Thomas Koberda
E-mail: koberda at math dot harvard dot edu
Office: Science Center 425b
Mailing Address:
Harvard University
Department of Mathematics
1 Oxford St
Cambridge, MA 02143
Here is my CV: pdf
Teaching
I am the CA for Math 231a in the fall of 2011. Solutions to problem sets: 2, 3, 4, 5, 6.
Research
I am a fifth year graduate student, studying with Curt McMullen. I also talk a lot with Benson Farb. My research is best described as geometric group theory. I am especially interested in mapping class groups of surfaces. I am also interested in the geometry and topology of 3-manifolds. Next fall I will be joining the mathematics department at Yale as a Gibbs Assistant Professor and an NSF fellow under Yair Minsky.
Here are my papers. In an effort to spam the arXiv as little as possible, the pdf versions on the Harvard server (when available) are more up-to-date than the arXiv versions.
"Teichmüller polynomials, Alexander polynomials and finite covers of surfaces." (Preprint) pdf
"The action of mapping classes on nilpotent covers of surfaces." (Preprint) pdf
"Embedability between right-angled Artin groups." Joint with Sang-hyun Kim. (Preprint) pdf, arXiv link
"Ping-pong lemmas with applications to geometry and topology." (To appear in the Institute for Mathematical Sciences Lecture Notes Series) 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, arXiv link
"Right-angled Artin groups and a generalized isomorphism problem for finitely generated subgroups of mapping class groups." (Preprint) pdf, arXiv link
"Entropy of automorphisms, homology and the intrinsic polynomial structure of nilpotent groups." (To appear in Proceedings of the 2011 Ahlfors-Bers Colloquium) pdf
"Residual properties of fibered and hyperbolic 3-manifolds." (Preprint) pdf arXiv link
"Effective indices of subgroups in one-relator groups with free quotients." (Communications in Algebra 39 (2011) 1-6) 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, arXiv link
"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
Reviews written
Richard Hain. "Relative weight filtrations on completions of mapping class groups." review
Koji Fujiwara. "Subgroups generated by two pseudo-Anosov elements in a mapping class group. I. Uniform exponential growth." review
R.B.J.T. Allenby, Goansu Kim, C.Y. Tang. "Conjugacy separability of Seifert 3-manifold groups over non-orientable surfaces." review
Andrés Navas and Cristobál Rivas. "Describing all bi-orderings on Thompson's group F." review
Takao Satoh. "On the fourth Johnson homomorphism of the automorphism group of a free group." review
Ilya Kapovich and Martin Lustig. "Ping-pong and outer space." review
T. Banakh, J. Higes and I. Zarichnyi. "The coarse classification of countable abelian groups." review
Louis Funar and Daniele Ettore Otera. "On the wgsc and qsf tameness conditions for finitely presented groups." review
Henry Wilton and Pavel Zalesskii. "Profinite properties of graph manifolds." review
Nermin Salpeci. "Real elements in the mapping class group of T2." review
Mahan Mj. "Cannon-Thurston maps and bounded geometry." review
Marc Lackenby. "Detecting large groups." review
Mohammad N. Abdulrahim and Madline Al-Tahan. "On a class of irreducible representations of the braid group Bn." review
Jon P. Bannon and Nicholas Noblett. "A note on nonresidually solvable hyperlinear one-relator groups." review
Khalid Bou-Rabee. "Parasurface groups." review
Jon P. Bannon. "A non-residually solvable hyperlinear one-relator group." review
Tetsuya Ito. "On finite Thurston-type orderings of braid groups." review
Tetsuya Ito. "A note on geometric constructions of bi-invariant orderings." review
Nigel Boston and Jordan S. Ellenberg. "Random pro-p groups, braid groups, and random tame Galois groups." review
Darren D. Long and Alan W. Reid. "Grothendieck's problem for 3-manifold groups." review
K.B. Wong and P.C. Wong. "Conjugacy separability and outer automorphism groups of certain HNN extensions." review
Jason Behrstock, Cornelia Druţu and Mark Sapir. "Median structures on asymptotic cones and homomorphisms into mapping class groups." review
Jason Behrstock, Cornelia Druţu and Mark Sapir. "Addendum: Median structures on asymptotic cones and homomorphisms into mapping class groups." review
Saeko Yamagata. "The girth of convergence groups and mapping class groups." review
Lior Bary-Soroker, Katherine F. Stevenson and Pavel A. Zalesskii. "Subgroups of profinite surface groups." review
Adam Clay. "Exotic left-orderings of the free groups from the Dehornoy ordering." review