Algebras and Rings in Colorado Springs
Members

ARCS members are researchers in the Colorado Springs area who work on Rings, Algebras, and related topics.

University of Colorado at Colorado Springs Colorado College
    Dr. Gene Abrams     Dr. Luis David García Puente
    Dr. Zak Mesyan     Dr. Beth Malmskog
    Dr. Greg Oman     Dr. Mike Siddoway
    Dr. K.M. Rangaswamy    
    Dr. Mark Tomforde    



Bios of ARCS Members


      user Dr. Gene Abrams
Ph.D., University of Oregon, 1981
M.S., University of Oregon, 1978
B.A., University of California, San Diego, 1976

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Gene Abrams has been a faculty member at UCCS since 1983. He very much enjoys all three aspects of the faculty triad: teaching, research and service.

For the past fifteen years his research has been focused on Leavitt path algebras. In earlier years of his career he did work in the areas of Morita equivalence; rings with local units; categories of graded modules; infinite matrix rings, and incidence rings.

He has received college-, campus-, and region-wide teaching awards. He was designated a University of Colorado President’s Teaching Scholar in 1996. He is the author of more than five dozen research articles (many coauthored), and has given lectures on his research throughout the world. He has been very active in community outreach, including: helping to develop the CU-Succeed and MathOnline programs at UCCS; developing and delivering Sky Sox Math Youth Days; working with MathPath and Epsilon Camp; and making presentations in Science on Tap.

Selected publications:

Books:
  • Leavitt Path Algebras, with P. Ara and M. Siles Molina, Lecture Notes in Mathematics 2191, Springer Verlag Publishers, London, (2017), xiii+287 pages.
Papers:
  • Leavitt path algebras of Cayley graphs C jn, with S. Erickson and C. Gil Canto, Mediterr. J. Math. 15 (2018), no. 5, Paper No. 197, 23pp.

  • Leavitt path algebras are Bézout, with F. Mantese and A. Tonolo, Israel J. Math. 228 (2018), no. 1, 53--78.

  • Chains of Semiprime and Prime Ideals in Leavitt Path Algebras, with B. Greenfeld, Z. Mesyan, and K.M. Rangaswamy, Advances in Rings and Modules, Contemporary Mathematics Series vol. 715, American Mathematical Society (2018), pp. 1--16.

  • WHAT IS . . . a Leavitt path algebra?, Notices Amer. Math. Soc. 63 (2016), no. 8, 910--911.

  • Leavitt path algebras: the first decade, Bull. Math. Sci. 5 (2015), no. 1, 59--120.

  • On prime non-primitive von Neumann regular algebras, with J. Bell and K.M. Rangaswamy, Trans. Amer. Math. Soc. 366 (2014), no. 5, 2375--2392.

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

  • Isomorphism and Morita equivalence of graph algebras, with M. Tomforde, Trans. Amer. Math. Soc. 367 (2011), no. 7, 3733--3767.

  • Isomorphisms between Leavitt algebras and their matrix rings, with P.N. Ánh and E. Pardo, J. Reine Angew. Mat. (Crelle’s Journal) 624 (2008), no. 7, 103--132.

  • The Leavitt path algebra of a graph, with G. Aranda Pino, J. Algebra 293 (2005), no. 2, 319--334.

  • On dense subrings of RFM(R), J. Algebra 110 (1987), no. 1, 243--248.

  • Morita equivalence for rings with local units, Comm. Algebra 11 (1983), no. 8 801--837.




      user Dr. Luis David García Puente
Ph.D., Virginia Tech, 2004
B.S., Universidad Nacional Autonoma de Mexico, 1999
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Luis David García Puente was born and raised in Mexico City. He received his Bachelor’s degree in Mathematics from the Universidad Nacional Autónoma de México and his Ph.D. in Mathematics from Virginia Tech. He has held postdoctoral appointments at the Mathematical Sciences Research Institute and at Texas A&M University. Currently, he is Professor of Mathematics and Computer Science at Colorado College.

His research focuses on computational and applied algebraic geometry. He uses and develops methods from algebra, discrete mathematics, and symbolic computation to understand and solve problems in industrial and applied mathematics. His research has been focused on addressing problems arising in biology, geometric modeling, physics, and statistics.

His professional activities are motivated by the need to increase the number of underrepresented students that pursue advanced degrees in mathematics and the sciences. He is an active member of the Society for Advancement of Chicanos/Hispanics and Native Americans in Science and The National Alliance for Doctoral Studies in the Mathematical Sciences. He has directed undergraduate research projects for 20 years, involving close to 100 undergraduate students in his work.

Selected publications:

  • Arithmetical structures on bidents. Discrete Mathematics, with Kassie Archer, Abigail Bishop, Alexander Diaz-Lopez, Darren Glass, and Joel Lowsma, Volume 343, Issue 7, July 2020, 111850.

  • Gröbner bases of neural ideals, with Rebecca Garcia, Ryan Kruse, Jessica Liu, Dane Miyata, Ethan Petersen, Kaitlyn Phillipson, and Anne Shiu, International Journal of Algebra and Computation. Vol. 28, No. 04, pp. 553–571 (2018).

