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Recent talks:
-
Numerical Algebraic Geometry, A Macaulay 2 conference (Cornell University, Ithaca, New York), Mar 2008.
- Galois groups of
Schubert problems via Numerical Algebraic Geometry (Seattle,
Washington), Jan 2008.
- Numerical primary
decomposition, AMS meeting at DePaul University (Chicago,
Illinois), October 2007.
- Computing Monodromy via
Parallel Homotopy Continuation, PASCO 2007 (London, Ontario),
July 2007.
- Computing embedded solution
components via deflation, ACA 2007 (Auburn Hills, Michigan),
July 2007.
- Parallel computations of
Gröbner bases in the Weyl algebra (MSRI, Berkeley),
January 2007.
- Gröbner bases
computations in the Weyl algebra, Theoretical effectivity and
practical effectivity of Gröbner bases (Kyoto, Japan), January
2007.
- Interfacing with
the numerical homotopy algorithms in PHCpack, The second
International Congress of Mathematical Software, (Castro Urdiales,
Spain), August 2006.
Computer software:
- D-modules for Macaulay 2:
Algorithms in D-module theory (with Harry Tsai)
- PHCmaple: A Maple
interface to the numerical homotopy algorithms
- HoG:
Galois group computation of Schubert problems (with Frank
Sottile)
- SuperReduce: Parallel
computation of Grobner bases
Publications:
- Degree Bounds for
Gröbner
Bases in Algebras of Solvable Type, preprint (with Matthias
Aschenbrenner).
- Galois groups of
Schubert problems
via homotopy computation, preprint (with Frank Sottile).
- Numerical primary
decomposition, preprint.
- Computing Monodromy via
Parallel Homotopy Continuation, extended abstract for PASCO 2007.
(with Frank Sottile)
- Higher-order deflation for
polynomial systems with isolated singular solutions, The IMA
Volumes in Mathematics and its Applications, 146, 2008 (with Jan
Verschelde
and Ailing Zhao).
- Computing the support of local
cohomology modules, Journal of Symbolic
Computation, 41(12):1328–1344, 2006. (with Josep Alvarez
Montaner)
- Interfacing with
the numerical homotopy algorithms in PHCpack, Proceedings
of ICMS
2006,
LNCS 4151, pp. 354-360, 2006 (with Jan Verschelde).
- Parallel homotopy
algorithms to solve polynomial systems, Proceedings of ICMS
2006,
LNCS 4151, pp.225-234, 2006 (with Jan Verschelde and Yang Zhuang).
- Decomposing Solution Sets of
Polynomial Systems: A New Parallel Monodromy Breakup Algorithm, to
appear in Int. Journal of Comp.Science and Eng., (with Jan Verschelde)
- Newton's Method with
Deflation for Isolated Singularities of Polynomial Systems,
Theoretical Computer Science 359(1-3): 111-122, 2006. (with
Jan Verschelde
and Ailing Zhao)
- Anurag Singh and Uli Walther (edts.) 24 hours of
local cohomology: the Snowbird notes. Lecture notes from the
AMS-IAS-SIAM summer school in commutative algebra 2005 at Snowbird, UT.
Lectures by S. Iyengar, G. Leuschke, A. Leykin, C. Miller, E. Miller,
A. Singh and U. Walther; 2005. To appear in AMS “Graduate Studies in
Mathematics” series.
- Evaluation of Jacobian Matrices
for Newton's Method with Deflation to approximate Isolated Singular
Solutions of Polynomial Systems, In SNC 2005 Proceedings, pp.
19-28, 2005. (with Jan Verschelde and Ailing Zhao)
- Factoring Solution Sets of
Polynomial Systems in Parallel, Proceedings of the ICPP 2005
Workshops, High Performance Scientific and Engineering Computing, pp.
173-180, 2005. (with Jan Verschelde)
- PHCmaple: A Maple Interface
to the Numerical Homotopy Algorithms in PHCpack. In Proceedings of
ACA’2004, 2004. (with Jan Verschelde)
- On parallel computation of
Gröbner bases , Proceedings of ICPP'2004 workshops (2004)
- Algorithmic proofs of two
theorems of Stafford, Journal of Symbolic Computation,
38(6):1535–1550, 2004.
- D-modules for Macaulay 2,
Mathematical Software: ICMS 2002, World Scientific (2002), pp. 169-179.
- Computing local cohomology in
Macaulay 2, Lecture Notes in Pure and Applied Mathematics 226,
Marcel Dekker (2001).
- Constructibility of the Set
of Polynomials with a Fixed Bernstein-Sato Polynomial: an Algorithmic
Approach, Journal of Symbolic Computation 32, (2001), no. 6, pp.
663-675.
Thesis: Algorithms
in computational algebraic analysis (2003).
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