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Vikram SharmaEmail:
vikram at imsc dot res dot in |
Research Interests
- Computational Algebra
- Numerical Analysis
- Symbolic-Numeric Computation
Publications
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Thesis: Complexity Analysis of Algorithms in Algebraic Computation
Advisor: Prof. Chee Yap - Robust Approximate Zeros, with Zilin Du and Chee Yap. Appeared in ESA'05.
- Amortized Bound for Root Isolation Via Sturm Sequences, with Zilin Du and Chee Yap. Appeared in SNC'05.
- Almost Tight Recursion Tree Bounds for the Descartes Method, with Arno Eigenwillig and Chee Yap. Appeared in ISSAC 2006.
- Robust Approximate Zeros in Banach Space. Appeared in Mathematics in Computer Science.
- Complexity of Real Root Isolation Using Continued Fractions. Appeared in ISSAC 2007. Definitive version appears here in Theoretical Computer Science (TCS).
- Bounds on Absolute Positiveness of Multivariate Polynomials, with Prashant Batra. Published in JSC 2010.
- Robust Geometric Computation, with Chee Yap. Encyclopedia of Algorithms, 2008.
- Applications of Dimensionality Reduction and Exponential Sums to Graph Automorphism, with Madhusudan Manjunath. Theoretical Computer Science, 2011..
- Isotopic Arrangement of Simple Curves: an Exact Numerical Approach based on Subdivision, with Gert Vegter and Chee Yap. 2012.
- Near Optimal Tree Size Bounds on a Simple Real Root Isolation Algorithm, with Chee Yap. In ISSAC, 2012
- Towards Exact Numerical Voronoi Diagrams, with Chee Yap and Jyh-Ming Lien. In International Symposium on Voronoi Diagrams (ISVD), 2012.
- Analytic Root Clustering: A Complete Algorithm using Soft Zero Tests, with Chee Yap and M. Sagraloff. Invited paper, special session Computational Complexity in the Continuous Computability in Europe (CiE2013), Milan, Italy, 2013.
Recent Positions
Nov. 2006 - Oct. 2007: Postdoc in GALAAD, INRIA, Sophia Antipolis.
Nov. 2007 - Oct. 2009: Postdoc in Algorithms and Complexity Group, MPII, Saarbruecken, Germany.
Education
- August 2001 - Oct. 2006
Ph. D. student in Computer Science at New York University, New York, USA. Thesis Advisor: Prof. Chee Yap. - August 1997 - May 2001
B.Tech. in Computer Science and Engineering from IT-BHU, Varanasi.