Charles V. Schaefer, Jr. School of Engineering and Science
 
 
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MA-810A: Geometric and Asymptotic Group Theory (Fall 2012)

Lectures
Friday, Sep 7 Introduction to the course. Free groups. (A. Miasnikov)
Friday, Sep 14 Diagrams (M. Sapir)
Monday, Sep 17 Basic equations in free groups (A. Miasnikov)
Friday, Sep 21 No class (conference day)
Monday, Sep 24 Small cancelation conditions and basic techniques (M. Sapir)
Friday, Sep 28 Asymptotic cones and applications to Dehn functions (M. Sapir)
Notes
Monday, Oct 1 Makanin-Razborov algorithm preliminaries (A. Miasnikov)
Friday, Oct 5 Asymptotoic cones and Denn functions. Hyperbolic groups (M. Sapir)
Notes
Monday, Oct 8 Algebraic geometry over groups (A. Miasnikov)
Friday, Oct 12 Dehn functions of nilpotent groups. Groups with quadratic Dehn functions (M. Sapir)
Notes
Monday, Oct 15 Rewriting systems in groups (S. Hermiller).
Friday, Oct 26 Conjugacy problem and Dehn functions (M. Sapir)
Notes
Friday, Nov 9 S-machines (M. Sapir)
Notes
Monday, Nov 12 S-machines (M. Sapir)
Friday, Nov 16 S-machines (M. Sapir)
Friday, Nov 30 Makanin-Razborov algorithm: elementary transformations (A. Miasnikov)
Wednesday, Dec 5
4:15pm (Kidde 104)
Discussion of current problems in Group Theory related to the course material (M. Sapir)
Course materials

  1. General reading guidelines

  2. M. Sapir Asymptotic invariants, complexity of groups and related problems, Bull. Math. Sci. (2011), Volume 1, Number 2, 277-364

  3. C. Drutu, M. Sapir Tree-graded spaces and asymptotic cones of groups, Topology (2005), Volume 44, Number 5, 959-1058

  4. C. Drutu, M. Sapir Groups acting on tree-graded spaces and splittings of relatively hyperbolic groups, Adv. Math. (2008), Volume 217, Number 3, 1313-1367

  5. C. Drutu, S. Mozes, M. Sapir Divergence in lattices in semisimple Lie groups and graphs of groups, Trans. Amer. Math. Soc. (2010), Volume 362, 2451-2505

  6. J. Behrstock, C. Drutu, M. Sapir Median structures on asymptotic cones and homomorphisms into mapping class groups, Proc. London Math. Soc. (2011), Volume 102, Number 3, 503--554

  7. J. Behrstock, C. Drutu, M. Sapir Addendum: Median structures on asymptotic cones and homomorphisms into mapping class groups, Proc. London Math. Soc. (2011), Volume 102, Number 3, 555--562