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MA-810A: Geometric and Asymptotic Group Theory (Fall 2012)
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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)
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Friday, Nov 16 |
S-machines (M. Sapir)
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Friday, Nov 30 |
Makanin-Razborov algorithm: elementary transformations (A. Miasnikov)
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Wednesday, Dec 5 4:15pm (Kidde 104) |
Discussion of current problems in Group Theory related to the course material (M. Sapir)
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Course materials |
- General reading guidelines
- M. Sapir Asymptotic invariants, complexity of groups and related problems, Bull. Math. Sci. (2011), Volume 1, Number 2, 277-364
- C. Drutu, M. Sapir Tree-graded spaces and asymptotic cones of groups, Topology (2005), Volume 44, Number 5, 959-1058
- 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
- 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
- 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
- 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
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Stevens Institute of Technology •
Hoboken, NJ • (201) 216-5000
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