups." Joint with Johanna Mangahas and Samuel J. Taylor. (Trans. Amer. Math. Soc. 369 (2017), no. 11, 8179-8208) pdf

18. "Injective maps between flip graphs." Joint with Javier Aramayona and Hugo Parlier. (Ann. Inst. Fourier 65 (2015), no. 5, 2037-2055) pdf

17. "Right-angled Artin subgroups of the C diffeomorphism group of the real line." Joint with Hyungryul Baik and Sang-hyun Kim. (Israel J. Math. 213 (2016), no. 1, 175-182) pdf

16. "Anti-trees and right-angled Artin subgroups of planar braid groups." Joint with Sang-hyun Kim. (Geom. Topol. 19 (2015), no. 6, 3289-3306) pdf

15. "An effective algebraic detection of the Nielsen-Thurston classification of mapping classes." Joint with Johanna Mangahas. (J. Top. Analysis 7 (2015), no. 1, 1-21) pdf

14. "Right-angled Artin groups and finite subgraphs of curve complexes." Joint with Sang-hyun Kim. (Osaka J. Math. 53 (2016), 705-716) pdf

13. "The geometry of the curve graph of a right-angled Artin group." Joint with Sang-hyun Kim. (Int. J. Algebra Comput. 24 (2014), no. 2, 121-169) pdf

12. "An obstruction to embedding right-angled Artin groups in mapping class groups." Joint with Sang-hyun Kim. (Int. Math. Res. Not. IMRN 2014, no. 14, 3912-3918) pdf

11. "Alexander varieties and largeness for finitely presented groups." (J. Homotopy Rel. Structures 9 (2014), no. 2, 513-531) pdf

10. "Embedability between right-angled Artin groups." Joint with Sang-hyun Kim. (Geom. Topol. 17 (2013), no. 1, 493-530) pdf appendix

9. "Ping-pong lemmas with applications to geometry and topology." (Geometry, topology and dynamics of character varieties, 139-158, Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap., 23, World Sci. Publ., Hackensack, NJ, 2012) I cannot post this paper on my website due to the copyright agreement.

8. "Faithful actions of automorphisms on the space of orderings of a group." (New York J. Math. 17 (2011) 783-798) journal

7. "Right-angled Artin groups and a generalized isomorphism problem for finitely generated subgroups of mapping class groups." (Geom. Funct. Anal. 22 (2012), no. 6, 1541-1590) pdf

6. "Entropy of automorphisms, homology and the intrinsic polynomial structure of nilpotent groups." (In the tradition of Ahlfors-Bers. VI, 87-99, Contemp. Math., 590, Amer. Math. Soc., Providence, RI, 2013) pdf

5. "Residual properties of fibered and hyperbolic 3-manifolds." (Topology Appl. 160 (2013), no. 7, 875-886) pdf

4. "Effective indices of subgroups in one-relator groups with free quotients." (Comm. Alg. 39 (2011), no. 11, 4336-4341) arxiv

3. "Asymptotic linearity of the mapping class group and a homological version of the Nielsen-Thurston classification." (Geom. Dedicata 156 (2012), 13-30) journal

2. "On ergodic transformations that are both weakly mixing and uniformly rigid." Joint with J. James, K. Lindsey, C.E. Silva and P. Speh. (New York Journal of Mathematics 15 (2009) 393-403) journal

1. "Measurable Sensitivity." Joint with J. James, K. Lindsey, C.E. Silva and P. Speh. (Proceedings of the American Mathematical Society 136 (2008) 3549-3559) journal

Other writings:

1. "Class field theory and the MKR dictionary for knots." This was my minor thesis at Harvard. I am not a number theorist and I expect that there are many mistakes and inaccurate statements contained therein. It is expository and does not contain many proofs. pdf

2. "Notes on recent work of Dani Wise." pdf

3. "Representations of Galois Groups on the Homology of Surfaces." Joint with A. Silberstein. arxiv

4. "On some of the residual properties of finitely generated nilpotent groups." arxiv

5. "Teichmüller polynomials, Alexander polynomials and finite covers of surfaces." (Eternal preprint) pdf