Paolo Grazieschi
SAMBa PhD Student at the University of Bath
Hello! I am a SAMBa PhD student at the University of Bath studying probability, SPDEs and interacting particle systems. My supervisor is Prof. Hendrik Weber. My PhD project concentrates on the study of the convergence of the three-dimensional Ising-Kac model to $\phi^4_3$: the Ising-Kac model, particularly, is a variant of the Ising model where particles have a long-range type interaction with a radius of interaction descreasing to $0$ in a non-trivial way; the $\phi^4_3$ equation, on the other hand, is formally described as $(\partial_t - \Delta) \phi = - \phi^3 + \xi$, with $\xi$ being space-time white noise, and its solution requires non-classical approaches.
My Specialities
Probability and Stochastic Analysis
My research is on Stochastic Partial Differential Equations (SPDEs) and convergence of interacting particle systems. On top of that, I have successfully completed graduate level courses on brownian motion, Itô calculus, mathematical statistics, mathematical finance and discrete probability.
The $\phi^4_3$ theory and the Ising-Kac model
A part of my PhD project is the understanding of the $\phi^4_3$ equation, the criticalities involved because of the low regularity of white noise and ultimetely how to make sense of that equation. This part leads to the Theory of Regularity Structures. The other part of my PhD project is proving convergence of the Ising-Kac particle system to the solution of that equation, which is also meaningful to understand the modeling properties of $\phi^4$ itself.
Stochastic particle Systems models of neuronal networks
At the end of my Master's Degree, under the supervision of Prof. Marco Romito (Università di Pisa), I concentrated on the study of biological stochastic models describing the human brain: particularly, the so called 'Integrate and Fire model' is at the heart of the mean-field theory developed by Delarue, Inglis, Rubenthaler and Tanré (here and here). After my graduation from Pisa, I then spent one month and a half at a Summer School in Marseille to develop variations of that model and to simulate them numerically.
Education
SAMBa PhD student
University of Bath
United Kingdom, Bath
MASDOC PhD student
University of Warwick
United Kingdom, Coventry
Master's Degree in Mathematics with honours
University of Pisa
Italy, Pisa
Bachelor's Degree in Mathematics with honours
University of Perugia
Italy, Perugia
Erasmus Exchange Program
Technische Universität Berlin
Germany, Berlin
High School Diploma
Liceo Scientifico "Italo Calvino"
Italy, Città della Pieve
Skills
CODING SKILLS
OTHER COMPUTER RELATED SKILLS
Research Experiences, Talks and Publications
In this this article possible modifications of a model for the human brain developed by Delarue, Inglis, Rubenthaler and Tanré are explored and their behaviour is simulated numerically.
Contact
4 West 2.15
Dept of Mathematical Sciences
University of Bath
Bath, BA2 7AY, United Kingdom
p [dot] grazieschi [at] bath.ac.uk