Research interests
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My area of research interest is in general noncommutative algebras.
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I study algebras using Hochschild cohomology and homological algebra. I am interested in understanding the Lie algebra structure on Hochschild cohomology of quiver algebras, especially quivers of tame and wild representations.
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I am also interested in Hopf algebra actions on other algebras and similar mathematical objects.
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A copy of my current research statement is available upon request. (Long version).
Preprints
- Bracket structure on Hochschild cohomology of Koszul quiver algebras using homotopy liftings.
ArXiv
- Actions of Drinfeld doubles of finite groups on Artin-Schelter regular algebras, (with
E. Kirkman, W.F. Moore), in preparation
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Invited talks
- Jan 3-6, 2024, Inner-faithful actions of the Drinfeld double of a finite group, JMM, special session on Homological techniques in noncommutative algebra" , San Francisco, CA.
- **May 5-7, 2023, Inner-faithful actions of the Drinfeld double of a finite group, AMS Spring sectional Meeting, special session on Artin Schelter regular algebras and related topics, California State University, Fresno, CA.
- April 15-16, 2023, Hochschild cohomology of Koszul quiver algebras and connections to deformation theory, AMS Spring sectional Meeting, special session on Interractions between Noncommutative Ring Theory and Algebraic and Algebraic geometry, University of Cincinnati, OH.
- October 22-23, 2022, Can the Drinfel'd double of a finite group be a reflection Hopf algebra, AMS Fall Sectional Meeting, special session on Interractions Between commutative algebra and nearby areas, University of Utah, Salt Lake city.
- *March 11-13, 2022, An algorithmic approach to the Gerstenhaber bracket structure on Hochschild cohomology, AMS Spring Southeastern Section Meeting, special session on Interractions Between Noncommutative Ring Theory and Algebraic Geometry, University of Virginia, Charlottesville.
- *January 5-8, 2022, An algorithmic approach to the Gerstenhaber bracket structure on Hochschild cohomology, Joint Mathematics Meeting, special session on Noncommutative algebra and noncommutative invariant theory, University of Washington, Seattle, Washington.
- November 20-21, 2021, Lie bracket structure on Hochschild cohomology of some twisted tensor products using homotopy lifting, AMS Section Meeting, special session on Geometric and algebraic aspects of quantum groups and related topics, University of South Alabama, Mobile Alabama.
- October 9-10, 2021, On the Hochschild cohomology of a family of quiver algebras, AMS Section Meeting, special session on Quiver representations: Bridging theory and applications, Creighton University, Omaha.
- March 31, 2021, On the Hochschild cohomology of a family of quiver algebras, Algebra and Number theory seminar, Texas Tech University.
- March 20-21, 2021,
Homotopy liftings and Hochschild cohomology of some twisted tensor products,
AMS Sectional Meetings, special session on Hopf algebras, tensor categories and related homological methods.
- January 9, 2021, Gerstenhaber bracket on Hochschild cohomology of Koszul algebras using homotopy liftings, Joint Mathematical Meetings, special session on interactions between non-commutative algebra and non-commutative algebraic geometry.
- January 7, 2021, Homotopy liftings and Hochschild cohomology of some twisted tensor products, Joint Mathematical Meetings, special session on commutative algebra meets representation theory.
- October 10, 2020,
What are DG algebras and DG coalgebras?
, AMS Gathering in Graduate Expository Mathematics (GIG'EM) Conference, Texas A&M University.
- June 27, 2020,
Lie algebra structure on Hochschild cohomology of associative algebras,
Early Commutative Algebra Researchers (eCARs) conference, Zoom online meeting.
- **April 25-26, 2020,
Lie structure on Hochschild cohomology of a family of quiver algebras,
URiCA KUMUNUjr Conference, University of Nebraska-Lincoln.
- November 2, 2019,
Cup product on Hochschild cohomology of a family of quiver algebras,
AMS Fall Sectional Meeting, special session on homological algebra, University of Florida, Gainesville.
