Students joining SAMBa in 2020

###### Theodora Syntaka

Theodora completed the Undergraduate Program in Mathematics at the University of Ioannina in Greece, in 2018.

Funded by the Leverhulme Trust.

Theodora completed the Undergraduate Program in Mathematics at the University of Ioannina in Greece, in 2018. Then she graduated from the same department in Greece, with a Master’s degree in “Mathematics (Analysis-Algebra-Geometry)”, in 2020. Her Master’s project was in partial differential equations with the thesis’s title: “The Cauchy problem for the Navier-Stokes and Euler equations in three-dimensional space and the vanishing viscosity limit”. Outside of Mathematics, she enjoys listening to music, jogging, and drinking beer.

**Research project title:**

Justification of kinetic equations using graph structures

**Supervisor(s):**

Karsten Matthies

**Project description:**

The derivation of continuum equations from a discrete deterministic system of particles is of major interest. This is an area of research in mathematical physics originating from Hilbert’s Sixth Problem in 1900. This problem has been approached in two steps using the Boltzmann equation as a mesoscopic description. The first one is to derive kinetic equations, such as the Boltzmann equation, from a system of particles and the second is to derive continuum equations, such as Navier-Stokes and Euler equations, from the Boltzmann equation. Kinetic equations such as the Boltzmann equation are iconic because they illustrate the phenomenon that irreversible dynamics can be the result of reversible microscopic motion. My project focuses on developing a novel approach which combines tools from Probability theory and Analysis to systematically approximate the particle dynamics with simpler evolutions.