Geometric Group Theory RFG: Graduate Seminar

Seminar meeting time: Tuesdays 2-4pm in MSB 3106

Organizers: Moon Duchin, Misha Kapovich, Lucas Sabalka

This seminar is an activity of the VIGRE RFG.

April 3Marion Moore: defs and examples
TH April 12, 2pm Yvonne Lai: geometrization results
April 17 Vish Viswanath/Alex Woo
May 1Rohit Thomas: graphs of groups
May 8 Matt Rathbun: groups acting on trees
May 15Anne Thomas
May 29Aaron Abrams
TBAMoon Duchin

main sources for Coxeter groups:

  • Coxeter chapter from Angela Barnhill's thesis (pdf)
  • Mike Davis's book (huge file) Of particular interest are Chapters 1,2,3,6,7,12. Marion will mostly talk about Ch 3 and Yvonne about Ch 7/12.

    secondary sources for Coxeter groups:

  • Coxeter's 1934 paper "Discrete groups generated by reflections" (pdf)
  • Humphrey's book Reflection groups and Coxeter groups
  • Coxeter's book Regular polytopes

    some recent papers of interest on Coxeter groups and related topics :

  • Sankaran Viswanath, "On growth types of quotients of Coxeter groups by parabolic subgroups" (arxiv)
  • Angela Barnhill, "The FA_n conjecture for Coxeter groups" (arxiv)
  • Daniel Allcock, "Infinitely many hyperbolic Coxeter groups through dimension 19" (pdf)
  • Ruth Charney, "An introduction to right-angled Artin groups" (arxiv)

    sources for Bass-Serre theory and groups acting on trees:

  • Scott-Wall, "Topological methods in group theory" (scanned pdf)
  • Serre's Trees
  • M.Davis's Appendix E on "Complexes of groups" (see link above, page 407)

    secondary sources for Bass-Serre theory and groups acting on trees:

  • Lubotzky's Tree lattices and lattices in Lie groups, in Combinatorial and Geometric Group Theory
  • Bestvina, "R-trees in geometry, topology, and group theory" (ps)

    some recent papers of interest on Bass-Serre theory and related topics:

  • Anne Thomas, "Lattices acting on right-angled buildings" (arxiv)
  • Peter Shalen, "Three-manifold topology and the tree for PSL_2: The Smith conjecture and beyond" (dvi)
  • Lisa Carbone, "Non-minimal Tree Actions and the Existence of Non-uniform Tree Lattices" (pdf)
  • Benson Farb and Chris Hruska, Commensurability invariants for nonuniform tree lattices (pdf)

    Past quarters: Fall (hyperbolic groups) ; Winter (mapping class groups)