Gene Abrams

Abrams is credited as one of the founders of the subject of Leavitt path algebras.Sec. 1.7 of Leavitt path algebras. Lecture Notes in Mathematics, 2191. Springer, London, 2017. xiii+287 pp. {{ISBN|978-1-4471-7343-4}}; 978-1-4471-7344-1. {{citation|url=https://academics.uccs.edu/gabrams/documents/versionsenttoSpringer4April2017.pdf|title=Online Copy}} Leavitt path algebras were simultaneously introduced in 2005 by Abrams and Gonzalo Aranda PinoAbrams, Gene; Aranda Pino, Gonzalo; The Leavitt path algebra of a graph. J. Algebra 293 (2005), no. 2, 319--334. as well as by Ara, Moreno, and Pardo,Pere Ara, María A. Moreno, and Enrique Pardo. Nonstable K-theory for

graph algebras. Algebr. Represent. Theory, 10(2):157–178, 2007. with neither of the two groups aware of the other's work.Sec. 1.7 of Leavitt

path algebras. Lecture Notes in Mathematics, 2191. Springer, London, 2017. xiii+287 pp. {{ISBN|978-1-4471-7343-4}}; 978-1-4471-7344-1. {{citation|url=https://academics.uccs.edu/gabrams/documents/versionsenttoSpringer4April2017.pdf|title=Online Copy}} Abrams has stated that his inspiration for Leavitt path algebras came after attending a CBMS Conference hosted by Paul Muhly, David Pask, and Mark Tomforde at the University of Iowa in 2004.Title slide and p.23 of "Leavitt path algebras: Entering Adulthood (d.o.b. May 31, 2004; Iowa City, Iowa)", slides from a talk given by Gene Abrams at the University of Iowa on March 30, 2018.

{{citation|url=https://academics.uccs.edu/gabrams/UIowaMarch2018%20copy.pdf|title=Online Copy}} The topic of this CBMS conference was graph C*-algebras,{{citation|url=https://www.cbmsweb.org/archive/NSF/2004_conf.htm|title=List of 2004 CBMS conferences}} a particular class of C*-algebras studied in functional analysis, and the talks at the conference gave Abrams the idea to introduce Leavitt path algebras as algebraic analogues of the graph C*-algebras. The Leavitt path algebras are so-named because they are constructed from the path algebra of a graph and they also generalize Leavitt algebras.

Leavitt path algebras have been investigated by dozens of mathematicians since their introduction, and Abrams has been instrumental in the development of the theory.Leavitt path algebras: the first decade. Bull. Math. Sci. 5 (2015), no. 1, 59--120. The study of Leavitt path algebras has also promoted interactions between Analysis and Algebra, and there have been multiple conference on Leavitt path algebras aimed at bringing algebraists and analysts together to collaborate and share ideas.Workshop on Graph Algebras at Málaga, Spain in 2006 {{citation|url=http://agt.cie.uma.es/~wga06/|title=website}}{{citation|url=http://jointmathematicsmeetings.org/meetings/national/jmm/2124_program_ss21.html|title=AMS Special Session on Graph Algebras in Analysis and Algebra}} held at the Joint Mathematics Meetings in 2010.Graph algebras: Bridges between graph C*-algebras and Leavitt path algebras, a five-day workshop held at Banff International Research Station from April 21--April 26, 2013. {{citation|url=http://www.birs.ca/events/2013/5-day-workshops/13w5049|title=Conference Website}}, {{citation|url=https://www.math.uh.edu/~tomforde/GraphAlgebraProblems/GraphAlgebraProblemPage.html|title=Online Problem Page from the Workshop.}} Abrams is also one of the coauthors, with Pere Ara and Mercedes Siles Molina, of the book Leavitt path algebras,Leavitt path algebras: a primer and handbook. Lecture Notes in Mathematics, 2191. Springer, London, 2017. xiii+287 pp. {{ISBN|978-1-4471-7343-4}}; 978-1-4471-7344-1. {{citation|url=https://www.springer.com/in/book/9781447173434|title=Springer Book Page}} {{citation|url=https://academics.uccs.edu/gabrams/documents/versionsenttoSpringer4April2017.pdf|title=Online Copy}} published by Springer. In 2020 Leavitt path algebras were added to the Mathematics Subject Classification with code 16S88 under the general discipline of Associative Rings and Algebras.{{citation|url=https://mathscinet.ams.org/msnhtml/msc2020.pdf|title=2020 Mathematics Subject Classification}}

Abrams has been active in mathematics outreach and worked to popularize mathematical topics for general audiences. He is a member and organizer of the Colorado Math Circle.{{citation|url=http://www.coloradomath.org/index.htm|title=The Colorado Math Circle, members and organizers}} He has spoken{{citation|url=https://www.cafescicolorado.org/Abrams.htm|title=Colorado Café Scientifique talk by Gene Abrams}} at the Colorado Café Scientifique,{{citation|url=https://www.cafescicolorado.org/index.htm|title=Colorado Café Scientifique website}} an organization based on the French Café Philosophique, where members of the general public receive an

introduction to an interesting current scientific topic from an expert. Abrams also wrote an article for the MAA FOCUS describing his experiences at the Colorado Café Scientifique and encouraging more mathematicians to become involved in this kind of public outreach.Café Scientifique Mathematics in the Microbrewery: Fermat Meets Fermentation, MAA FOCUS, Volume 27, Issue 6, August/September 2007 {{citation|url=https://academics.uccs.edu/gabrams/documents/FOCUSarticleAug2007justcoverandarticle.pdf|title=Online Copy}}

Abrams was awarded the Carl B. Allendoerfer Award of the Mathematical Association of America in 2011 for his paper with Jessica Sklar, The Graph Menagerie: Abstract Algebra and the Mad Veterinarian.The Graph Menagerie: Abstract Algebra and the Mad Veterinarian, Gene Abrams and Jessica K. Sklar, Math. Mag. 83 (2010), no. 3, 168--179.{{citation|url=https://www.maa.org/sites/default/files/pdf/upload_library/22/Allendoerfer/Abrams2011.pdf|title=Online Copy}} The paper describes and provides a general solution to a topic in recreational math known as the "Mad veterinarian puzzles". One example of a Mad Veterinarian Puzzle is the following:

{{quote|"Suppose a mad veterinarian creates a transmogrifier that can convert one cat into two dogs and five mice, or one dog into three cats and three mice, or a mouse into a cat and a dog. It can also do each of these operations in reverse. Can it, through any sequence of operations, convert two cats into a pack of dogs? How about one cat?"1 Plus 1 Makes Engaging Book: Mother and Daughter Bridge Generations and Disciplines by Dana Mackenzie (January 2013), Swarthmore College Bulletin. {{citation|url=https://bulletin.swarthmore.edu/bulletin-issue-archive/archive_p=988.html|title=Online Copy}}}}

• Carl B. Allendoerfer Award, 2011
• Rocky Mountain Section of the Mathematical Association of America Award for Distinguished University Teaching, 2002{{citation|url=http://sections.maa.org/rockymt/BWJonesAward.php|title=The Burton W. Jones Distinguished Teaching Award of the Rocky Mountain Section of the MAA, list of recipients}}
• University of Colorado systemwide President's Teaching Scholar, 1996

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Category:20th-century American mathematicians

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