Department of Mathematics
University of Kansas
Office: 502 Snow Hall
Phone: 785-864-5180
email: mandal@math.ku.edu

Satya Mandal

Update (August 2015)

My research interest has shifted to Higher Algebraic K-theory and related topics (namely, Grothendieck Witt theory and Witt theory).
Other than that, instead of working on affine schemes (commutative rings), I consider wider variety of algebraic objects (schemes).
Some of the information below would be out dated. However, I would be building on my expertize in the following.

What would it take to get a PhD with Satya?

Following a short list of papers and books that will take you to the forefront of research:

  1. Mandal, Satya, Projective modules and complete intersections, Lecture Notes in Mathematics, 1672. Springer-Verlag, Berlin, 1997. viii+114 pp. ISBN: 3-540-63564-5

  2. Bhatwadekar, S.M., Sridharan, R.: The Euler class group of a Noetherian ring. Compos. Math. 122, 183-222 (2000)

  3. Mandal, Satya, Homotopy of sections of projective modules, Algebraic Geom. 1 (1992), no. 4, 639--646.

What kind of Research I do?

We will use the notation A for a commutative noetherian ring.

  1. At a basic level, I work on projective modules and minimal number of generators of ideals (and modules). Given an ideal I in A and an integer r ≥ 1, we ask whether there is a projective module P of rank r that maps onto I?

  2. At a slightly more sophisticated level, we work on a so called "Obstruction Theory". I will try to explain it, with some over simplification (i.e. hiding some of the details). We define obstructions groups E(A). Given a projective A-module P, we define an obstruction class e(P ) in E(A). For an ideal I, we also define a class [I] in E(A). We ask, if e(P )= [I], whether P maps on to I and conversely?

  3. There is a parallel theory of obstructions that is much more abstract and sophisticated. Among my projects is to try to reconcile these two theories.

  4. Most of what I do would be obvious when the ring is local. So, our rings are non-local.