Collin Bleak
1521 B. St.
Lincoln, NE 68502
Phone: (402) 472-9119
Email: [email protected]
Education
2005
1994
1991
Ph.D. Mathematics, Binghamton University
Dissertation: “Solvability in Groups of Piecewise-linear
Homeomorphisms of the Unit Interval”
Advisor: Matthew G. Brin
M.A. Mathematics, Binghamton University
B.A. Mathematics, Princeton University
Senior Thesis: “Investigation of Knots”
Advisor: William Thurston
Primary Areas of Research Interest
Algorithmic and geometric group and semigroup theory. Applying topological dynamics
to the study of groups via actions.
Employment
2007-present
2006-2007
2004-2006
2003-2004
1997-2003
Research Assistant Professor, University of Nebraska, Lincoln (UNL)
Visiting Assistant Professor, Cornell University
Lecturer, Binghamton University
Adjunct Professor, Broome Community College
Industry (Adone, llc., Deutsche Bank, Illura, llc. (partnership))
Information technology consulting, software development,
and foreign exchange research.
Summer Positions
2009, 2008, 2007
Visiting Assistant Professor, Cornell University
2006
Summer Chairman, Mathematics, Binghamton University
Grants and Awards
• LMS Scheme 2 Grant (Ref 2805) for £1200 supporting a November 2009 trip to
the UK to give talks at the University of Glasgow, the University of Southampton,
and Newcastle University. PI Sarah Rees.
• NSF Grant DMS-0855953, ($25,000) conference support for the conference
(ICGS) “International Conference on Geometric and Combinatorial Methods in
Group theory and Semigroup Theory.” PI Susan Hermiller, Co-PI's Collin Bleak,
John Meakin.
• 2008 Teaching award from the Parents Association and the Teachers Council of
the University of Nebraska at Lincoln.
• 2006 Nomination for the Cornell Department of Mathematics Teaching Award.
Publications
Appeared or accepted
1. “A geometric classification of some solvable groups of homeomorphisms.” Journal of
the London Mathematical Society (2008), 78: pp 352 –372.
2. “An algebraic classification of some solvable groups of homeomorphisms.” Journal of
Algebra (2008) 319, pp. 1368-1397.
3. “Some questions about the dimension of a group action.” Bulletin of the London
Mathematical Society, 2008 40(5), pp. 770-776.
4. “Twisted conjugacy classes in R. Thompson’s group F” With Daciberg Gonҫalves and
Alexander Fel'shtein. Pacific Journal of Mathematics, Vol. 238 (2008), no. 1, pp. 1—6.
5. “A minimal non-solvable group of homeomorphisms.” Groups, Geometry, and
Dynamics, 3 (2009), 1-37.
6. “A family of non-isomorphism results” pp. 1—7. To appear, Geometriae Dedicata.
Co-author Daniel Lanoue. Arxiv: 0907.4955
Preprints or Drafts available
7. “Structure Theorems for subgroups of homeomorphism groups.” With Martin
Kassabov and Francesco Matucci. Submitted. arXiv: 0910.0218
8. “Free products in R. Thompson’s group V.” With Olga Salazar-Díaz. Submitted.
ArXiv: 0911.0979
9. “Roots, Centralizers, and the conjugacy problem in subgroups of homeomorphism
groups of R and S^1.” With Martin Kassabov and Francesco Matucci. arXiv:
0807.2871, Ch 7.
10. “Finite index subgroups of R. Thompson's group F." With Bronlyn Wassink. ArXiv:
0711.1014
11. “Solvability in Groups of Piecewise-linear Homeomorphisms of the Unit Interval.”
Dissertation, pp iv+105, July 2005, Binghamton University. arxiv: GR/0510399
In Preparation
12. “Rotation numbers in Stein-Thompson groups.” In preparation with Daniel Farley
and Melissa Yeung.
13. “Roots and centralizers in the generalized Higman-Thompson Groups." In
preparation with Alison Gordon, Jacob Hughes, Garrett Graham, Francesco Matucci,
Hannah Newfield-Plunkett, and Jenya Sapir.
14. “On finitely-generated minimal subgroups in groups of homeomorphisms.” In
Preparation.
15. “A class of non-equationally-Noetherian groups.” In Preparation.
