Mark V. Sapir

IMAGE: It's me.

My older daughter's web page is here.

My sister's Web page is here.

My mother's Web page is here.

Here is the photo of my 5th grade class at school 43, Sverdlovsk, U.S.S.R., 1968-1969.

My first award, Journal Pioneer, 1970, no. 6, "For the most elegant solution of the problems about weights of coins".

Here is how I looked like in 1980-1981 (I was a graduate student then).

My Google scholar profile

Me in the Russian Internet.


Scientifically, I am one of about 105000 descendants of Nilos Kabasilas who was a bishop of Thessalonika, Greece, in the 14th century AD. Other descendants include Leonardo da Vinci, Nikolai Lobachevsky and Lev Shevrin (my PhD advisor).

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Mark V. Sapir
Centennial Professor
1522 Stevenson Center
Department of Mathematics
Vanderbilt University
(615) 322-6657 (office)
(615) 343-0215 (fax)

Combinatorial algebra: syntax and semantics.

The book can be found here.

Seminar "Group theory and topology"

To look at the 2017/2018 schedule, click here. The schedule of the previous years is here (2010/11), here(2011/12), here (2012/13)., here (2014/15), here (Spring 2016), here (Fall 2016), here (Spring 2017)

My blog at Wordpress

Graduate students:

  • Sam Corson defended his PhD in April of 2016. He is working on topology, logic and geometric group theory. Thesis: Subgroups and Quotients of Fundamental Groups.
  • Gili Golan (co-advisor Boaz Tsaban, Bar Ilan) defended her PhD in 2015, in Bar Ilan, Israel. She is working on combinatorial and geometric group theory. Thesis: Coloring Theorems of Semigroups.
  • Curt Kent defended his PhD in March, 2013. He is working on topological properties of asymptotic cones of groups. Thesis: Topological properties of asymptotic cones of nitely generated groups.
  • Iva Špakulová (Kozáková) defended her PhD in December, 2008. She is working on percolation in Cayley graphs of groups, and other probabilistic aspects of group theory. Thesis: "Percolation and Ising model on tree-like graphs".
  • I was also a PhD advisor (together with John Meakin) of Tatyana Jajcayova. Thesis: "HNN extensions of inverse semigroups".
  • Teaching:

    In the Spring of 2017, I am teaching Math 4300/6300, Modern Algebra. The syllabus is here, homework assigments will be here.

    Words of encouragement

    I often hear complains that I don't encourage my students enough. I am told that students work very hard and need to feel good about themselves. And I make them feel good very rarely. So I decided to make a special "feel good about yourself" page for my students. Click and hear (perhaps the first time) words of encouragement coming from your Professor (better viewed with IE)`. Here is some discussion of the WOE on and IAmA there.

    Linear Algebra WebNotes

    Click here to see the WebBook on Linear Algebra that I wrote in 1996-1997. It contains complete set of my lectures, an on-line calculator, homework assignments with solutions, discussion pages, etc.

    Editorial boards

    I am the editor-in-chief of Journal of Combinatorial Algebra.

    I am a member of editorial boards of the following journals

  • Algebra and Discrete Mathematics.
  • Groups Complexity Cryptology.

    Research Interests

    I am interested in combinatorial algebra: algorithmic, geometric and probabilistic invariants of groups, semigroups and algebras. Click here to see some of my publications and my CV. Here are my papers in the arXiv.

    Videos of my talks

  • On subgroups of the R. Thompson group F
  • Tarski numbers of groups
  • On Jones' subgroup of the R. Thompson group F

    Slides of talks

  • "Uniform embeddings of groups", Baltimore (AMS meeting), January 18, 2014.
  • "The Tarski numbers of groups", Vanderbilt, January 15, 2014.
  • "On free Burnside groups", New York, December 7, 2012.
  • "On the dimension growth of groups", Barcelona, Spain, September 6, 2012, Hoboken, NJ, September 21, 2012.
  • "Aspherical groups and manifolds with extreme properties", Autrans, France, July 6, 2012, Oberwolfach, Germany, July 19, 2012.
  • "On the dimension growth of groups", Honolulu, HI, March 3, 2012.
  • "Hilbert space compression and dimension growth", Embeddings workshop, Cambridge, UK, January 10. 2011 (video of the lecture).
  • "Higman Embeddings", International Conference on Algebras and Lattices, Prague, June 24, 2010.
  • "Geometry of groups and computational complexity", 75 KAM Colloquium, Prague, June 17, 2010.
  • "Conjugacy growth of groups", Starkville, MS, March 20, 2010.
  • "Polynomial maps over fields and residually finite groups", Lecture 4. Bath, UK, August 2009.
  • "Polynomial maps over fields and residually finite groups", Lecture 3. Bath, UK, August 2009.
  • "Polynomial maps over fields and residually finite groups", Lecture 2. Bath, UK, August 2009.
  • "Polynomial maps over fields and residually finite groups", Lecture 1. Bath, UK, August 2009.
  • "Polynomial maps over fields and residually finite groups", Banff (Canada), October 14, 2008, AMS sectional meeting, Huntsville, AL, October, 24, 2008.
  • "Percolation on transitive graphs", Ottawa (Canada), December 14, 2007.
  • "Hilbert space compression of R.Thompson group and wreath products", Lausanne (Switzerland), January 25, 2007.
  • "Hilbert space compression of groups", New Orleans (LA, USA), January 5, 2007.
  • "Cut-points in asymptotic cones", Manresa, (Spain), September, 2006.
  • "Asymptotic and algorithmic invariants", ICM-2006 (August, 2006)
  • "Groups acting on tree-graded spaces", Oberwolfach (May, 2006)
  • "Groups acting on tree-graded spaces", Toronto (May, 2006)
  • "Tree-graded spaces and asymptotic cones", Shanks-2006, Nashville (May 2006)
  • "Residually finite groups and dynamics of polynomial maps", Tel Aviv (January, 2006)

    Roo and Robby

    When I was in Russia, I wrote a textbook "Informatics" together with Gejn, Linetsky and Sholokhovich. There were 5 editions, total number of copies is more than 2,500,000. I also was the author of the software support of this textbook. This software was written for some primitive Z-80 computers made by Yamaha. An adaptation of this software to IBM PC was made by Linetsky and myself. The software is called Roo and Robby/SchoolWorks and consists of 5 programs. Roo and Robby are machines which understand simple languages (Roo is a kangaroo and Robby is a snake); the SchoolWorks contains a spreadsheet, a database and a text processor. There was a nice review article about Roo and Robby in the November issue, 1990 of PC/Computing, and in Visions (Spring/Summer 1993). If you want to download Roo, click here . If your computer is running Windows XP or later versions of Windows, you will need to install the Dosbox first and run the software under Dosbox (i.e. first start Dosbox, then in the Dosbox window mount the directory of R&R, change to that directory and then start r&r, the batch file. The Dosbox can be downloaded for free here.
    In 1992-1994 we together with Linetsky had programming classes in Lincoln (NE) for kids 4-7 grades where we tought them Roo and Robby.

    All comments mail to: m.sapir(AT) This is your local time

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