  • Hybrid schemes for exact conditional inference in discrete exponential families, with D. Kahle and R. Yoshida, Ann. Inst. Stat. Math. 70, 983–1011 (2018).

  • An algebra-based method for inferring gene regulatory networks, with P. Vera-Licona, A. Jarrah, et al., BMC Syst. Biol. 8, 37 (2014).

  • Toric degenerations of Bézier patches, with Frank Sottile and Chungang Zhu, ACM Transactions on Graphics, Volume 30, Issue 5, October 2011, Article No. 110, pp 1-10.


      user Dr. Beth Malmskog
Ph.D., Colorado State University, 2011
M.S., Colorado State University, 2007
B.S., University of Wyoming, 2002

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Beth Malmskog is an Assistant Professor of Mathematics at Colorado College. She works in algebra, number theory, arithmetic geometry, coding theory, and applied discrete mathematics, including applications of graph theory to cognitive science and fair redistricting.

Selected publications:

  • A graph-theoretic approach to identifying acoustic cues for speech sound categorization, with Anne Marie Crinnion and Joseph Toscano, Psychonomic Bulletin and Review, published online July 15, 2020, print to follow.

  • The de Rham Cohomology of the Suzuki Curves C jn, with R. Pries and C. Weir, Arithmetic geometry: Computation and Applications. Contemporary Mathematics Series, AMS Publishing, 2019, pp.105--120.

  • What (quilting) circles can be squared?, with K. Haymaker, Mathematics Magazine 92 (3) (2019), 173--186.

  • Locally recoverable codes with availability t≥2 from fiber products of curves, with K. Haymaker and G. Matthews, Advances in Mathematics of Communication 12 (2) (2018), 317--336.

  • Picard curves over Q with good reduction away from 3, with C. Rasmussen, LMS Journal of Computation and Mathematics 19 (2016), 382--408.

  • The a-numbers of Jacobians of Suzuki Curves, with H. Freilander, D. Garton, R. Pries, and C. Weir, Proceedings of the American Mathematical Society 141 (2013), 3019–-3028.

  • The Automorphism Groups of a Family of Maximal Curves, with R. Guralnick and R. Pries, and C. Weir, Journal of Algebra 361 (2012), 92--106.


      user Dr. Zak Mesyan
Ph.D., University of California, Berkeley, 2006
Sc.B., Brown University, 2001

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Dr. Mesyan is a professor at the University of Colorado at Colorado Springs. He is a ring theorist by training, but enjoys working with all sorts of algebraic objects, including semigroups, groups, modules, and categories. Much of his recent work focuses on infinite-dimensional linear algebra, topological algebra, and Leavitt path algebras.

Selected publications:

  • Infinite-dimensional triangularizable algebras, Forum Math. 31 (2019), 19--33.

  • Realizing posets as prime spectra of Leavitt path algebrass, with G. Abrams, G. Aranda Pino, and C. Smith, J. Algebra 476 (2017), 267--296.

  • Infinite-dimensional diagonalization and semisimplicity, with M. C. Iovanov and M. L. Reyes, Israel J. Math. 215 (2016), 801--855 .

  • Topological graph inverse semigroups, with J. D. Mitchell, M. Morayne, and Y. Peresse, Topol. Appl. 208 (2016), 106--126.

  • Polynomials of small degree evaluated on matrices, Lin. Multilin. Alg. 61 (2013), 1487--1495.

  • Conjugation of injections by permutations, Semigroup Forum 81 (2010), 297--324.

  • Endomorphism rings generated using small numbers of elements, Bull. London Math. Soc.39 (2007), 290--300.

  • Commutator rings, Bull. Austral. Math. Soc. 74 (2006), 279--288.




      user Dr. Greg Oman
Ph.D., Ohio State, 2006
B.A., Ohio State, 1998
                                                                       
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Publications


Dr. Oman is an associate professor at the University of Colorado at Colorado Springs. His research interests include algebra, logic, and problem-posing. Dr. Oman has directed several Ph.D. dissertations and Masters theses, and he has directed multiple undergraduate research projects, several of which have culminated in published results.

Selected publications:

  • Elementarily lambda-homogeneous binary functions, Algebra Universalis 78 2017, no. 2, 147--157.

  • Factorization theory of root closed monoids of small rank, with Jim Coykendall, Communications in Algebra 45 (2017), no. 7, 2795--2808.

  • Turning automatic continuity around: automatic homomorphisms, with Ryan Berndt, Real Analysis Exchange 41 (2016), no. 2, 271--286.

  • Divisible multiplicative groups of fields, Journal of Algebra 453 (2016), 177--188.

  • A note on strongly Jonsson binary relational structures, Algebra Universalis 73 (2015), no. 1, 97--101.

  • Strongly Jonsson and strongly HS modules, Journal of Pure and Applied Algebra 218 (2014), no. 8, 1385--1399.

