Rajesh S. Kulkarni

Department of Mathematics
Michigan State University
Wells Hall
East Lansing, MI 48823

Contact information:

Phone: (517) 353-8145
Fax: (517) 432-1562
Email: kulkarni at math dot msu dot edu
Office: D303 Wells Hall


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

Students and Postdocs (mentored):


Manish Kumar (also mentored by Greg Pearlstein) (currently assistant professor at the Indian Statistical Institute, Bangalore, India)

Adam Chapman (current postdoc at MSU, working on Clifford algebras, central simple algebras and related topics)

Former students

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

Current students

Casey Machen (Ph.D. student working on generalizations of the Kuga-Satake construction)

Charlotte Ure (Ph.D. student working on essential dimension of forms of higher degree)

Undergraduate students

Brandon Alberts (Spring 2012-Spring 2013, currently a graduate student at the University of Wisconsin, Madison)

Jonathan Jonker (Spring 2012-Spring 2014, currently a graduate student at the University of Washington, Seattle)


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.

In November 2012, I gave a talk at the Banff International Research Station, Banff, Canada on Ulrich bundles and Clifford algebras. The talk is available on streaming video here.

Lecture Notes (available upon request)

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.

Topics in Brauer Groups: These are based on a Special Topics course I taught in Fall 2012. The goal was to introduce basic theory of central simple algebras and Brauer groups.


Spring Term 2015:

MATH 990: "Class Field Theory" . Ths class is based on J. S. Milne's excellent notes available here.

Web-pages for classes in previous semesters are available at

Past teaching

Kinawa MathCircle (Math Circle for middle school students)

I have been involved with the Kinawa MathCircle for over two years. Until last year, it was mostly run by Prof. Leszek Gawarecki (Kettering University). Since Fall 2014, I have been running the MathCircle with immense help from Mrs. Marian Murembya (6th grade teacher, Kinawa 5-6 School, Okemos), Ms. Kellie Stinson (an undergraduate student from MSU) and my colleague in the Math department Prof. Michael Shapiro. We meet on Mondays at Kinawa School 6:15PM-7:30PM. If you are interested, please come and join us! The handouts are available here and at Mrs. Murembya's class page at Kinawa School.