I am currently a PhD student. My supervisors are Vincent Cossart (University of Versailles) and Mohab Safey El Din (PolSys Team (formerly SALSA team), INRIA/LIP6/University of Paris 6). I work on solving the global optimization problem for polynomials. To this end, I use several approaches, including both numerical methods and computer algebra.

Software

EXAGON (EXact Algebraic Global OptimizatioN): Maple library for solving exact algebraic global optimization problem. Note that the FGb package is required.
Standard Release [tar.gz] (library and documentation, requires FGb)
Some examples [.mpl]

Research

Journal Papers

• Global Optimization of Polynomials Restricted to a Smooth Variety Using Sums of Squares
  A. Greuet, F. Guo, M. Safey El Din, L. Zhi
  Journal of Symbolic Computation 47 (2012), no. 5, 503-518
  Preliminary version [pdf]
  Final version [DOI link]
  BibTeX file

Articles in conference proceedings

• Deciding reachability of the infimum of a multivariate polynomial
  Aurélien Greuet, Mohab Safey El Din.
  Proceedings of the International Symposium on Symbolic and Algebraic Computation 2011 (ISSAC 2011).
  Preliminary version [pdf]
  Final version [DOI link]
  BibTeX file

Communications in international conferences

• Deciding reachability of the infimum of a multivariate polynomial
  Aurélien Greuet, Mohab Safey El Din.
  International Symposium on Symbolic and Algebraic Computation 2011
  San Jose, California. 06/11, 2011
  

Short-term visits

• December 2010:
  Mathematics Mechanization Research Center, Institute of Systems Science
  Chinese Academy of Sciences, Beijing, China.
  Supported by ANR/NSFC EXACTA Project.

Talks in workshops

• Polar Varieties and Global Optimisation Problem
  Fields Institute Workshop on Hybrid Methodologies for Symbolic-Numeric Computation (Website)
  Invited as young researcher
  Waterloo, Canada, 11/19, 2011.
  
• Exact Polynomial Optimization: Algorithms, Complexity and Implementation
  Asian Symposium on Computer Mathematics (Website)
  Invited speaker
  Beijing, China, 10/27, 2012.
  

Talks in seminars

• Constrained optimization of polynomials using polar varieties and sums of squares
  Seminar of the Academy of Mathematics and Systems Science (Chinese Academy of Sciences)
  Beijing 12/23, 2010.
  
• Polar varieties and optimization
  Team Algorithm Seminar
  INRIA Paris/Rocquencourt 01/31 (France), 2011.
• Deciding the reachability of an infimum of a multivariate polynomial
  Team SALSA Seminar
  LIP6/UPMC/INRIA 02/11 (France), 2011.
• Solving optimisation problems using polar varieties
  Seminar on Algebra and Geometry
  University of Versailles (France) 04/05, 2011.
• Using Polar varieties for solving optimization problems
  Seminar on Computer Algebra
  University of Limoges (France) 10/13, 2011.

Teaching

I am teaching assistant ("moniteur") at the University of Versailles.

• Fall 2010: Elementary Mathematics (Undergraduate);
• Fall 2011: Elementary Mathematics (Undergraduate);
• Fall 2011: Effective Algebra (M.Sc).
• Fall 2012: Computer Algebra and Numerical Algorithms (Undergraduate).
• Spring 2012: Groups and Geometry (Undergraduate).

I have contributed to MathC2+, a project of popularization of mathematics and computer science for highschool students. My course notes (in French):

• An introduction to the computer algebra system Sage
• Symmetric-key cryptography and cryptanalysis. Key exchange using elliptic curves.
• Sage source code corresponding to the course on cryptography. To import it in Sage:
  • on a mac or linux machine, if the file is in the folder /home/user/, it can be imported in Sage using "attach(/home/user/mathc2+_code.sage)".
  • On a windows machine, a shared folder must be mounted following http://wiki.sagemath.org/. Then it can be imported using "attach(/media/sf_<shared folder name>/mathc2+_code.sage)").

Software

Soon...

Resume

A short resume.