Thomas Church - Papers

Papers

All my papers are available on the arXiv.

23. Which groups are amenable to proving exponent two
for matrix multiplication?, 23 pages
with Jonah Blasiak, Henry Cohn, Joshua Grochow, and Chris Umans

22. On finite generation of the Johnson filtrations, 32 pages
with Mikhail Ershov and Andrew Putman

21. Linear and quadratic ranges in representation stability, 27 pages
      with Jeremy Miller, Rohit Nagpal, and Jens Reinhold
      Advances in Mathematics 333 (2018), 1–40.
      doi: 10.1016/j.aim.2018.05.025

20. On cap sets and the group-theoretic approach to matrix multiplication, 27 pages
      with Jonah Blasiak, Henry Cohn, Joshua Grochow, Eric Naslund, Will Sawin, and Chris Umans
      Discrete Analysis, 2017:3, 27pp.
      doi: 10.19086/da.1245.

19. The codimension-one cohomology of SL_nZ, 26 pages
      with Andrew Putman
      Geometry and Topology 21-2 (2017), 999–1032.
      doi: 10.2140/gt.2017.21.999.

18. Homology of FI-modules, 34 pages
      with Jordan Ellenberg
      Geometry and Topology 21-4 (2017), 2373–2418.
      doi: 10.2140/gt.2017.21.2373.

17. Integrality in the Steinberg module and
      the top-dimensional cohomology of GL_nO_K, 31 pages
      with Benson Farb and Andrew Putman
      to appear in American Journal of Mathematics

16. Generating the Johnson filtration, 27 pages
      with Andrew Putman
      Geometry and Topology 19-4 (2015), 2217–2255.
      doi: 10.2140/gt.2015.19.2217.

15. Representation stability in cohomology and
      asymptotics for families of varieties over finite fields, 57 pages
      with Jordan Ellenberg and Benson Farb
      Contemporary Mathematics 620 (2014), 1–54.
      doi: 10.1090/conm/620/12395.

14. Rotor-routing and spanning trees on planar graphs, 16 pages
      with Melody Chan and Joshua Grochow
      International Mathematics Research Notices 2015 (2015) 11, 3225–3244.
      doi: 10.1093/imrn/rnu025.

13. FI-modules over Noetherian rings, 32 pages
      with Jordan Ellenberg, Benson Farb, and Rohit Nagpal
      Geometry and Topology 18-5 (2014), 2951–2984.
      doi: 10.2140/gt.2014.18.2951.

12. A stability conjecture for the unstable cohomology
      of SL_nZ, mapping class groups, and Aut(F_n), 18 pages
      with Benson Farb and Andrew Putman
      Contemporary Mathematics 620 (2014), 55–70.
      doi: 10.1090/conm/620/12366.

11. FI-modules and stability for representations of symmetric groups, 54 pages
      with Jordan Ellenberg and Benson Farb
      Duke Mathematical Journal 164 (2015) 9, 1833–1910.
      doi: 10.1215/00127094-3120274.

10. Invariance properties of Miller-Morita-Mumford
      characteristic numbers of fibre bundles, 15 pages
      with Martin Crossley and Jeffrey Giansiracusa
      Quarterly Journal of Mathematics 64 (2013) 3, 729–746.
      doi: 10.1093/qmath/has029.

9. The rational cohomology of the mapping class group
     vanishes in its virtual cohomological dimension, 4 pages
     with Benson Farb and Andrew Putman
     International Mathematics Research Notices (2012) 21, 5025–5030
     doi: 10.1093/imrn/rnr208.

8. Orbits of curves under the Johnson kernel, 42 pages
American Journal of Mathematics 136 (2014), 943–994.
doi: 10.1353/ajm.2014.0025.

7. Homological stability for configuration spaces of manifolds, 33 pages
Inventiones Mathematicae 188 (2012) 2, 465–504
doi: 10.1007/s00222-011-0353-4.

6. On the geometric nature of characteristic classes of surface bundles, 26 pages
     with Benson Farb and Matthew Thibault
     Journal of Topology 5 (2012) 3, 575–592
     doi: 10.1112/jtopol/jts014.

5. Representation theory and homological stability, 91 pages
     with Benson Farb
     Advances in Mathematics (2013) 250--314
     doi: 10.1016/j.aim.2013.06.016.

4. Parametrized Abel-Jacobi maps and abelian cycles in the Torelli group, 29 pages
     with Benson Farb
     Journal of Topology 5 (2012) 1, 15–38
     doi: 10.1112/jtopol/jtr026.

3. Infinite generation of the kernels of the Magnus and Burau representations, 13 pages
     with Benson Farb
     Algebraic and Geometric Topology 10 (2010), 837–851
     doi: 10.2140/agt.2010.10.837.

2. Some groups of mapping classes not realized by diffeomorphisms, 15 pages
     with Mladen Bestvina and Juan Souto
     Commentarii Mathematici Helvetici 88 (2013) 1, 205–220
     doi: 10.4171/cmh/283.

1. Separating twists and the Magnus representation of the Torelli group, 15 pages
     with Aaron Pixton
     Geometriae Dedicata 155 (2011) 1, 177–190
     doi: 10.1007/s10711-011-9584-1.