Department of Mathematics
abrams 'at' math.uccs.edu
Office: Room 272 EAS Building
(719) 255-3182 (office)
|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, and January 2018 - present.
- 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".
"Leavitt path algebras" (with P. Ara, M. Siles Molina). Lecture Notes in Mathematics Vol. 2191, Springer Verlag, 2017.
Here are some errata: List of errata, updated July 2019
Recent Journal Publications:
- "Prufer modules over Leavitt path algebras" (with F. Mantese, A. Tonolo), Journal of Algebra and its Applications 18(8), 2019, 1950154, 28 pages.
- "Leavitt path algebras of Cayley graphs C_n^j" (with C. Gil Canto, S. Erickson), Mediterranean J. Math. 15:197, 2018, 23 pages.
- "Leavitt path algebras are Bezout" (with F. Mantese, A. Tonolo), Israel J. Math. 228(1), 2018, pp 53-78.
- "Chains of Semiprime and Prime Ideals in Leavitt Path Algebras" (with B. Greenfeld, Z. Mesyan, K.M. Rangaswamy), Advances in rings and modules, 1–16, Contemporary Mathematics Series Volume 715, American Mathematical Society Publishers, Providence, RI, 2018. (volume in honor of Bruno Mueller)
- "Realizing posets as prime spectra of Leavitt path algebras" (with G. Aranda Pino, Z. Mesyan, C. Smith), Journal of Algebra 476, 2017, pp. 267 - 296.
- "Leavitt path algebras having Unbounded Generating Number" (with T.G. Nam, N.T. Phuc), Journal of Pure and Applied Algebra 221, 2017, pp. 1322 - 1343.
- "WHAT IS ... a Leavitt path algebra?", Notices of the American Mathematical Society 63(8), 2016, pp. 910-911.
- "The Leavitt path algebras of generalized Cayley graphs" (with G. Aranda Pino), Mediterranean J. Math 13(1), 2016, pp. 1-27.
- "Cohn path algebras have Invariant Basis Number" (with M. Kanuni), Communications in Algebra 44, 2016, pp. 371-380.
- "Extensions of simple modules over Leavitt path algebras" (with F. Mantese, A. Tonolo), Journal of Algebra 431, 2015, pp. 78-106.
- "Leavitt path algebras: the first decade", Bulletin of Mathematical Sciences 5(1), 2015, pp. 59-120.
- "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 Volume 634, 2015, pp. 1-10.
- "A class of C*-algebras that are prime but not primitive" (with M. Tomforde), Muenster J. Math 7, 2014, pp. 489-514.
- "The prime spectrum and primitive ideal space of a graph C*-algebra" (with M. Tomforde), International J. Math, 25(7), 2014, pp. 1450070(01) - 1450070(22).
- "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.
Recent Seminars / Colloquia: (all talks 50 - 60 mins unless otherwise indicated)
Leavitt path algebras: something for everyone. Vietnam Institute of Mathematics, May 2018
Leavitt path algebras are Bezout. Vietnam Institute for Advanced Study in Mathematics, May 2018
Chen simple modules and Prufer modules over Leavitt path algebras. Vietnam Institute for Advanced Study in Mathematics, May 2018.
Leavitt path algebras: entering adulthood. University of Iowa Department of Mathematics Colloquium, March 2018.
FloripaDynSys-III, Workshop on Leavitt path algebras (three one-hour introductory lectures), Florianopolis, Brazil, March 2017
OSU - Denison conference May 2016 (20 minutes)
CIMPA program on graph algebras, Nesin Mathematics Center, Sirince, Turkey, June 2015
University of New Mexico, April 2015
Arizona State University C*-algebra seminar, March 2015
West Coast Operator Algebra Seminar, Denver University, November 2014
Syracuse University, October 2014
UCCS, September 2014
University of Malaga (Spain), June 2014
Conference on Algebraic Structures and Applications, Spineto, Italy, June 2014 (20 minutes)
Seattle University, May 2014
Pacific Lutheran University, May 2014
Colorado College, April 2014
Saint Peter's University, April 2014
Rutgers University, April 2014
University of California San Diego, October 2013
Stefan Banach Center, Bedlewo, Poland July 2013 (20 minutes)
Universite d'Artois (Lens, France), July 2013 (30 minutes)
Additional talks since 2008 include : AMS Sections Conference at University of Hawaii, March 2012; Math Institute at Oberwolfach (Germany), April 2012; Ohio University, May 2012; Ohio State University, May 2012; University of Southern California, November 2012; 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
Recent Professional Activities:
- Peer Revue June 2016 https://youtu.be/N6fFREdG2KE
- 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.)
- Author of the article "A mathematician does the New York Times Sunday Crossword Puzzle" which appears in the book "Mathematics in Popular Culture: Essays on Appearances in Film, Fiction, Games, Television, and Other Media", McFarland and Co. Publishers, 2012, pp. 123-135.
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?" A 2.5 hour Math Teacher Circle Activity.
Rocky Mountain Math Teachers' Circle (Denver), October 3, 2015;
Rocky Mountain Math Teachers' Circle (Denver), May 4, 2013;
Pikes Peak Math Teachers' Circle (Estes Park, CO), June 2012;
San Francisco Math Teachers' Circle, March 6, 2012.
- 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
Sky Sox Math Youth Days
Content developer for Sky Sox Math Youth Days, 2002 - present.
Link to: Sky Sox Math Youth Day webpage
Hobbies and recreational pursuits include:
-- with my wife Mickey, Hurricane Ridge (Olympic National Park, WA) August 2018
-- with my wife Mickey, near Hoa Binh reservoir outside of Hanoi, Vietnam, May 2018.
-- with my wife Mickey, at the summit of Serra do rio do rostro (near Florianopolis, Brazil), March 2017. (Thanks for the suggestion, Daniel!)
-- with my wife Mickey, at the Monastery of Montserrat (near Barcelona, Spain), June 2015
-- with my wife Mickey, at the top of Passo Giau (near Cortina d'Ampezzo, Italy), July 2013
-- with my wife Mickey, riding up Pikes Peak ("Assault the Peak Challenge"), August 2010