Department of Mathematics
abrams 'at' math.uccs.edu
Office: Room 288 EAS Building (719) 255-3182 (office)
Spring 2014 Teaching Schedule:
|Background and Professional Information|
- Ph.D. in Mathematics, University of Oregon, 1981. (B.A., Math, U.C. San Diego, 1976)
- Department Chair, September 1995 - August 1998.
- Recipient of the UCCS campuswide Chancellor's Award, 2010.
- Recipient (with J. Sklar) of 2010 Allendoerfer Award (for expository writing), Mathematical Association of America.
(full vita available on request)
I am an algebraist, with interest in noncommutative rings and their categories of modules. Since 2005 my primary focus has been on a class of rings called "Leavitt path algebras".
Recent Articles:(much of this research is supported by a Simons Foundation Collaboration Grant in Mathematics)
- "The Leavitt path algebras of generalized Cayley graphs" (with G. Aranda Pino), submitted.
- "Cohn path algebras have Invariant Basis Number" (with M. Kanuni), submitted.
- "A class of C*-algebras that are prime but not primitive" (with M. Tomforde), Muenster J. Math., to appear.
- "Leavitt path algebras of Cayley graphs arising from cyclic groups" (with B. Schoonmaker), Proceedings of the conference "Noncommutative rings and their applications, Lens, France, July 2013", American Mathematical Society Contemporary Mathematics Series, to appear.
- "On prime non-primitive von Neumann regular algebras" (with J. Bell, K.M. Rangaswamy), Transactions of the American Mathematical Society 366(5), 2014, 2375-2392.
- "Simple Lie algebras arising from Leavitt path algebras" (with Z. Mesyan), J. Pure Applied Algebra 216(10), 2012, 2302-2313.
- "A Mathematician Does the New York Times Sunday Crossword Puzzle", pp. 123-135 in Mathematics in Popular Culture: Essays on Appearances in Film, Fiction, Games, Television, and Other Media, J.Sklar and E.Sklar eds., McFarland Publishers, North Carolina, 2012.
- "Two-sided chain conditions in Leavitt path algebras over arbitrary-sized graphs" (with J. Bell, P. Colak, and K.M. Rangaswamy), Journal of Algebra and its Application .11(3), 2012, pp. 1250044-1 through 1250044-23.
- "Row-finite equivalents exist only for row-countable graphs" (with K.M. Rangaswamy), in New Trends in Noncommutative Algebra (A Conference in Honor of Ken Goodearl's 65th Birthday, University of Washington, August 9-14, 2010), Ara et.al., editors, Contemporary Mathematics 562, pp. 1-10, American Mathematical Society, 2012.
- "Dixmier Moeglin equivalence for Leavitt path algebras" (with J. Bell and K.M. Rangaswamy), Algebras and Representation Theory 15(3), 2012, 407-425.
Recent Professional Activities:
- In residence, Universita di Padova (Italy), May 20 - July 31, 2013. (Duties included teaching a Ph.D. course at U. di Padova on the topic of Leavitt path algebras.)
- Co-organizer of sponsored conference "Graph algebras: Bridges between graph C*-algebras and Leavitt path algebras", held at Banff International Research Station, April 2013.
- Principal Investigator, Partnership for Innovative Preparation of Educators and Students (PIPES), 2008 - 2013.
- Instructor at Epsilon Camp (Summer 2012), and at MathPath (Summers 2009 and 2011), held at Colorado College.
- co-organizer, Pikes Peak Mathematics Teacher Circle Academy and Worshops. Academy: Breckenridge, CO, June 2009, June 2010, and June 2011; Estes Park, June 2012. Workshops: Monthly through the academic year, Fall 2009 through Spring 2013.
- Mathematical content developer, Colorado Springs Sky Sox Math Youth Day, annually since 2002. Here's an article about it.
- "Math on Tap: The constant flow of new ideas and new results in mathematics research"; presentation made at Jack Quinn's Irish Pub, Colorado Springs, July 2011, as part of the "Science on Tap" series. (I've made additional public presentations about mathematics as part of the Cafe Scientifique Series. Here's an article about those.)
Recent Seminars / Colloquia: (all talks 50 - 60 mins unless otherwise indicated)
Saint Peter's University, April 2014
Rutgers University, April 2014
University of California San Diego, October 2013
Stefan Banach Center, Bedlewo, Poland (20 minutes)
Universite d'Artois (Lens, France), July 2013 (30 minutes)
Additional talks since 2008 include : University of South Alabama, November 2011; Baylor University, October 2011; Universidad de Malaga (Spain), September 2011; University of Nebraska - Lincoln, April 2011; University of Iowa, April 2011; University of Wisconsin - Milwaukee, April 2011; University of California San Diego, March 2011; University of Washington, August 2010; Universidad de Granada (Spain), July 2010; Universidad de Malaga (Spain), July 2010; George Mason University, April 2010; University of Oregon, April 2009; DePaul University, October 2008; University of California at Berkeley, June 2008; University of California at Santa Barbara, March 2008; University of Houston, February 2008
Activities related to Mad Veterinarian Puzzles:
"The graph menagerie: Abstract algebra and the Mad Veterinarian" (with J. Sklar), Mathematics Magazine 83(3), 2010, 168-179. (Earned 2010 Allendoerfer Prize from MAA.)
Seminars / colloquia:
-"The Graph Menagerie: Abstract Algebra meets the Mad Veterinarian", University of San Francisco Math Department Colloquium, March 7, 2012.
Hands-on activities (to various teacher groups and student groups):
- "Mad Veterinarian Puzzles: Grids, Groups, Graphs; Gerbils, Groundhogs, Giraffes?" Rocky Mountain Math Teacher's Circle (Denver), May 4, 2013; also presented at the San Francisco Math Teachers' Circle, March 6, 2012. (2.5 hour activity)
- Mobile Alabama Math Circle, November 14, 2011
- Breakout sessions of MathPath 2011, Colorado College, July 12-15, 2011
- Plenary sessions of MathPath 2009, Colorado College, July 8 and 9, 2009.
- Colorado Math Circle, Boulder, CO, April 26, 2009
Hobbies and recreational pursuits include:
1) with my wife Mickey, at the top of Passo Giau (near Cortina d'Ampezzo, Italy), July 2013
2) with my wife Mickey, riding up Pikes Peak ("Assault the Peak Challenge"), August 2010