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 August 1983 through December 2024. (Professor Emeritus status pending)
• Department Chair, September 1995 - August 1998, and January 2018 - June 2019.
• Co-developer of and teacher in the CU-Colorado Springs MathOnline program.
• Recipient (with J. Sklar) of 2010 Allendoerfer Award (for expository writing), Mathematical Association of America.
• Recipient of the UCCS campuswide Chancellor's Award, 2010.
• Recipient of the 2002 Burton W. Jones Award for Distinguished University Teaching, Rocky Mountain Section of the Mathematical Association of America.
• Designated as University of Colorado systemwide President's Teaching Scholar, 1996.
• Recipient of the UCCS campuswide Outstanding Teaching Award, 1988.

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Wikipedia page 

Research interests

Publications since 2014

Book:

• "Leavitt path algebras" (with P. Ara, M. Siles Molina). Lecture Notes in Mathematics Vol. 2191, Springer Verlag, 2017.

Journal Publications:

"Monoids, dynamics, and Leavitt path algebras" (with R. Hazrat), to appear, Expositiones Mathematicae. 

"Recasting the Hazrat conjecture: relating shift equivalence to graded Morita equivalence" (with E. Ruiz, M. Tomforde), Algebras and Representation Theory 27, 2024, 1477-1511. 

"Injectives over Leavitt path algebras of graphs with disjoint cycles" (with F. Mantese, A. Tonolo), J. Pure Applied Algebra 228, 2024, 27 pages. 

"Connections between Abelian sandpile models and the K-theory of weighted Leavitt path algebras" (with R. Hazrat), European Journal of Mathematics 9, 2023, 21 pages. 

"Morita equivalence for graded rings" (with E. Ruiz, M. Tomforde), Journal of Algebra 617, 2023, pp. 79-112. 

"Realizing corners of Leavitt path algebras as Steinberg algebras, with corresponding connections to graph C*-algebras" (with M. Dokuchaev, T.G. Nam), Journal of Algebra 593, 2022, pp. 72-104. 

"Injective modules over the Jacobson algebra K < X,Y | XY=1 >" (with F. Mantese, A. Tonolo), Canadian Bulletin of Mathematics 64(2), 2021, pp. 323-339. 

"A matrix viewpoint for various algebraic extensions" (with P.N. Ánh), Elemente der Mathematik 75, 2020, pp. 1-17. 

"Products of ideals in Leavitt path algebras" (with Z. Mesyan, K. M. Rangaswamy), Communications in Algebra 48, 2020, pp. 1853-1871. 

"Corners of Leavitt path algebras of finite graphs are Leavitt path algebras" (with Nam), Journal of Algebra 547, 2020, pp 494-518. 

"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, 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 

Seminars / Colloquia since 2014

(all talks 50 - 60 mins unless otherwise indicated).

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• Final pre-retirement Lecture, presented in the UCCS Department of Mathematics Colloquium Series: “A Whale of a Catch, but Moby Dick Still Swims Free”, November 21, 2024. (recorded version available: https://math.uccs.edu/research/colloquia). 
• “Current status of the two most important outstanding questions in Leavitt path algebras”, presentation given in Fields Institute C*-algebra Seminar, Toronto, October 2024. 
• "Sandpile models and weighted Leavitt path algebras". Delivered four times in 2022: Cochin University of Science and Technology (India) (online, March); Baylor University Algebra Seminar (online, March); Ohio State University Algebra Seminar (online, April); University of Padova (Italy) Conference for Alberto Tonolo (in person, October). 
• Some activities related to linear algebra over the integers ('Rompicapi di un Veterinario Pazzo'). University of Padova, September 2019 (Two one-hour talks.)
• 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
• Workshop on Leavitt path algebras (three one-hour introductory lectures), FloripaDynSys-III, 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

Various Professional Activities since 2010

• Ph.D. short course: "V-monoids, Grothendieck groups, the Bergman Realization Theorem, and applications to Leavitt path algebras", University of Padova (Italy), September 9-10, 2024.
• Graduate course “Algebra”, with focus on Leavitt path algebras, Scuola Matematica Interuniversitaria, Perugia (Italy), four weeks, Summer 2023.
• In residence, Universita di Padova (Italy), September 15 - October 30, 2019. (Duties included teaching a Ph.D. seminar on linear algebra over the integers)
• Peer Revue, June 2016 (a comedy skit on math, as part of the Peer Revue science-in-comedy series, Stargazer's Theater, Colorado Springs, June 22, 2016). (YouTube Video) 
• 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, three games per year 2002 through 2018. 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

Article:

• " The graph menagerie: Abstract algebra and the Mad Veterinarian" (with J. Sklar), Mathematics Magazine 83(3), 2010, 168-179. (Article awarded 2010 Allendoerfer Prize from the 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):

• (online via Zoom) "The First Workshop on Mathematics Specialised for High School Students; Abstract Algebra and Mad Veterinarian", Tehran (Iran), January 28, 2022
• "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

Hobbies and Recreational Pursuits

• Cycling (mountain biking and road biking)
• Skiing (cross country, alpine touring, downhill)
• New York Times Sunday Crossword Puzzle
• Baseball (playing, attending, listening on radio, eating, sleeping, breathing)

UCCS Department of Mathematics 

University of Colorado 

Colorado Springs, CO 80918