# Department of **Mathematics**

## Directory

## Adela Vraciu

Title: |
Assistant Chair Professor |

Department: |
Mathematics College of Arts and Sciences |

Email: |
vraciu@math.sc.edu |

Phone: |
803-777-4757 |

Office: |
LeConte 300C |

Office Hours: |
Tuesday and Thursday 1:00-2:30pm |

Resources: |

#### Education

Ph.D. in Mathematics, University of Michigan, June 2000

B.S. in Mathematics, University of Bucharest (Romania), June 1995

#### Experience

2017—present: Assistant Chair, Department of Mathematics, University of South Carolina

2014—present: Full Professor, University of South Carolina

2010—2014: Associate Professor, University of South Carolina

2003—2010: Assistant Professor, University of South Carolina

2000—2003: Visiting Assistant Professor, University of Kansas

#### 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

#### Research

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.

#### 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.