Successful Dissertation on Real Algebraic Geometry for Physics and Optimization

We congratulate Dmitrii Pavlov on the successful defense of his thesis: „Real Algebraic Geometry for Physics and Optimization“! His next career step takes him to TU Dresden. Heartfelt congratulations!

In his research, Dmitrii investigates how methods of real algebraic geometry can be applied to problems in physics and optimization: 

“Algebraic geometry studies geometric objects defined by polynomial equations. Classical algebraic geometry was developed over complex numbers, and it’s methods work best in this setting. However, for real life applications this is sometimes a little too abstract, since they often provide geometric objects defined by polynomial equations over real numbers. Such objects are studied by real algebraic geometry.”

Dmitrii describes his thesis as follows: “In my thesis, I considered a range of problems from quantum information, particle scattering and algebraic optimization, and studied the geometric objects related to them. These include varieties defining quantum graphical models, Grassmann polytopes, and semialgebraic sets arising in regularization methods for linear and semidefinite programming. Apart from their connections to applications, these geometric objects are interesting in their own right. Their properties were studied using methods from computational algebraic geometry and combinatorics. This provides a new point of view on the problems that have not been studied algebraically before.“

Before Dmitrii Pavlov joined the MPI, he studied mathematics and mechanics at Moscow State University. At our institute, he completed his PhD under the supervision of Bernd Sturmfels and Simon Telen. Dmitrii will now join the "Real Algebraic Geometry" group of Jun.-Prof. Dr. Mario Kummer at TU Dresden as a postdoc.