MathOnline Program

UCCS Math Department Home Page

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

abrams@math.uccs.edu

Professor

Department of Mathematics
University of Colorado
Colorado Springs, CO 80918

(on sabbatical assignment,

Spring 2013)

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

-  Ph.D. in Mathematics, University of Oregon, 1981.
-  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.
-  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, current director 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.

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".  

Recent Articles and Activities:

"Cohn path algebras have Invariant Basis Number" (with M. Kanuni), submitted.

"On prime non-primitive von Neumann regular algebras" (with J. Bell, K.M. Rangaswamy), Transactions of the American Mathematical Society, to appear.

"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.  

Beamer files for seminars / colloquia on Leavitt path algebras delivered since Spring 2010 at various universities. 

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

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 1;  Lecture 2;  Lecture 3

Australian Mathematical Science Institute National Seminar Series, February 2013

University of Southern California, November 2012

Ohio State University May 2012

Ohio University May 2012

Mathematisches Forschungsinstitut Oberwolfach April 2012

University of Hawaii (AMS Sectional Conference)  March 2012  (20 minutes)

University of South Alabama November 2011,

Baylor University October 2011,    

Universidad de Malaga September 2011,   

University of Nebraska 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   (30 minutes)

Universidad de Granada July 2010, 

Universidad de Malaga July 2010,   

George Mason University April 2010

Additional talks since 2005 include :  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,  Lafayette College November 2007,  University of Colorado at Boulder September 2007,  Colorado College September 2007,   Universidad de Murcia July 2006,   Universidad de Malaga July 2006,  Universidad de Autonoma de Barcelona June 2006, University of Nebraska April 2006,  Rutgers University November 2005,  Universidad de Granada June 2005,  Temple University April 2005,  University of Washington January 2005.

Activities related to Mad Veterinarian Puzzles:

    "The Graph Menagerie:  Abstract Algebra meets the Mad Veterinarian", University of San Francisco Math Department Colloquium, March 7, 2012.

     "Mad Veterinarian Puzzles:  Grids, Groups, Graphs; Gerbils, Groundhogs, Giraffes?"  San Francisco Math Teachers' Circle, March 6, 2012.

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

     "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 about Mad Vet Puzzles made in: 

 - 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

       Posts to NYTimes blog about Mad Vet Puzzles can be found at:   http://wordplay.blogs.nytimes.com/2011/06/27/numberplay-the-mad-vet/

     Additional activities and resources include:   

            -  Original Mad Vet Puzzle website   (by Bob Harris):

                            http://www.bumblebeagle.org/madvet/index.html

            -  Lincoln (Nebraska) Math  Teachers' Circle:

                            http://scimath.unl.edu/mathteacherscircle/#lincoln_2008

            -   San Diego Math Teachers' Circle  (by David Patrick): 

                             www.sdmathteacherscircle.org/handouts/IntroProblemSolving.pdf

            -   Marin (California) Math Circle    (December 10, 2010;  by Joshua Zucker): 

                             http://www.marinmathcircle.org/archives.html 

Instructor at Epsilon Camp (Summer 2012), and at MathPath (Summers 2009 and 2011), held at Colorado College.

"Flow invariants in the classification of Leavitt path algebras" (with A. Louly, E. Pardo, C. Smith), Journal of Algebra 333, 2011, 202-231.

"Isomorphism and Morita equivalence of graph algebras" (with M. Tomforde), Transactions of the American Mathematical Society 363(7), 2011, 3733-3767.

"The socle series of a Leavitt path algebra" (with K.M. Rangaswamy and M. Siles Molina), Israel Journal of Mathematics 184, 2011, 413-435.

"On the simplicity of Lie algebras associated to Leavitt algebras (with D. Funk-Neubauer), Communications in Algebra, 39(11), 2011, 4059-4059.

"The matrix type of purely infinite simple Leavitt path algebras (with C. Smith), Acta Mathematica Hungarica 128(4), 2010, 381-385.

Convocation Address to the University of Colorado at Colorado Springs Incoming Class of 2014, "The 5000th Lecture: Some reflections on Randy Pausch's The Last Lecture", 18 August 2010.

co-organizer (with M. Tomforde), Special Session on Graph Algebras in Algebra and Analysis, to be held at the annual American Mathematical Society national meeting, San Francisco, January 14, 2010.

"Regularity conditions for arbitrary Leavitt path algebras" (with K.M. Rangaswamy), Algebras and Representation Theory 13, 2010, 319-334.

"Number theoretic conditions which yield isomorphisms and equivalences between matrix rings over Leavitt algebras", Rocky Mountain J. Math 40(4), 2010, 1069-1084.

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 since Fall 2009.

Participant in the Math Teachers' Circle Workshop at the American Institute of Mathematics, Palo Alto, CA, June 16-21, 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).

Mathematical content developer, Colorado Springs Sky Sox Math Youth Day, annually since 2002.  Here's an article about it. 

Public presentations about the nature of mathematics:  

   - "Math on Tap:  The constant flow of new ideas and new results in mathematics research"; at Jack Quinn's Pub, Colorado Springs (July 2011) (part of the "Science on Tap" series).

   -  "Mathematics Research:  What is it, what's the Next Big Thing, and why should you care?";  at The Wynkoop Brewery, Denver (March 2006), The Phantom Canyon Brewery, Colorado Springs (August 2006), and the RedFish Brewery, Boulder (September 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 Puzzle
4. Baseball (playing, attending, listening on radio, eating, sleeping, breathing)

with my wife Mickey, riding up Pikes Peak ("Assault the Peak Challenge"), August 2010 ...