Invited Presentations/Workshop Participation:
1. University of Virginia, Topology Seminar, Nov. 19 2009.
2. University of Virginia, Algebra Seminar, Nov. 18, 2009.
3. University of Nebraska at Lincoln, Mathematics Colloquium, Dec. 8, 2008.
4. University of Southampton, Pure Mathematics Colloquium, Nov. 28, 2008.
5. University of Glasgow, Algebra Seminar, two presentations, Nov. 19, 2008.
6. Newcastle University, Geometry and Algebra Seminar, Nov. 20, 2008.
7. CIRM Conference "Thompson's Groups: New Developments and Interfaces,"
Marseilles, June 5, 2008.
8. AIM workshop “Dichotomy Amenable/Nonamenable in Combinatorial Group
Theory,” Palo Alto, Ca., Oct. 6—13, 2007.
9. University of Nebraska at Lincoln, Mathematics Colloquium, Oct. 5, 2007.
10. Miami University of Ohio, Mathematics Colloquium, November 2006.
11. Miami University of Ohio, Topology Seminar, November 2006.
12. Vanderbilt University, the combinatorial and geometric group theory conference held
in celebration of A. Yu. Ol’Shanskii’s 60’th birthday, May 2006.
13. Topology and Geometric Group Theory Seminar of Cornell University, April 2006.
14. American Mathematical Society Spring Regional Meeting, Special Session, Durham,
NH, April 2006.
15. American Mathematical Society Fall Regional Meeting, Special Session, Annandaleon-Hudson, 2005.
16. Mathematical Association of America, Spring Cortland Seaway Meeting, 2004.
Presentations:
1. University of Nebraska at Lincoln Groups, Semigroups, and Topology seminar.
Fourteen presentations, 2007—2009.
2. Smorgasboard Seminar of Cornell University. Three presentations, 2007—2009.
3. Topology and Geometric Group Theory Seminar of Cornell University. Two
Presentations, Fall 2006, Spring 2007.
4. Binghamton University Algebra Seminar, January 2006.
Editing, Reviewing and Refereeing
• Editor for a special issue of the International Journal of Algebra and Computation
for the conference proceedings for the ICGS conference mentioned below.
•
Referee for the journal Glasgow Mathematical Journal, the journal Groups,
Geometry and Dynamics, the International Journal of Algebra and Computation,
and the Journal of Pure and Applied Algebra.
•
Reviewer for ZentralBlatt.
Graduate Mentoring
Graduate Student: Nathan Corwin (UNL)
Teaching Experience
2007-present University of Nebraska at Lincoln
Graduate: Point Set Topology, Differential Topology
Undergraduate: Geometry, Permutation Puzzles and Group Theory,
Calculus I, II & III
2006-2007
Cornell University
Calculus I, II, & III
2004-2006
Binghamton University
Calculus I, II, III, Linear Algebra, Discrete Mathematics, Ordinary
Differential Equations, (undergraduate) Complex Analysis,
Intermediate Algebra, Algebra and Trigonometry,
Actuarial Test Preparation
2003-2005
Broome Community College
Algebra and Trigonometry, Algebra and Trigonometry for Engineers,
Calculus I, Calculus for Engineers, Math Explorations II
Special teaching experience
Mentoring Through Critical Transition Points, undergraduate research mentor (Fall
2008, Spring 2009, Fall 2009, UNL):
Directing MCTP Awardee Kevin Ahrendt in his studies of Asynchronous Cellular
Automata and sequential dynamical systems.
Project Leader, Cornell 2009 REU:
Our group studied piecewise linear actions on high dimensional n-cubes. We
also studied the Piecewise-Integral-Projective groups introduced by Thurston.
Project Leader, Cornell 2008 REU:
Our group showed that the generalized R. Thompson groups nV are pair-wise
non-isomorphic, and that each is finitely presented. We also found normal forms
for elements and we wrote software to help explore questions such as the
conjugacy problem.
Project Leader, Cornell 2007 Summer REU
Our group classified the group structure of element centralizers for arbitrary
elements of R. Thompson’s group V.
Binghamton Educational Opportunity Program Mathematics Instructor (2005, 2006):
Duties included preparing educationally disadvantaged inner-city prefreshman students for university level mathematics courses.
Service
Conference co-organizer for ICGS 2009.
Served on the organizing committee for the conference. Our role was to organize the
themes, speakers, advertisements and invitations, and financial support of the conference.
Member of the University Postdoctoral Advisory Committee at UNL, May 2008-present.
Committee to facilitate improved postdoctoral outcomes for both UNL and for the
individual postdoctoral students at UNL. We organized luncheons with postdoctoral
students, administration, and international speakers on postdoctoral issues. We work to
establish new support structures for postdoctoral students on campus to better facilitate
their growth and also their ability to support UNL.