


MA810A: 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 
MakaninRazborov 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 
Smachines (M. Sapir)
Notes 
Monday, Nov 12 
Smachines (M. Sapir)

Friday, Nov 16 
Smachines (M. Sapir)

Friday, Nov 30 
MakaninRazborov 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 
 General reading guidelines
 M. Sapir Asymptotic invariants, complexity of groups and related problems, Bull. Math. Sci. (2011), Volume 1, Number 2, 277364
 C. Drutu, M. Sapir Treegraded spaces and asymptotic cones of groups, Topology (2005), Volume 44, Number 5, 9591058
 C. Drutu, M. Sapir Groups acting on treegraded spaces and splittings of relatively hyperbolic groups, Adv. Math. (2008), Volume 217, Number 3, 13131367
 C. Drutu, S. Mozes, M. Sapir Divergence in lattices in semisimple Lie groups and graphs of groups, Trans. Amer. Math. Soc. (2010), Volume 362, 24512505
 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, 503554
 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, 555562






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