Papers
Click after the title to see the paper.

Irrationality of the general smooth quartic $3$fold using intermediate Jacobians
pdf
preprint, July 2024, 5 pages.

The smooth MordellWeil group and mapping class groups of elliptic surfaces
pdf
(with E. Looijenga) preprint, revised May 2024, 31 pages.

Moduli spaces and period mappings of genus one fibered K3 surfaces
pdf
(with E. Looijenga) preprint, March 2023, 31 pages.

Rigidity of moduli spaces and algebrogeometric constructions
pdf
in Chern: a great geometer of the 20th century,
Surveys in Differential Geometry, vol. 26, 3149 (2024).

Essential dimension via prismatic cohomology
pdf
(With M. Kisin and J. Wolfson), Duke Math. Jour., to appear.

Global rigidity of the period mapping
pdf
Jour. of Algebraic Geometry, 33 (2024), 199212.

The Nielsen Realization problem for K3 surfaces
pdf
(With E. Looijenga), Jour. Diff. Geom. (JDG),
Vol.127, no.2, 505549 (2024).

Roger Alperin memorial article
pdf
(With P. Shalen), Notices AMS , Vol.67, No.11, Dec. (2020).

Modular functions and resolvent problems
pdf
(With M. Kisin and J. Wolfson, appendix by N. Harman),
Math. Annalen, 386 (2023), no. 12, p.113150.

Geometry of the WimanEdge pencil and the Wiman curve
pdf
(With E. Looijenga), Geometriae Dedicata ,
208, no. 3, (2018), 879930.

Arithmeticity of the monodromy of the WimanEdge pencil
pdf
(With E. Looijenga), Annales l'Institut Fourier,
Vol. 71 (2021), no. 4, p.13251361.

Essential dimension of congruence covers
pdf
(With M. Kisin and J. Wolfson), Compositio Math. ,
Vol.157 (2021), no. 11, p.24072432.

Resolvent degree, Hilbert's 13th Problem and geometry
pdf
(With J. Wolfson), Enseign. Math. 65 (2019), no. 34, 303376.

Geometry of the WimanEdge pencil, I: algebrogeometric aspects
pdf
(With I. Dolgachev and E. Looijenga), Eur. J. Math. 4 (2018), no. 3, 879930.

Coincidences of homological densities, predicted by arithmetic
pdf
(With M. Wood and J. Wolfson), Advances in Math. , Vol. 352 (2019), 670716.

Finite covers of graphs, their primitive homology, and representation theory
pdf
(With S. Hensel), New York Jour. of Math. , Volume 22 (2016) 13651391.

Etale homological stability and arithmetic statistics
pdf
(with J. Wolfson), Quart. Jour. Math. 69 (2018), no. 3, 951974.

Topology and arithmetic of resultants, II: the resultant=1 hypersurface
pdf
(with J. Wolfson, appendix by C. Cazanave),
Algebraic Geometry 4 (2017), no. 3, 337352.

Moving homology in finite covers of graphs
pdf
(with S. Hensel), Israel J. Math. 220 (2017), no. 2, 605615.

Topology and arithmetic of resultants, I
pdf
(with J. Wolfson), New York Jour. of Math., Vol.22, (2016), 801821. [Revised Version]

A vanishing theorem for the homology of
discrete subgroups of ${\rm Sp}(n,1)$ and $F_4^{20}
pdf
(with C. Connell and D.B. McReynolds), Jour. of the London
Math. Soc. (2) 94 (2016), no. 2, 357376.

Integrality in the Steinberg module and the topdimensional cohomology of $GL_n{\cal O}_K$
pdf
(with T. Church and A. Putman), American Jour. of Math. Vol.141, no.5 (2019), 13751419.

Torelli buildings and their automorphisms
pdf
(with N. Ivanov), preprint, Dec. 2014, 39 pages.

On being Thurstonized
pdf
appeared in Notices AMS, Jan. 2016.

