Vikram Sharma
Email:
vikram at imsc dot res dot in
Phone:
+91 44 2254 3312
Fax:
+91 44 2254 1586
Research Interests
Computational Algebra
Numerical Analysis
Symbolic-Numeric Computation
Publications
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..
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. Appeared in Computability in Europe (CiE2013), Milan, Italy, 2013.
Isotopic Arrangement of Simple Curves: an Exact Numerical Approach based on Subdivision
, with Jyh-Ming Lien, Gert Vegter and Chee Yap. Inl. Cong. on Mathematical Softwares (ICMS), Seoul, 2014.
Near Optimal Algorithms for Real Root Isolation
, with P. Batra, in ISSAC, 2015.
Journal version JSC, 2017.
Complexity Analysis of Root Clustering for a Complex Polynomial
, with R. Becker, M. Sagraloff, J. Xu, C. Yap in ISSAC, 2016.
A Lower Bound for Computing Lagrange's Real Root Bound
, with Swaroop N.P., in CASC, 2016.
Improved Bounds on Absolute Positiveness of Multivariate Polynomials
, with Swaroop N.P., ISSAC, 2017.
Journal version JSC, 2019.
Bounds on Distance to Variety in Terms of Coefficients of Bivariate Polynomials
, arxiv. 2017.
A Simple Near-Optimal Subdivision Algorithm for Complex Root Isolation based on Pellet Test and Newton Iteration
, with R. Becker, M. Sagraloff, C. Yap. JSC, 2018.
Complexity of a Root Clustering Algorithm
, with P. Batra, CCA, 2018.
Stronger Tradeoffs for Orthogonal Range Querying in the Semigroup Model
, with Swaroop N.P., FSTTCS, 2018.
Complexity of a root clustering algorithm
, with P. Batra, submitted. Complete version of the abstract appearing in CCA, 2018.
Generalizing The Davenport-Mahler-Mignotte Bound -- The Weighted Case
, ISSAC, 2020.
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.
Courses
Feb -- May 2010:
Algorithmic Geometry of Numbers
Aug -- Dec 2010:
Discrete Mathematics
Aug -- Dec 2011:
Discrete Mathematics
Jan -- May 2012:
Algorithms for Solving Polynomial Equations
Aug -- Dec 2012:
Discrete Mathematics
Jan -- May 2013: Algebraic and Probabilistic Tools and Techniques for Theoretical Computer Science.
Aug -- Dec 2013: Algebra and Computation.
Jan -- May 2014: Linear Programming and Combinatorial Optimization.
Sept -- Dec 2014:
Algorithms for Solving Polynomial Equations
Aug -- Dec 2015:
Linear Programming and Combinatorial Optimization
Aug -- Dec 2016: Discrete Mathematics.
Aug -- Dec 2018:
Discrete Mathematics.
Aug -- Sept 2019: Discrete Mathematics.
Aug -- Dec 2019:
Linear Programming and Combinatorial Optimization.