Gene Abrams

Gene Abrams is an American mathematician and Professor of Mathematicsat University of Colorado Colorado Springs. He works in the area of Algebra, and heearned his Ph.D. in mathematics at the University of Oregon in 1981.Abrams' research interests are in noncommutativerings and their categories of modules, and he is known for his contributionsto Morita equivalence, particularly Moritaequivalence for nonunital rings.

Abrams is credited as one of the founders of the subject of Leavitt path algebras.Leavit path algebras were simultaneously introduced in 2005 byAbrams and Gonzalo Aranda Pino as well as by Ara, Moreno, and Pardo, with neither of the two groups aware of the other's work.Abrams has stated that his inspiration for Leavitt path algebras came afterattending a CBMS Conference hosted byPaul Muhly, David Pask, and Mark Tomfordeat the University of Iowa in 2004.The topic of this CBMS conference was graphC*-algebras, a particular class of C*-algebras studied in functional analysis, and the talks at the conferencegave 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.The study of Leavitt path algebras has also promoted interactions between Analysisand Algebra, and there have been multiple conference onLeavitt path algebras aimed at bringing algebraists and analyststogether to collaborate and share ideas.Abrams is also one of the coauthors,with Pere Ara and Mercedes Silkes Molina, of the book Leavitt path algebras: a primer and handbook, published by Springer.

Abrams has been active in mathematics outreach and worked to popularizemathematical topics for general audiences.He is a member and organizer of theColorado Math Circle.Hehas spoken at the Colorado Café Scientifique, an organization based on theFrench Café Philosophique, where members of the general public receive anintroduction 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 andencouraging more mathematicians to become involvedin this kind of public outreach.

Abrams was awarded the Carl B. Allendoerfer Award of theMathematical Association of America in 2011 for his paper with Jessica Sklar,The Graph Menagerie: Abstract Algebra and the Mad Veterinarian.The paper describes and provides a general solution to a topic in recreational math known asthe "Mad veterinarian puzzles".One example of a Mad Veterinarian Puzzle is the following:

"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?"

• Carl B. Allendoerfer Award, 2011
• Rocky Mountain Section of the Mathematical Association ofAmerica Award for Distinguished University Teaching, 2002
• University of Colorado systemwide President's Teaching Scholar, 1996