# Department of **Mathematics**

## Directory

## Adela Vraciu

Title: |
Professor |

Department: |
Mathematics College of Arts and Sciences |

Email: |
vraciu@math.sc.edu |

Office: |
LeConte 430 |

Office Hours: |
MWF 11:00am-12:00pm |

Resources: |

### Research Interests

My research is in Commutative Algebra. I have worked on problems related to tight closure and Hilbert-Kunz functions, which are phenomena specific to case of positive characteristic. Another area I have worked in is homological commutative algebra, specifically problems about existence of modules and ideals with special homological properties (in particular totally reflexive modules).

My research has been funded by the National Science Foundation and the National Security Agency.

### Education

- Ph.D. in Mathematics,
*University of Michigan*(2000) - B.S. in Mathematics,
*University of Bucharest, Romania*(1995)

### Experience

- Professor,
*University of South Carolina*(2014 – present) - Assistant Chair,
*Department of Mathematics, University of South Carolina*(2017 – 2022) - Associate Professor,
*University of South Carolina*(2010 – 2014) - Assistant Professor,
*University of South Carolina*(2003 – 2010) - Visiting Assistant Professor,
*University of Kansas*(2000 – 2003)

### Courses Taught

- MATH 122: Calculus for Business Administration and Social Sciences
- MATH 141: Calculus I
- MATH 142: Calculus II
- MATH 172: Mathematical Modeling for the Life Sciences
- MATH 300: Transition to Advanced Mathematics
- MATH 544: Linear Algebra
- MATH 546: Algebraic Structures I
- MATH 547: Algebraic Structures II
- MATH 580: Elementary Number Theory
- MATH 701: Algebra I
- MATH 702: Algebra II
- MATH 748: Topics in Commutative Algebra

### Selected Publications

- Totally reflexive modules over rings that are close to Gorenstein (with A. Kustin), Journal of Algebra, to appear.
- Poincare series of compressed level local Artinian rings with odd socle degree (with A. Kustin and L. M. Sega), Journal of Algebra 505 (2018), 383–419.
- On the existence of non-free totally reflexive modules (with J. Atkins), Journal of Commutative Algebra, to appear.
- An observation on generalized Hilbert-Kunz functions, Proceedings of the Amer. Math. Soc., 144 (2016), 3221–3229.
- On quasi-complete intersection ideals (with A. Kustin and L. Sega), Illinois Journal of Mathematics, 58 (2014), 867–889.