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 Mordell-Weil 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 algebro-geometric constructions pdf
  in Chern: a great geometer of the 20th century,
  Surveys in Differential Geometry, vol. 26, 31--49 (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), 199--212.
  
  
• The Nielsen Realization problem for K3 surfaces pdf
  (With E. Looijenga), Jour. Diff. Geom. (JDG), Vol.127, no.2, 505--549 (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. 1-2, p.113--150.
  
  
• Geometry of the Wiman-Edge pencil and the Wiman curve pdf
  (With E. Looijenga), Geometriae Dedicata , 208, no. 3, (2018), 879--930.
  
  
• Arithmeticity of the monodromy of the Wiman-Edge pencil pdf
  (With E. Looijenga), Annales l'Institut Fourier, Vol. 71 (2021), no. 4, p.1325--1361.
  
  
• Essential dimension of congruence covers pdf
  (With M. Kisin and J. Wolfson), Compositio Math. , Vol.157 (2021), no. 11, p.2407--2432.
  
  
• Resolvent degree, Hilbert's 13th Problem and geometry pdf
  (With J. Wolfson), Enseign. Math. 65 (2019), no. 3-4, 303-376.
  
  
• Geometry of the Wiman-Edge pencil, I: algebro-geometric aspects pdf
  (With I. Dolgachev and E. Looijenga), Eur. J. Math. 4 (2018), no. 3, 879--930.
  
  
• Coincidences of homological densities, predicted by arithmetic pdf
  (With M. Wood and J. Wolfson), Advances in Math. , Vol. 352 (2019), 670--716.
  
  
• Finite covers of graphs, their primitive homology, and representation theory pdf
  (With S. Hensel), New York Jour. of Math. , Volume 22 (2016) 1365--1391.
  
  
• Etale homological stability and arithmetic statistics pdf
  (with J. Wolfson), Quart. Jour. Math. 69 (2018), no. 3, 951--974.
  
  
• Topology and arithmetic of resultants, II: the resultant=1 hypersurface pdf
  (with J. Wolfson, appendix by C. Cazanave), Algebraic Geometry 4 (2017), no. 3, 337--352.
  
  
• Moving homology in finite covers of graphs pdf
  (with S. Hensel), Israel J. Math. 220 (2017), no. 2, 605--615.
  
  
• Topology and arithmetic of resultants, I pdf
  (with J. Wolfson), New York Jour. of Math., Vol.22, (2016), 801--821. [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, 357--376.
  
  
• Integrality in the Steinberg module and the top-dimensional cohomology of $GL_n{\cal O}_K$ pdf
  (with T. Church and A. Putman), American Jour. of Math. Vol.141, no.5 (2019), 1375-1419.
  
  
• 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, 1173--1196.
  
  
• Representation stability in cohomology and asymptotics for families of
  varieties over finite fields pdf
  (with T. Church and J. Ellenberg), Contemporary Mathematics 620 (2014), 1-54.
  
  
• FI-modules over Noetherian rings pdf
  (with T. Church, J. Ellenberg, and R Nagpal), Geometry and Topology 18-5 (2014), 2951-2984.
  
  
• 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) 55-70.
  
  
• FI-modules and stability for representations of symmetric groups pdf
  (with T. Church and J. Ellenberg), Duke Mathematical Journal, Vol. 164, No. 9, (2015), 1833-1910.
  
  
• 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), 5025-5030.
  
  
• On the geometric nature of characteristic classes of surface bundles pdf
  (with T. Church and M. Thibeault), Journal of Topology , Vol. 5 (2012), 575-592.
  
  
• Representation theory and homological stability. pdf
  (with T. Church), Advances in Math. , Vol. 245 (2013), 250-314.
  
  
• Remembering John Stallings pdf
  (edited with D. Calegari), Notices of the AMS, Vol. 56, No. 11, Dec. 2009, p.1410-1417.
  
  
• The extremal symmetry of arithmetic simplicial complexes. pdf
  (with A. Mohammadi), Advances in Math. , Vol. 231 (2012), no. 2, 843--854.
  
