Name | : | Clare D'Cruz |
Position | : | Professor |
Address | : | Chennai Mathematical Institute |
92, G. N. Chetty Road | ||
Chennai 600 017, India. | ||
: | clare@smi.ernet.in | |
Thesis Advisor | : | J. K. Verma |
Education:
Ph.D | 1998 | Indian Institute of Technology, | Mumbai, India. |
M. Sc | 1991 | Indian Institute of Technology, | Mumbai, India. |
B.Sc | 1989 | St. Xaviers College , | Mumbai, India. |
Professional Experience:
Fellow | 1999- | Chennai Mathematical Institute, | Chennai, India. |
Visiting Scholar | 1997-1998 | Northeastern University, | Boston, U.S.A. |
Visiting Fellow | 1996-1998 | Tata Institute of Fundamental Research, | Mumbai, India |
Teaching Experience: Macaulay-I, Refresher course on Groebner Basis, 1996University of Bombay. Differential Calculus
Differential Calculus, Northeastern University, U.S.A. 1997-1998.
Algebra-II, Chennai Mathematical Institute, January 1999.
Macaulay-II, Winter School on Algorithms in Invariant Theory and
Algebraic Geometry, Pune University, December 1999.
Algebra-II, Chennai Mathematical Institute, January 2000.Awards:
1989-1991 | N.B.H.M. Fellowship for M.Sc program in Mathematics. |
1991-1996 | N.B.H.M. Fellowship for Ph.D program in Mathematics. |
Research Interests:
Primary: Commutative Algebra
Secondary: Computational algebra, Algebraic Geometry
Other Interests: Drawing, Painting, Swimming.
Computer Knowledge:
C programming, Unix
Macaulay 2, A package for Commutative Algebra and Algebraic Geometry.
Publications:
1. Cohen-Macaulay fiber Cones Commutative Algebra, Algebraic Geometry
and Computational Methods (Hanoi 1996) Spinger-Verlag, (1999),
233-246 (with J. K. Verma and K. N. Raghavan).
2. Multigraded Rees algebras of $m$-primary ideals in rings of dimension
greater than one Journal of Pure and Applied algebra (to appear).
3. Quadratic transform of complete ideals in regular local rings
Comm. Algebra 28 (2000), 693-698.
4. On the number of generators of Cohen-Macaulay ideals Proc. Amer. Math.
Soc. (to appear)
(with J. Verma).
5. Multigraded extended Rees algebras of $m$-primary ideals with minimal
multiplicity Nagoya Journal (to appear).
6. High order vanishing ideals at $n+3$ points of ${\mathbf P}^n$ Proc.
Buchsbaum Conference, Catania (to appear) (with A. Iarrobino) .
7. A formula for the multiplicity if the multigraded extended Rees algebra,
Comm. Algebra (to appear).
Talks and Conferences Attended:
1. Cohen-Macaulay Rees algebras and fiber cones with minimal multiplicity,
T.I.F.R., Bombay (October 1996).
2. Cohen-Macaulay Fibers, I.I.T. , Bombay, March 1997.
3. Rees algebras with minimal multiplicity, Midwest Algebraic Conference,
University of Norte Dame , Norte Dame, USA, November 1997.
4. Complete ideals in regular local rings, Northeastern University ,
U.S.A. , January 1998.
5. Cohen-Macaulay fiber cones, University of Kansas , Kansas, USA, May 1998.
6. Cohen-Macaulay fiber cones, Purdue University , USA, May 1998.
7. On the number of generators of Cohen-Macaulay ideals, Chennai Mathematical
Institute, Chennai, July 1998.
8. Complete ideals in regular local rings, Institute of Mathematical Sciences,
Madras, July 1998.
9. Hoskin-Deligne formula for complete ideals in regular local rings,
Second National Conference on Commutative Algebra and Algebraic Geometry,
Metha Research Institute , March 1999.
10. Complete ideals in regular local rings, Mehta Research Institute ,
Allahabad, September 1999.
11. Complete monomial ideals, Trends in Commutative Algebra,
I.I.T.-Bombay, January 2000.