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A popular talk organized by Department of Mathematics, Indian Institute of Technology Jodhpur & Indian Women and Mathematics

Speaker: 
        Prof. Marie-Françoise Roy
 
Affiliation:
        University of Rennes, France
 
Date & Time :       
       12th February, 2020, 4:00 pm, LH 105, Lecture Hall Complex, IIT Jodhpur
 
Area of Research:
         Real algebraic geometry and complexity of algorithms in real algebraic geometry
Title of the Talk:
      Bernstein polynomials, computer-aided geometric design and real algebraic applications.
 
Abstract
Bernstein polynomials serve as the mathematical foundation for modern computer-aided geometric design (CAGD). Popular programs, like Adobe's Illustrator and Flash, and font imaging systems such as Postscript, utilize Bernstein polynomials to form what are known as Bézier curves. Introduced in the 1960's, Bézier curves were first implemented in automobile design but quickly gained popularity in other areas of CAGD with the expansion of the digital age. The Bernstein polynomials, however, came about long before the invention of computers and were introduced by the Russian mathematician, Sergei Natanovich Bernstein, as a means to prove the Weierstrass Approximation Theorem. These polynomials are currently widely used in approximation theory, probability, but also provide certificates of positivity in real algebraic geometry