Probability and Computation on Groups. Lectures and References

I gave several lectures on the subject, with the following being videotaped. Below are the links to the videos and selected references.

Lectures:

1. Probability and computation on groups

Magnus Seminar, New York, November 5, 1999.
The lecture (streaming video) is available here (1 hour).

2. Generating random group elements

MSRI Workshop, Combinatorial Algebra, January 10-14, 2000.
The lecture (streaming video) is available here (40 min.)

3. Testing group properties: Probabilistic and algorithmic approaches

City College of New York Workshop, Probabilistic Methods in Group Theory, December 8, 2000.
The lecture (streaming video) is available here (50 min.)

References

Computational Group Theory: survey articles

• G. Cooperman, L. Finkelstein, Combinatorial tools for computational group theory, Groups and computation I, 53--86, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., vol. 11, AMS, Providence, RI, 1993.

• J. Neubuser, An invitation to computational group theory, Groups'93 Galway/St. Andrews, Vol. 2, 457-475, London Math. Soc. Lecture Note Ser., 212, Cambridge Univ. Press, Cambridge, 1995

• A. Seress, An introduction to computational group theory, Notices Amer. Math. Soc., vol. 44 (1997), no. 6, 671-679

• W.K. Kantor, Simple Groups in Computational Groups Theory, Proc. ICM, Vol. II, Berlin, 1998, 77-86.

The Product Replacement Algorithm

• F. Celler, C.R. Leedham-Green, S.H. Murray, A.C. Niemeyer, and E.A. O'Brien, Generating random elements of a matrix group, Comm. Algebra, vol. 23 (1995), no. 13, 4931-4948.

• P. Diaconis, L. Saloff-Coste, Walks on generating sets of Abelian groups, Probability Theory Related Fields, vol. 105 (1996), 393-421.

• F.R.K. Chung, R.L. Graham, Random walks on generating sets for finite groups, Electron. J. Combin. 4 (1997), no. 2, Research Paper 7.
  The abstract and the full paper are available here

• P. Diaconis, L. Saloff-Coste, Walks on generating sets of groups, Invent. Math., vol. 134 (1998), 251-300.
  

• I. Pak, On the graph of generating sets of a simple group, preprint, 1999.
  Download .dvi file or .ps file.

• L. Babai, I. Pak, Strong bias of group generators: an obstacle to the ''product replacement algorithm'', Proc. SODA'00, 627-635.
  Download .dvi file, .ps file, or .pdf file.

• A. Lubotzky, I. Pak, The product replacement algorithm and Kazhdan's property (T) , preprint, 1999, Journal of the AMS, vol. 52 (2000), no. 12, 5525-5561.
  Download .dvi file, .ps file, or .pdf file.

• I. Pak, What do we know about the product replacement algorithm?, to appear in "Groups and Computation III" (W. Kantor, A. Seress, eds.), deGruyter, Berlin, 2000, 301-347.
  Download .dvi file or .ps file.

• I. Pak, The product replacement algorithm is polynomial, Proc. FOCS'2000.
  Download .dvi file or .ps file of the extended abstract.

Testing group properties

• L. Babai, R. Beals, D. Rockmore, Deciding finiteness of matrix groups in deterministic polynomial time, Proc. ISSAC'1993, 117-126.

• R. Beals, Algorithms for matrix groups and the Tits alternative, J. Comput. System Sci. 58 (1999), no. 2, 260-279.

• S. Bratus, I. Pak, Fast constructive recognition of a black box group isomorphic to S_n using Goldbach conjecture, J. of Symbilic Computation, vol. 29, 2000, 33-57.
  Download .dvi file (no pictures), .ps file, or .pdf file

• I. Pak, Testing commutativity of a group and the power of randomization, preprint, 2000
  Download .dvi file or .ps file.

Click here to return to Igor Pak Home Page.

To e-mail me click here and delete .zzz

Last updated 1/10/2001