## Contact information:

Phone: (517) 353-8145

Fax: (517) 432-1562

Email: kulkarni at math dot msu dot edu

Office: D303 Wells Hall

## Research

My research is in noncommutative algebra and algebraic geometry. I use techniques from one of these areas to think about problems in another. I have worked on sheaves on noncommutative algebras called maximal orders on varieties (in particular, smooth projective surfaces).
In this program, we used geometry of the underlying surface to classify the sheaves of maximal orders.

More recently, I have studied Brauer groups of fields and also Ulrich bundles on smooth projective varieties. My work in both of these research areas is closely related to Clifford algebras and their representations.
My research has been partially supported by the NSF since 2002. Please click on the links below to see description my publications/preprints.

Preprints and Publications

## Former students

Emre Coskun (currently assistant professor at Middle Eastern technical University, Ankara, Turkey).

## Talks

In February 2000, I gave a talk at MSRI, Berkeley on my thesis as part of the conference Interactions between noncommutative algebra and algebraic geometry
. This talk is available on streaming video here . You will need a real player to see it.

## Lecture Notes

Algebraic Curves: These are based on the graduate course I taught in Fall 2005. The material was mostly based on Hartshorne's chapter IV. Some background material was included from Serre's local fields.
Commutative algebra and algebraic geometry: These are based on the graduate course I taught in Spring 2001. The material was gathered from various sources. The topics include standard commutative algebra for a first course along with faithful flat descent and applications of these topics to affine and projective algebraic geometry.

Algebraic geometry: These are based on the graduate course I taught in Fall 2001. They include standard material for a first course in algebraic geometry. The main source is Joe Harris' book, in particular the examples (and the exercises) in this book.

## Teaching

Fall Term 2012:

MATH 133 (Section 9-12 and 14-16): Calculus II (for students, the information is available on the ANGEL website)

** MATH 991: Special Topics course titled "Recent developments in Brauer groups" **

Web-pages for classes in previous semesters are unavailable.

Past teaching