  • On modules whose proper homomorphic images are of smaller cardinality, with Adam Salminen, Canadian Mathematical Bulletin 55 (2012), no. 2, 378--389.

  • On the axiom of union, Archive for Mathematical Logic 49 (2010), no. 3, 283--289.


      user Dr. K.M. Rangaswamy
 
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Dr. Rangaswamy is a professor emeritus at the University of Colorado at Colorado Springs. His research interests include abelian groups, associative rings, and modules.

Selected publications:

  • Chains of semiprime and prime ideals in Leavitt Path Algebras, with B. Greenfeld, Z. Mesyan, and K.M. Rangaswamy, Advances in Rings and Modules, Contemporary Mathematics Series vol. 715, American Mathematical Society (2018), pp. 1--16.

  • The multiplicative ideal theory of Leavitt path algebras, J. Algebra 487 (2017), 173--199.

  • On intersections of two-sided ideals of Leavitt path algebras, with S. Esin and M. Kanuni, J. Pure Appl. Algebra 221 (2017), no. 3, 632--644.

  • On simple modules over Leavitt path algebras, J. Algebra 423 (2015), 239--258.

  • Finitely presented simple modules over Leavitt path algebras, with P. Ara, J. Algebra 417, (2014), 333–--52.




      user Dr. Mike Siddoway
Ph.D., Tulane University, 1988
M.S., Tulane University, 1985
B.S., University of Notre Dame, 1979

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A member of the Mathematics faculty at Colorado College since 1988, Dr. Siddoway's research interests are in commutative algebra, module theory, and history of mathematics. Soon after arriving at Colorado College, Mike’s affinity for liberal arts teaching was affirmed when he received a National Science Foundation grant to create a young scholars workshop that engaged high school students with Great Problems, as a means to acquaint them with opportunities and habits of inquiry in Mathematics. Working together with colleague Reinhard Laubenbacher, Mike was an innovator in the use of primary sources from the history of mathematics to motivate interest and understanding of mathematics by young students, with emphasis on those from groups underrepresented in STEM fields. He also related materials to teaching of the History of Mathematics capstone course at Montana State University, during his 2018--2019 sabbatical leave.

Selected publications:

  • Gauss’ lemma and valuation theory, with P.N. Ánh, Quaestiones Mathematicae, 2020, in press.

  • Divisibility theory of arithmetical rings with one minimal prime ideal, with P.N. Ánh, Communications in Algebra 44 (2) (2016), 823--836.

  • Divisibility theory of semi-hereditary rings, with P.N. Ánh, Proc. Amer. Math. Soc. 138 (2010), 4231--4242.

  • On endomorphism rings of modules over henselian rings, Communications in Algebra 18 (5) (1990), 4231--4242.


      user Dr. Mark Tomforde
Ph.D., Dartmouth College, 2002
M.A., Dartmouth College, 1999
B.A., Gustavus Adolphus College, 1997
                                                                       
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Publications


Dr. Tomforde is an associate professor at the University of Colorado at Colorado Springs. He has been the recipient of research grants from the NSF, NSA, and Simons Foundation. He has also supervised an NSF postdoc and served as thesis advisor to multiple Ph.D. and Masters students, as well as supervised over two dozen undergraduate research projects. Dr. Tomforde's research is in the areas of Functional Analysis and Algebra, and his research interests involve the study of Operator Algebras and C*-algebras, both of which heavily influenced by the theory of Rings and Algebras. Dr. Tomforde's specific interests include C*-algebras of graphs and dynamical systems, classification of C*-algebras, Leavitt path algebras, symbolic dynamics, and the use of algebraic techniques in the study of operator algebras.

Dr. Tomforde's teaching and outreach efforts have been recognized in several ways. He was a 2020 recipient of the Haimo Award (the highest teaching honor bestowed by the MAA), and he created and ran an outreach program, called CHAMP, that won the 2018 AMS Award for Mathematics Programs that Make a Difference and the Phi Beta Kappa Arts and Sciences Award for "innovative efforts to engage broad and diverse audiences with the arts, humanities, social sciences, natural sciences, or mathematics."

Selected publications:

  • Naimark's problem for graph algebras, with Nishant Suri, Illinois J. Math, Illinois J. Math 61 (2017), 479--495.

  • K-theory for Leavitt path algebras: computation and classification, with James Gabe, Efren Ruiz, and Tristan Whalen, J. Algebra 433 (2015), 35--72.

  • Isomorphism and Morita equivalence of graph algebras, with Gene Abrams, Trans. Amer. Math. Soc. 363 (2011), 3733--3767.

  • Uniqueness theorems and ideal structure for Leavitt path algebras, J. Algebra 318 (2007), 270--299.

  • Topological quivers, with Paul S. Muhly, Internat. J. Math. 16 (2005), 693--756.

  • The C*-algebras of arbitrary graphs, with Doug Drinen, Rocky Mountain J. Math. 35 (2005), 105--135.

  • A unified approach to Exel-Laca algebras and C*-algebras associated to graphs, J. Operator Theory 50 (2003), 345--368.