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UCCS Math Department Home Page

Math 414:  Modern Algebra

Math 131:

Calculus with Refresher Precalculus A

abrams@math.uccs.edu

Professor

Department of Mathematics
University of Colorado
Colorado Springs, CO 80933-7150

Office:  Room 288 EAS Building   (719) 255-3182 (office)
(719) 255-3605 (fax)

Research interests include:

1. Noncommutative Rings and their Categories of Modules
2. Graded Structures
3. Algebraic structure of graph C*-algebras ("Leavitt path algebras")

Recent Articles and Activities:

"Regularity conditions for arbitrary Leavitt path algebras" (with Rangaswamy), to appear, Algebras and Representation Theory.  

"Number theoretic conditions which yield isomorphisms and equivalences between matrix rings over Leavitt algebras", to appear, Rocky Mountain J. Math.

Participant in Park City Mathematics Institute "Designing Professional Development" workshops, Park City, UT,  July 13-18, 2008 and July 1 - 6, 2007.

Participant in the Math Teachers' Circle Workshop at the American Institute of Mathematics, Palo Alto, CA, June 16-21, 2008.   Member of organizing committe of the Pikes Peak Math Teachers' Circle (with Brock, Schoonmaker, Khaliqi, Dineen).

Colorado Math Circle presentation, "The mad veterinarian on mathematical safari", Boulder, CO, April 26, 2009.

"The Classification question for Leavitt path algebras" (with P.N. Anh, A. Louly, and E. Pardo), Journal of Algebra 320(5), 2008,  pp. 1983 - 2026.   Journal of Algebra version

"Evaluating the benefits of providing archived online lectures to in-class math students" (with Bates, Cascaval, Durham), Journal of Asynchronous Leavning Networks 12(3), 2008..

Participant in the Mathematicians in Mathematics Education Workshop, supported by the Institute for Mathematics and Education, University of Arizona, March 20-22, 2008.

Faculty Associate in support of the Partnership for Innovative Preparation of Educators and Students (PIPES), Summer 2007 (and beyond).    Principal Investigator, Summer 2008 (and beyond).

Seminars / colloquia on Leavitt path algebras delivered since Spring 2005 at various universities, including:  University of Oregon, DePaul University, University of California at Berkeley, University of California at Santa Barbara, University of Houston, Lafayette College, University of Colorado at Boulder, Colorado College, Universidad de Autonoma de Barcelona, Universidad de Murcia, Universidad de Malaga, University of Nebraska, Rutgers University, Universidad de Granada, University of Washington, Temple University.

"Chain conditions for Leavitt path algebras" (with G. Aranda Pino, M. Siles Molina, and F. Perera), to appear, Forum Mathematicum.

"Isomorphisms between Leavitt algebras and their matrix rings" (with P.N. Anh and E. Pardo), , J. reine angew. Math. (Crelle's Journal) 624 (2008), 103-132.     Crelle's J. version

"Cafe Scientifique. Mathematics in the Microbrewery:  Fermat meets Fermentation?", FOCUS Magazine (The Journal of the Mathematical Association of America), 27(6) (2007), 26-27.

"Locally finite Leavitt path algebras" (with G. Aranda Pino and M. Siles Molina), Israel J. Math. 165 (2008), 329-348.

"Leavitt path algebras", Notes from the Workshop on Graph Algebras (Malaga, Spain, July 2006).  Chapter 3 (pp. 85-140) of "Graph Algebras: Bridging the gap between algebra and analysis", (Aranda Pino, Siles Molina, Perera eds.)  2007, Servicio de Publicaciones de la Universidad de Malaga, ISBN 978-84-9747-177-0.

"The Leavitt path algebra of arbitrary graphs" (with G. Aranda Pino), Houston J. Math.  34(2) (2008), 423-442.

"Finite dimensional Leavitt path algebras"  (with G. Aranda Pino and M. Siles Molina), J. Pure Appl. Algebra, 209(3) (2007), 753-762.

"Purely infinite simple Leavitt path algebras" (with G. Aranda Pino),   Journal of Pure and Applied Algebra 207(3) (2006), 553-563.

Cafe Scientifique presentations:  The Wynkoop Brewery, Denver (March 2006), The Phantom Canyon Brewery, Colorado Springs (August 2006), and the RedFish Brewery, Boulder (September 2006).   Title:  "Mathematics Research:  What is it, what's the Next Big Thing, and why should you care?" 

Invited Keynote Speaker for the Celebration of the 90th Birthdayof Bill Leavitt, University of Nebraska, March 2006.

(Full vita available upon request)

Hobbies and recreational pursuits include:

1. Mountain biking and road biking
2. Cross country skiing
3. New York Times Sunday Crossword
4. Baseball (playing, attending, listening on radio, eating, sleeping, breathing)