Gene Abrams


Department of Mathematics
University of Colorado
Colorado Springs, CO 80918

abrams 'at'

Office:  Room 272 EAS Building  

(719) 255-3182 (office)
(719) 255-3605 (fax)

UCCS Math Department Home Page

Colorado Springs Algebra Seminar, a.k.a. "Rings and Wings"



Background and Professional Information


-  Ph.D. in Mathematics,  University of Oregon, 1981.  (B.A., Math, U.C. San Diego, 1976)
Faculty member in the Department of Mathematics at UCCS since 1983.    
Recipient of the UCCS campuswide Outstanding Teaching Award, 1988.

Department Chair, September 1995 - August 1998, and January 2018 - present.
-  Designated as University of Colorado systemwide President's Teaching Scholar, 1996.
-  Recipient of the 2002 Burton W. Jones Award for Distinguished University Teaching, Rocky Mountain Section of the Mathematical Association of America.
-  Co-developer of and teacher in the CU-Colorado Springs MathOnline program.

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)


Research interests:

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.



An interesting / mysterious number-theoretic construction


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

     Lecture 1

     Lecture 2

     Lecture 3

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)

University of Washington / PIMS Colloquium, May 2014

Seattle University, May 2014

Pacific Lutheran University, May 2014

University of Washington Algebra Seminar,  May 2014   (and Seminar Pretalk)

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)

University of Padua, June 2013

Banff International Research Station (BIRS)  April 2013

University of Colorado Boulder (AMS Sectional Conference)  April 2013   (20 minutes)

Univeristy of Victoria, March 2013

University of Western Sydney, February 2013:  Lecture 1Lecture 2Lecture 3

Australian Mathematical Science Institute National Seminar Series, February 2013


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

- 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.

      - "The Graph Menagerie", Colorado College Fearless Friday seminar series, October 22, 2010.    

      - "The Graph Menagerie", University of Colorado at Colorado Springs Math Colloquium,September 30, 2010.


  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:

Link to:   Sky Sox Math Youth Day webpage



Hobbies and recreational pursuits include:

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


Some photos:


-- 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

UCCS Department of Mathematics
University of Colorado
Colorado Springs, CO 80918
(719)255-3311 (office)
(719)255-3605 (fax)



































































































































































































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