  
• Parameterized Abel-Jacobi maps and abelian cycles in the Torelli group pdf
  (with T. Church), Jour. of Topology, 5 (2012), no. 1, 15--38.
  
  
• Infinite generation of the kernels of the Magnus and Burau representations. pdf
  (with T. Church), Alg. and Geom. Top. (AGT), 10 (2010), no. 2, 837--851.
  Click here for the accompanying Mathematica Notebook.
  
  
• Small dilatation pseudo-Anosovs and 3-manifolds. pdf
  (with C. Leininger and D. Margalit), Advances in Math. , Vol. 228 (2011), 1466--1502.
  
  
• Teichmuller geometry of moduli space, II: M(S) seen from far away. pdf
  (with H. Masur), In the tradition of Ahlfors-Bers. V, 71--79,
  Contemp. Math., 510, Amer. Math. Soc., 2010.
  
  
• Rigidity, locally symmetric varieties and the Grothendieck-Katz Conjecture. ps or pdf
  (with M. Kisin), Inter. Math. Res. Notices , Vol. 2009, No.22, pp. 4159-4167.
  
  
• Group actions and Helly's theorem ps or pdf
  Advances in Math, Vol. 222, Issue 5, 1574-1588 (2009).
  
  
• The intrinsic asymmetry and inhomogeneity of Teichmuller space. pdf
  (with S. Weinberger), Duke Math. Journal, Vol. 155 (2010), No. 1, 91--103.
  
  
• 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.), 515--560,
  Chicago Lectures in Math., Univ. Chicago Press, 2011.
  
  
• Teichmuller geometry of moduli space, I: Distance minimizing rays and
  the Deligne-Mumford compactification. ps or pdf
  (with H. Masur), Jour. Diff. Geom., Vol. 85 (2010), 187--227.
  
  
• Irreducible Sp-representations and subgroup distortion in the
  mapping class group. pdf
  (with N. Broaddus and A. Putman), Comment. Math. Helv. , Vol. 86, No. 3 (2011), 537--556.
  
  
• 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, 449--452.
  
  
• Commensurations of Out(F_n). ps or pdf
  (with Michael Handel), Publ. Math. IHES., No. 105 (2007), 1--48.
  
  
• (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. 11-55, June 2006.
  
  
• The lower central series and pseudo-Anosov dilatations. ps or pdf
  (with C. Leininger and D. Margalit), American Jour. Math, 130 (2008), no. 3, 799--827.
  
  
• The Birman-Craggs-Johnson homomorphism and abelian cycles in the
  Torelli group. dvi or ps or pdf
  (with T. Brendle), Math. Annalen, 338 (2007), no. 1, 33--53.
  
  
• Isometries, rigidity and universal covers. dvi or ps or pdf
  (with S. Weinberger), Annals of Math, Vol. 186, No.3, p.915-940 (2008)
  
  
• Commensurability invariants for nonuniform tree lattices. dvi or ps or pdf
  (with C. Hruska), Israel Jour. Math. 152 (2006), 125--142.
  
  
• 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. 111--119.
  
  
• The Torelli Geometry and its applications. dvi or ps or pdf
  (with N. Ivanov), Math. Research Letters., Vol. 12, pp. 293-301 (2005).
  
  
• Every mapping class group is generated by 6 involutions. dvi or ps or pdf
  (with T. Brendle), Journal of Algebra. , Vol. 278 (2004), 187-198.
  
  
• 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, 19--51.
  
  
• The Degree Theorem in higher rank. dvi or ps or pdf
  (with C. Connell), J. Diff. Geom., Vol. 65 (2003), 19--59.
  Erratum pdf
  
  
• Real-analytic, volume-preserving actions of lattices on 4-manifolds. dvi or ps or pdf
  (with P. Shalen), C.R. Acad. Sci Paris, Ser. I, Vol. 334 (2002), 1011-1014.
  
  
• Curvature and rank of Teichmuller space. dvi or ps or pdf
  (with J. Brock), American Jour. Math. , Vol. 128, No. 1 (2006), pp. 1-22.
  