Representation Stability
pdf
Proceedings of the ICM, Seoul 2014,
Vol. II, 11731196.

Representation stability in cohomology and asymptotics for families of
varieties over finite fields
pdf
(with T. Church and J. Ellenberg), Contemporary Mathematics 620 (2014), 154.

FImodules over Noetherian rings
pdf
(with T. Church, J. Ellenberg, and R Nagpal), Geometry and Topology 185 (2014), 29512984.

A stability conjecture for the unstable cohomology of mapping class
groups, SL_n(Z), and Aut(F_n)
pdf
(with T. Church and A. Putman), in Algebraic Topology: Applications
and New Directions, AMS Contemporary Math. Series, Vol. 620, (2014) 5570.

FImodules and stability for representations of symmetric groups
pdf
(with T. Church and J. Ellenberg), Duke Mathematical Journal, Vol. 164, No. 9,
(2015), 18331910.

The rational cohomology of the mapping class group vanishes
in its virtual cohomological dimension
pdf
(with T. Church and A. Putman), Inter. Math. Res. Notices , IMRN, no. 21 (2012), 50255030.

On the geometric nature of characteristic classes of surface bundles
pdf
(with T. Church and M. Thibeault), Journal of Topology , Vol. 5 (2012), 575592.

Representation theory and homological stability.
pdf
(with T. Church), Advances in Math. , Vol. 245 (2013), 250314.

Remembering John Stallings
pdf
(edited with D. Calegari),
Notices of the AMS, Vol. 56, No. 11, Dec. 2009, p.14101417.

The extremal symmetry of arithmetic simplicial complexes.
pdf
(with A. Mohammadi), Advances in Math. , Vol.
231 (2012), no. 2, 843854.

Parameterized AbelJacobi maps and abelian cycles in the Torelli group
pdf
(with T. Church), Jour. of Topology,
5 (2012), no. 1, 1538.

Infinite generation of the kernels of the Magnus and Burau representations.
pdf
(with T. Church), Alg. and Geom. Top. (AGT), 10 (2010), no. 2, 837851.
Click here for the accompanying Mathematica Notebook.

Small dilatation pseudoAnosovs and 3manifolds.
pdf
(with C. Leininger and D. Margalit),
Advances in Math. , Vol. 228 (2011), 14661502.

Teichmuller geometry of moduli space, II: M(S) seen from far away.
pdf
(with H. Masur),
In the tradition of AhlforsBers.
V, 7179,
Contemp. Math., 510, Amer. Math. Soc., 2010.

Rigidity, locally symmetric varieties and the GrothendieckKatz Conjecture.
ps or pdf
(with M. Kisin), Inter. Math. Res. Notices , Vol. 2009, No.22, pp. 41594167.

Group actions and Helly's theorem
ps or pdf
Advances in Math, Vol. 222, Issue 5, 15741588 (2009).

The intrinsic asymmetry and inhomogeneity of Teichmuller space.
pdf
(with S. Weinberger), Duke Math. Journal, Vol. 155 (2010), No. 1, 91103.

Problems on automorphism groups of nonpositively curved
polyhedral complexes and their lattices.
ps or pdf
(with C. Hruska and A. Thomas), in
Geometry, Rigidity, and Group Actions (B. Farb and D. Fisher, eds.),
515560,
Chicago Lectures in Math., Univ. Chicago Press, 2011.

Teichmuller geometry of moduli space, I: Distance minimizing rays and
the
DeligneMumford compactification.
ps or pdf
(with H. Masur), Jour. Diff. Geom., Vol. 85 (2010), 187227.

Irreducible Sprepresentations and subgroup distortion in the
mapping class group.
pdf
(with N. Broaddus and A. Putman),
Comment. Math. Helv. , Vol. 86, No. 3 (2011), 537556.

The Casson invariant and the word metric on the Torelli group.
ps or pdf
(with N. Broaddus and A. Putman), C.R. Acad. Sci Paris, Vol.
345 (2007),
no. 8, 449452.

