Jason Behrstock's Home Page



Department of Mathematics
Lehman College, CUNY  
250 Bedford Pk. Blvd  
Bronx, NY 10468  
Lehman Office: Gillet Hall 137G  
 
jason.behrstock@lehman.cuny.edu 
CUNY Graduate Center
365 5th Ave, NY NY 10016
GC Office: 4214-04
I'm the one upside down!

My primary interests are in geometric group theory and low dimensional topology.
My curriculum vitae and research statement.

I participate in the annual JDRF Walk to Cure Diabetes, please help us support crucial research!

Spring 2013 Course:

• Geometric Group Theory (Math 87200), at The Graduate Center. Syllabus.

Fall 2012:

• The Shape of Space (Lehman Scholars Program 350), at Lehman. Course page.

Summer 2012, Geometry/Topology Student Seminars:

Spring 2012:

• Calculus 1 Computer Lab, at Lehman.

Fall 2011:

• No teaching this semester, thanks to support as an Alfred P. Sloan Fellow. But I will be around and available by appointment.

Spring 2010:

• Topology, at Lehman.

Fall 2010:

• No teaching this semester, thanks to support as an Alfred P. Sloan Fellow. But I will be around and available by appointment.

Spring 2010:

• The Shape of Space (Lehman Scholars Program 350), at Lehman. Course page.
• Algebra and Number Systems I, at Lehman.

Fall 2009:

• Calculus 3 (Math 226) at Lehman. Syllabus.
• Topics in Group Theory, at the Graduate Center. Syllabus.

Papers:

(Available as PDF files, email me if you need an alternate format.)

•   Higher dimensional filling and divergence for mapping class groups, with C. Drutu
      Preprint.
•   Cubulated groups: thickness, relative hyperbolicity, and simplicial boundaries, with M. Hagen
      Preprint.
•   Divergence, thick groups, and short conjugators, with C. Drutu
      Preprint.
•   Homomorphisms into mapping class groups. An addendum, with C. Drutu and M. Sapir
      Proceedings of the London Mathematical Society, vol. 3, (2011) 555--562.
      Online published version.
•   Divergence and quasimorphisms of right-angled Artin groups, with R. Charney
      Mathematische Annalen, vol. 352, (2012) 339--356 .
     Online published version.
•   Quasi-isometric classification of non-geometric 3-manifold groups, with W. Neumann
      Crelle's Journal, to appear.
•   Quasi-isometric classification of some high dimensional right-angled Artin groups, with T. Januszkiewicz and W. Neumann
      Groups, Geometry, and Dynamics, vol. 4, (2010) 681-692.
•   Median structures on asymptotic cones and homomorphisms into mapping class groups, with C. Drutu and M. Sapir
      Proceedings of the London Mathematical Society, vol. 3, (2011) 503--554.
      Online published version.
•   Centroids and the rapid decay property in mapping class groups, with Y. Minsky
      Journal of the London Mathematical Society, to appear.
•   Growth of intersection numbers for free group automorphisms, with M. Bestvina and M. Clay
      Journal of Topology, vol. 3, (2010) 280-310.
•   Geometry and rigidity of mapping class groups, with B. Kleiner, Y. Minsky, and L. Mosher
      Geometry & Topology, to appear.
•   Commensurability and QI classification of free products of finitely generated abelian groups, with T. Januszkiewicz and W. Neumann
      Proceedings of the American Mathematical Society, 137, 811-813, 2009.
•   Quasi-isometric classification of graph manifolds groups, with W. Neumann
      Duke Mathematical Journal, 141 (2): 217-240, 2008.
      Duke University Press online published version, subscription required.
•   Thick metric spaces, relative hyperbolicity, and quasi-isometric rigidity, with C. Drutu and L. Mosher
      Mathematische Annalen, vol. 344, (2009), 543--595.
•   Dimension and rank for mapping class groups, with Yair Minsky
      Annals of Mathematics, 167: 1055-1077, 2008.
      Online published version.
•   Curve complexes and finite index subgroups of mapping class groups, with Dan Margalit.
      Geometriae Dedicata 118 (1): 71-85, 2006.
      Springer online published version, subscription required.
•   Asymptotic Geometry of the Mapping Class Group and Teichmuller Space
      (The last two sections of this paper contains new results not in the Ph.D. thesis.)
      This final published version is more current than the one at the arXiv.
      Geometry & Topology 10: 1523-1578, 2006.
•   Asymptotic Geometry of the Mapping Class Group and Teichmuller Space
      SUNY Stony Brook Ph.D. Thesis, May 2004.

Summer 2008 REU:

The Tower of Hanoi (Homepage with links to publications by the undergraduate participants in the group)
If you are not familiar with the Tower of Hanoi, here is a video of my daughter Kaia (age 4), playing the game.



Relevant seminars in New York City:

• CUNY Geometry and Topology Seminar
• Columbia Geometric Topology Seminar
• Magnus Seminar (Group Theory Seminar at CUNY Graduate Center)

Upcoming/recent conferences I'm organizing:

• March 2010, Banff, Canada - Quasi-isometric rigidity in low dimensional topology
• October 2010, CUNY Graduate Center - Conformal Dynamics and Hyperbolic Geometry to celebrate the contributions of Linda Keen
• March 2011, Spring Southeastern Section Meeting (Special section on Geometric Group Theory)
• June 6-10, 2011, Faces of Geometry: 3-manifolds, Groups, and Singularities
• August 1-5, 2011, CBMS-NSF conference: 3-Manifolds, Artin Groups, and Cubical Geometery. Videos of all the lectures are now available.
• April 2013, Banff, Canada - Mapping Class Groups and Categorification

Some upcoming/recent conferences I'll be attending:

• January 2009, Gyeongju, Korea - The 5th East Asian School of Knots and Related Topics
• June 2009, Muenster, Germany - Geometry and Topology
• September 2009, Tokyo, Japan - Topology and Computer
• October 2009, New York City - Finitely Presented Groups: Where do we go from here
• April 2010, Oberwolfach, Germany - Non-positive Curvature and Geometric Structures in Group Theory
• July 2010, Purdue University - Algebra and Algebraic Geometry with Applications: Celebration of the Eightieth Birthday of Professor S. S. Abhyankar
• August 2010, Montreal, Canada - Geometric, Asymptotic, Combinatorial Group Theory with Applications
• June 2012, Lille, France - Coarse Geometry of Infinite Groups


Mathematical Games

Expacon: Baumslag's group theory game.
Teruaki: A Mapping Class Group game.
Geometry and Topology games: Classics by Jeff Weeks. (Also available for the iphone!)

Misc

Pictures of family, especially: Kaia and Ela Behrstock.
Pictures of friends.
Parts of this material is based upon work supported by the National Science Foundation under Grants No. 0604524, 0812513, and 1006219.
Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.