  
• Groups of homeomorphisms of one-manifolds, III: Nilpotent subgroups. pdf
  (with J. Franks), Ergodic Theory Dynam. Systems 23 (2003), no. 5, 1467--1484 [Corrected Version, 10-28-18]
  
  
• Convex cocompact subgroups of mapping class groups. dvi or ps or pdf
  (with L. Mosher), Geometry and Topology, Vol. 6 (2002), 91-152.
  
  
• Groups of homeomorphisms of one-manifolds, I: Actions of nonlinear groups . dvi or ps or pdf
  (with J. Franks), in ``What's next?'', Annals of Math. Stud., 205, 116--140 (2020)
  
  
• Groups of homeomorphisms of one-manifolds, II: Extensions of Holder's Theorem. dvi or ps or pdf
  (with J. Franks), Trans. Amer. Math. Soc. , Vol. 355 (2003), no. 11, 4385--4396.
  
  
• 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), 235--243.
  
  
• The geometry of surface-by-free groups. dvi or ps or pdf
  (with L. Mosher), Geom. Funct. Anal (GAFA), Vol.12 (2002), no. 5, 915--963.
  
  
• 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, 1001--1026.
  
  
• 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), 581-597.
  
  
• 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 abelian-by-cyclic groups. dvi or ps or pdf
  (with L. Mosher). Acta Math. , Vol. 184, No.2 (2000), 145-202.
  
  
• Groups of real-analytic diffeomorphisms of the circle. dvi or ps
  (with P. Shalen). Ergodic Theory and Dynam. Syst. , Vol. 22 (2002), 835-844.
  
  
• Lattice actions, 3-manifolds, and homology. dvi or ps
  (with P. Shalen). Topology , Vol. 39 (2000), no. 3, 573-587.
  
  
• Real-analytic actions of lattices. dvi or ps
  (with P. Shalen). Inventiones Math. , Vol. 135 (1998), 273-296.
  
  
• A remark about actions of lattices on free groups. dvi or ps
  (with M. Bridson). Topology Appl. , Vol. 110, No. 1 (2001), 21-24.
  
  
• Harmonic splittings of surfaces. dvi or ps
  (with M. Wolf). Topology, Vol. 40, No.6 (2001), 1395-1414.
  
  
• Superrigidity and mapping class groups. dvi or ps
  (with H. Masur). Topology , Vol. 37, No.6 (1998), 1169-1176.
  
  
• Quasi-isometric rigidity for the solvable Baumslag-Solitar groups, II. dvi or ps
  (with L. Mosher) Inventiones Math. , Vol. 137 (1999), No. 3, 273-296.
  
  
• The quasi-isometry classification of lattices in semisimple Lie groups. dvi or ps
  Math. Res. Letters, Vol. 4, No.5, Sept. 1997, 705-718.
  
  
• A rigidity theorem for the solvable Baumslag-Solitar groups. dvi or ps
  (with L. Mosher). Inventiones Math. , Vol. 131, No.2 (1998), 419-451.
  
  
• Quasi-flats and rigidity in higher rank symmetric spaces. dvi or ps
  (with A. Eskin). Journal AMS. , Vol. 10, No.3, July 1997, 653-692.
  
  
• Quasi-flats in H²xH². dvi or ps
  (with A. Eskin). Proceedings of the International Colloquium on Lie groups and
  Ergodic Theory, Tata Institute 1996.
  
  
• The large-scale geometry of Hilbert modular groups. dvi or ps
  (with R. Schwartz). J. Diff. Geom. 44, No.3 (1996), 435-478.
  
  
• Relatively hyperbolic groups. dvi or ps
  Geom. Funct. Anal. (GAFA), Vol.8 (1998), 1-31.
  
  
• Filling-invariants at infinity for manifolds of nonpositive curvature. dvi or ps
  (with N. Brady). Trans. Amer. Math. Soc., Vol.350, No.8 (1998), 3393-3405.
  
  
• 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, 57-67.
  
  
• The Extrinsic geometry of subgroups and the generalized word problem. dvi or ps
  Proc. London Math. Soc. (3) 68 (1994), 577-593.
  
  
• (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), 291-313.