Commensurations of Out(F_n).
ps or pdf
(with Michael Handel),
Publ. Math. IHES., No. 105 (2007), 148.

(Book)
Problems on Mapping Class Groups and Related Topics.
pdf
This is a (June 2006) version of a book that appeared as
Proc. Symp. Pure and Applied Math., Volume 74, 2006.
It is the
final online version. 402 pages.

Some problems on mapping class groups and moduli space.
dvi or
ps or pdf
in ``Problems on Mapping Class Groups and Related Topics",
ed. by B.
Farb,
Proc. Symp. Pure and Applied Math., Vol. 74, pp. 1155,
June 2006.

The lower central series and pseudoAnosov dilatations.
ps or pdf
(with C. Leininger and D. Margalit),
American Jour. Math, 130 (2008), no. 3, 799827.

The BirmanCraggsJohnson homomorphism and abelian cycles in the
Torelli
group.
dvi or ps or pdf
(with T. Brendle), Math. Annalen, 338
(2007), no. 1, 3353.

Isometries, rigidity and universal covers.
dvi or ps or pdf
(with S. Weinberger), Annals of Math,
Vol. 186, No.3, p.915940 (2008)

Commensurability invariants for nonuniform tree lattices.
dvi or ps or pdf
(with C. Hruska), Israel Jour. Math.
152 (2006), 125142.

Hidden symmetries and arithmetic manifolds.
dvi or ps or pdf
(with S. Weinberger), in
Geometry, spectral theory, groups, and dynamics ,
Contemp. Math., Vol. 387, Amer. Math. Soc., pp. 111119.

The Torelli Geometry and its applications.
dvi or ps or pdf
(with N. Ivanov), Math. Research Letters., Vol. 12,
pp. 293301 (2005).

Every mapping class group is generated by 6 involutions.
dvi or ps or pdf
(with T. Brendle),
Journal of Algebra. , Vol. 278 (2004), 187198.

Some recent applications of the barycenter method in geometry.
dvi or ps or pdf
(with C. Connell), in
Topology and Geometry of Manifolds ,
Proc. Symp. in Pure Math., G. Matic and C. McCrory, Eds., 2003,
1951.

The Degree Theorem in higher rank.
dvi or ps or pdf
(with C. Connell), J. Diff. Geom., Vol. 65 (2003), 1959.
Erratum pdf

Realanalytic, volumepreserving actions of lattices on 4manifolds.
dvi or ps or pdf
(with P. Shalen), C.R. Acad. Sci Paris, Ser. I,
Vol. 334 (2002), 10111014.

Curvature and rank of Teichmuller space.
dvi or ps or pdf
(with J. Brock), American Jour. Math. , Vol. 128, No. 1
(2006), pp. 122.

Groups of homeomorphisms of onemanifolds, III: Nilpotent subgroups.
pdf
(with J. Franks), Ergodic Theory Dynam.
Systems 23 (2003), no. 5, 14671484 [Corrected Version, 102818]

Convex cocompact subgroups of mapping class groups.
dvi or ps or pdf
(with L. Mosher), Geometry and Topology, Vol. 6 (2002), 91152.

Groups of homeomorphisms of onemanifolds, I: Actions of nonlinear
groups .
dvi or ps or pdf
(with J. Franks), in ``What's next?'', Annals of Math. Stud., 205, 116140 (2020)

Groups of homeomorphisms of onemanifolds, II: Extensions of
Holder's Theorem.
dvi or ps or pdf
(with J. Franks), Trans. Amer. Math. Soc. , Vol. 355 (2003),
no. 11, 43854396.

A strong Schottky Lemma for nonpositively curved singular spaces.
dvi or ps or pdf
(with R. Alperin and G. Noskov),
Geometriae Dedicata , Vol. 92 (2002), 235243.

The geometry of surfacebyfree groups.
dvi or ps or pdf
(with L. Mosher), Geom. Funct. Anal (GAFA),
Vol.12 (2002), no. 5, 915963.

