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Mark Tomforde is an American mathematician and Professor of Mathematics at
University of Colorado Colorado Springs The University of Colorado Colorado Springs (UCCS) is a public research university in Colorado Springs, Colorado. It is one of four campuses that make up the University of Colorado system. As of Fall 2017, UCCS had over 12,400 undergraduate an ...
. He works in the areas of
functional analysis Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. Inner product space#Definition, inner product, Norm (mathematics)#Defini ...
and
algebra Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary a ...
, and he earned his Ph.D. in mathematics at
Dartmouth College Dartmouth College (; ) is a private research university in Hanover, New Hampshire. Established in 1769 by Eleazar Wheelock, it is one of the nine colonial colleges chartered before the American Revolution. Although founded to educate Native A ...
in 2002. Tomforde's research interests are in
operator algebra In functional analysis, a branch of mathematics, an operator algebra is an algebra of continuous linear operators on a topological vector space, with the multiplication given by the composition of mappings. The results obtained in the study of ...
s and
C*-algebra In mathematics, specifically in functional analysis, a C∗-algebra (pronounced "C-star") is a Banach algebra together with an involution satisfying the properties of the adjoint. A particular case is that of a complex algebra ''A'' of continuous ...
s, and he has made contributions to the study of graph C*-algebras and Leavitt path algebras. He was an invited speaker at the 2015 Abel Symposium, and he is a founding member of the Algebras and Rings in Colorado Springs (ARCS) center. He has also received several awards for his teaching and outreach efforts.


Contributions to Graph C*-algebras and Leavitt Path Algebras

Tomforde has made fundamental contributions to the related areas of graph C*-algebras and Leavitt path algebras. With Doug Drinen, he is co-creator of the Drinen-Tomforde desingularization, often simply called desingularization. Desingularization allows one to extend many results for row-finite graphs to countable graphs, and it has become a standard tool in the study of graph C*-algebras and Leavitt path algebras. With
Gene Abrams Gene Abrams is an American mathematician and Professor of Mathematics at University of Colorado Colorado Springs. He works in the area of Algebra, and he earned his Ph.D. in mathematics at the University of Oregon in 1981. Abrams' research inter ...
, Tomforde has formulated the Abrams-Tomforde conjectures, which state that the Leavitt path algebras of two graphs are Morita equivalent as rings (respectively, isomorphic as rings) if and only if the C*-algebras of the two graphs are Morita equivalent as C*-algebras (respectively, isomorphic as C*-algebras). Abrams and Tomforde have verified certain special cases of the conjectures, and in 2020 Søren Eilers, Gunnar Restorff, Efren Ruiz, and Adam P.W. Sørensen completed a classification of unital graph C*-algebras that allowed them to verify the Abrams-Tomforde conjectures for graphs with a finite number of vertices. Tomforde is also the creator of ultragraph C*-algebras, which are C*-algebras constructed from a generalization of a directed graph, known as an ultragraph. The ultragraph C*-algebras simultaneously generalize the classes of graph C*-algebras and Exel-Laca algebras, and allow one to apply graph techniques to the study of Exel-Laca algebras. In his research, Tomforde has connected ideas from Functional Analysis and Algebra, and he has used techniques and methods from each subject to contribute to the study of the other. Tomforde has also been active in organizing several conferences on graph C*-algebras and their generalizations, with the goal of bringing together analysts and algebraists to share ideas and collaborate.


Teaching and Outreach

Tomforde's teaching and outreach activities have been recognized in several ways. He created and directed the Cougars and Houston Area Mathematics Program (CHAMP), which ran from Fall 2013 to Spring 2019 and used volunteer effort to provide tutoring and math circle activities to underserved high school and middle school students in Houston. In 2016 CHAMP received an award from
Phi Beta Kappa The Phi Beta Kappa Society () is the oldest academic honor society in the United States, and the most prestigious, due in part to its long history and academic selectivity. Phi Beta Kappa aims to promote and advocate excellence in the liberal a ...
for being an organization that serves as a national model for building creative exchanges with diverse audiences in the arts, humanities, social sciences, natural sciences or mathematics. In 2016 CHAMP also received the Award for Mathematics Programs that Make a Difference from the
American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...
. In 2017, Tomforde was appointed to the STEM Advisory Board for
KIPP The Knowledge is Power Program, commonly known as KIPP, is a network of free open-enrollment college-preparatory schools in low income communities throughout the United States. KIPP is America's largest network of charter schools. The head of ...
, to provide guidance and recommendations regarding STEM education in KIPP's Houston schools. In addition to numerous college and university teaching awards, in 2019 Tomforde was recognized with the MAA Texas Section's Distinguished College and University Teaching of Mathematics Award. In 2020 he was the recipient of the Deborah and Franklin Haimo Award for Distinguished College or University Teaching of Mathematics, the highest teaching honor bestowed by the
Mathematical Association of America The Mathematical Association of America (MAA) is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university, college, and high school teachers; graduate and undergraduate students; pure a ...
, for his "deep and positive impact at all levels of mathematics education".


Honors and awards


References


External links


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20th-century American mathematicians 21st-century American mathematicians Living people Year of birth missing (living people) Dartmouth College alumni Gustavus Adolphus College alumni {{cat improve, date=August 2020