# Shroff, Piyush

Contact Information
Piyush Shroff, Ph.D.
Senior Lecturer â€‹Curriculum vitae Home page Office: Derrick 311 Email: prs31@txstate.edu Phone: 512.245.1931 Research Interest:
Cohomology of algebras, Deformation theory, Hopf algebras, Graph and Hypergraph |

Education:

- Ph.D. Texas A&M University, 2012
- M.S. University of Pune, 2007
- B.S. MES Abasaheb Garware College, 2005

I am interested in cohomology of algebras, deformation theory and Hopf algebras. In particular, I study finite generation of cohomology of algebras. The property of being finitely generated is very important because it is much easier to understand a finitely generated algebra. A finitely generated commutative algebra is useful for geometric study via algebraic geometry.

I am interested in studying deformation theory of algebras & modules, and Hopf algebras. Recently, I started to work in the area of graphs and hypergraphs.

**Selected Publications:**

- Hochschild Cohomology of Group Extensions of Quantum Symmetric Algebras (with Deepak Naidu and Sarah Witherspoon), Proc. Amer. Soc. 139 (2011), 1553-1567.
- Finite Generation of Cohomology of Quotients of PBW Algebras, J. Algebra 390 (2013), 44-55.
- Quantum Drinfeld Orbifold Algebras, Communications in Algebra 43 (2015), 1563-1570.
- PBW Deformations of Quantum Symmetric Algebras and their Group Extensions (with Sarah Witherspoon), J. Algebra and Its Applications 15 (2016), no. 3.
- A proof of the Matrix Tree Theorem via Stirling covers and cycle activation (with Ellen Robinson, Lucas Rusnak and Martin Schmidt), in preparation.