Minimal entropy rigidity for lattices in products of rank one symmetric
spaces.
dvi or ps or pdf
(with C. Connell).
Comm. in Anal. and Geom. 11 (2003), no. 5,
10011026.

Rank one phenomena for mapping class groups.
dvi or ps or pdf
(with A. Lubotzky and Y. Minksy).
Duke Math Journal, Vol. 106, No.3 (2001), 581597.

Problems on the geometry of finitely generated solvable groups.
dvi or ps or pdf
(with L. Mosher), in ``Crystallographic Groups and their
Generalizations (Kortrijk, 1999)'',
(ed. P. Igodt, et. al.),
Cont. Math. 262, Amer. Math. Soc. (2000).

On the asymptotic geometry of abelianbycyclic groups.
dvi or ps
or pdf
(with L. Mosher).
Acta Math. , Vol. 184, No.2 (2000), 145202.

Groups of realanalytic diffeomorphisms of the circle.
dvi or ps
(with P. Shalen). Ergodic Theory and Dynam.
Syst. , Vol. 22 (2002), 835844.

Lattice actions, 3manifolds, and homology.
dvi or ps
(with P. Shalen). Topology , Vol. 39 (2000), no. 3,
573587.

Realanalytic actions of lattices.
dvi or ps
(with P. Shalen). Inventiones Math. , Vol. 135 (1998),
273296.

A remark about actions of lattices on free groups.
dvi or ps
(with M. Bridson). Topology Appl. , Vol. 110, No. 1 (2001),
2124.

Harmonic splittings of surfaces.
dvi or ps
(with M. Wolf). Topology, Vol. 40, No.6 (2001), 13951414.

Superrigidity and mapping class groups.
dvi or ps
(with H. Masur). Topology , Vol. 37, No.6 (1998),
11691176.

Quasiisometric rigidity for the solvable BaumslagSolitar
groups, II.
dvi or ps
(with L. Mosher) Inventiones Math. , Vol. 137 (1999),
No. 3, 273296.

The quasiisometry classification of lattices in semisimple Lie
groups.
dvi or ps
Math. Res. Letters, Vol. 4, No.5, Sept. 1997, 705718.

A rigidity theorem for the solvable BaumslagSolitar groups.
dvi or ps
(with L. Mosher). Inventiones Math. , Vol. 131, No.2 (1998),
419451.

Quasiflats and rigidity in higher rank symmetric spaces.
dvi or ps
(with A. Eskin).
Journal AMS. , Vol. 10, No.3, July 1997, 653692.

Quasiflats in H^{2}xH^{2}.
dvi or ps
(with A. Eskin).
Proceedings of the International Colloquium on Lie groups and
Ergodic Theory, Tata Institute 1996.

The largescale geometry of Hilbert modular groups.
dvi or ps
(with R. Schwartz). J. Diff. Geom. 44, No.3 (1996),
435478.

Relatively hyperbolic groups.
dvi or ps
Geom. Funct. Anal. (GAFA), Vol.8 (1998), 131.

Fillinginvariants at infinity for manifolds of nonpositive
curvature.
dvi or ps
(with N. Brady). Trans. Amer. Math. Soc., Vol.350, No.8
(1998), 33933405.

Relatively hyperbolic and automatic groups with applications to
negatively curved manifolds.
Thesis, Princeton University, May 1994.

Combing lattices in semisimple Lie groups.
dvi or ps
Groups  Korea '94, Proceedings of the international conference,
ed. by A.C. Kim and
D.L. Johnson, deGruyter 1994, 5767.

The Extrinsic geometry of subgroups and the generalized
word problem.
dvi or ps
Proc. London Math. Soc. (3) 68 (1994), 577593.

(Book)Noncommutative Algebra.
(book with R.K. Dennis),
Graduate Texts in Mathematics 144, 270 pages, Springer, New York, 1993.

Automatic groups: A guided tour.
dvi or ps
L'Enseignement Math., Vol. 38 (1992), 291313.