Thomas Koberda

photo

E-mail: firstname dot lastname at gmail dot com

Office: Leet Oliver Memorial Hall 211b

Mailing Address:
Yale University
Department of Mathematics
PO Box 208283
New Haven, CT 06520-8283

Here is my CV: pdf

Teaching

I taught a topics course on right-angled Artin groups at Yale in the spring of 2013. Here are some course notes.

I will be teaching Mathematics 350 (Abstract Algebra) and a section of Mathematics 120 (Multivariable Calculus) in the fall of 2014. More information is available on the course website.

Research

I am a Gibbs Assistant Professor at Yale, under Yair Minsky. I will be joining the faculty at the University of Virginia in 2015.

I was graduate student of Curt McMullen. I also talked a lot with Benson Farb. My research is best described as geometric group theory. I am especially interested in mapping class groups of surfaces and right-angled Artin groups. I am also interested in the geometry and topology of 3-manifolds, and have recently become interested in the topology of line arrangements.

Here are my papers. In an effort to spam the arXiv as little as possible, the pdf versions on the Yale server (when available) are more up-to-date than the arXiv versions.

"Right-angled Artin subgroups of the C diffeomorphism group of the real line." Joint with Hyungryul Baik and Sang-hyun Kim. (Submitted) pdf

"Anti-trees and right-angled Artin subgroups of planar braid groups." Joint with Sang-hyun Kim. (Submitted) pdf

"An effective algebraic detection of the Nielsen-Thurston classification of mapping classes." Joint with Johanna Mangahas. (To appear in J. Top. Analysis) pdf

"Right-angled Artin groups and finite subgraphs of curve complexes." Joint with Sang-hyun Kim. (Submitted) pdf

"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

"An obstruction to embedding right-angled Artin groups in mapping class groups." Joint with Sang-hyun Kim. (To appear in Int. Math. Res. Notices) pdf

"Alexander varieties and largeness for finitely presented groups." (To appear in J. Homotopy Rel. Structures) pdf

"Teichmüller polynomials, Alexander polynomials and finite covers of surfaces." (Preprint) pdf

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

"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.

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

"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

"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

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

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

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

"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) NYJM link

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

Non-original work and writings unsuitable for publication

"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

"Notes on recent work of Dani Wise." These are some recent expository notes which contain a new theorem as well. This is a new version, fixing two minor errors in the first version. The corrections are: 1. one needs a relative version of the main theorem to establish virtual fibering of cusped hyperbolic 3-manifolds, and 2. graph groups are residually finite rationally solvable, but it is not because they are residually torsion-free nilpotent. pdf

"Representations of Galois Groups on the Homology of Surfaces." Joint with A. Silberstein. arXiv link

"On some of the residual properties of finitely generated nilpotent groups." pdf, arXiv link