Research

I have been working in algebra and ring theory, in particular with rings of operators, involutive rings, graded rings, Leavitt path algebras, clean rings, rings of quotients, torsion theories, rings with derivations, Baer *-rings, and finite von Neumann algebras.

Selected Presentations

• Porcupine-quotient and the fourth primary color, Oberwolfach Workshop "Combinatorial *-algebras", March 10 - 15, 2024.
• Algebras of graphs, Howard University, Washington, DC, October 20, 2023.
• Cleanness of Von-Neumann algebras and alike rings, Hefei University of Technology, Hefei, China, September 28, 2022.
• Cancellation properties of nonunital and graded rings. Presentations at the 35th Ohio State - Denison Mathematics Conference, Columbus, OH, May, 2022.
• Notes for the short course "Introduction to Graph Algebras and Attempts at their Classification" at CIMPA School "From Dynamics to Algebra and Representation Theory and Back", Universidade Federal de Santa Catarina, Florianopolis, Brazil, February 7 to 18, 2022.
• The Graded Classification Conjecture for graph algebras. Presentation at the Western Sydney University Abend Seminar, September 3, 2020 and Rings and Wings, U of Colorado, Colorado Springs Algebra Seminar, March 17, 2021.
  Video of the presentation
• Dimension groups with group action and their realization. Presentation at the Asia-Australia Algebra Conference, Western Sydney University, Australia, January 21 - 25, 2019.
• Algebaization of operator theory. Presentation at several universities in Australia and New Zealand, February - April, 2017.
• K-theory classification of graded ultramatricial *-algebras. Extended version of presentations at the 33nd Ohio State - Denison Mathematics Conference, Columbus, OH, May, 2016 and AMS Sectional Meeting, Bowdoin College, Brunswick ME, Sept 2016.
• Connecting Leavitt and C*-algebras via traces. Presentation at Classification of C*-algebras, flow equivalence of shift spaces, and graph and Leavitt path algebras, Lafayette, LA, May 11 - 15, 2015.
• Rings with dimension. Presentation at the AMS Sectional Meeting, University of Colorado, Boulder, CO, April 13 - 14, 2013.
• T.Y. Lam's impact on my work. Presentation at the 31st Ohio State - Denison Mathematics Conference, Columbus, OH, May 25 - 27, 2012.
• Almost clean rings. Presentation at Southern Regional Algebra Conference, Clayton State University, Morrow, GA, March 30 - April 1, 2012.
• Algebras of quotients of some Leavitt path algebras. Presentation at X Days of Ring Theory, Universitat Autonoma de Barcelona, Spain, April 2010.
• Cleanness of von-Neumann-algebra-like rings. Presentation at Noncommutative rings and their applications, Faculte Jean Perrin, Lens, France, June 29 - July 2, 2009.
• Von-Neumann-algebra-like rings. Presentation at the Joint Mathematics Meeting, Section on Noncommutative Algebra, Washington, DC, January 5 - 8, 2009.
• Total right and symmetric rings of quotients. Presentation at the Conference on Algebra and its Applications, Ohio University, Athens, OH, June 18 - 21, 2008.
• Derivations on rings and modules of quotients. Presentation at the International Conference on Ring and Module Theory, Hacettepe University, Ankara, Turkey, August 18 - 22, 2008.
• Conquering dimensions. Undergraduate Seminar presentation at Salem State College, Salem, MA April 24, 2012.