# 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.

MARCH 1, 1992 BIRTH
ITALIAN NATIONALITY
ITALIAN (NATIVE), ENGLISH (FLUENT), GERMAN (BEGINNER) LANGUAGE

## 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

September 2018 - today

### SAMBa PhD student

#### University of Bath

United Kingdom, Bath

September 2017 - Septermber 2018

### MASDOC PhD student

#### University of Warwick

United Kingdom, Coventry

September 2014 - March 2017

### Master's Degree in Mathematics with honours

#### University of Pisa

Italy, Pisa

September 2011 - September 2014

### Bachelor's Degree in Mathematics with honours

#### University of Perugia

Italy, Perugia

March 2014 - August 2014

### Erasmus Exchange Program

#### Technische Universität Berlin

Germany, Berlin

September 2006 - July 2011

### High School Diploma

#### Liceo Scientifico "Italo Calvino"

Italy, Città della Pieve

## Skills

### CODING SKILLS

C#
Python
C/C++
Intermediate
MATLAB, R
Lower Intermediate

### OTHER COMPUTER RELATED SKILLS

Latex
70%
OpenOffice/Office
55%
Visual Studio
40%
Git & GitHub
25%

## Research Experiences, Talks and Publications

CEMRACS 2017

Marseille, France
Jul to Aug 2017

Summer school "Numerical methods for stochastic models: control, uncertainty quantification, mean-field": development and simulation of biological models for the behaviour of the human brain. Available online.
SRQ 2018

Cambridge, UK
Sept to Dec 2018

Invited participant to the research intensive event “Scaling limits, Rough paths, Quantum field theory” (SRQ) at the Isaac Newton Institute in Cambridge.
Master's Degree Thesis Presentation

Pisa, Italy
15 Feb 2017

Presentation of a mean-field model for the behaviour of large networks of neurons; discussion of its limit behaviour and of the implications of the theory. Based on two works by Delarue, Inglis, Rubenthaler and Tanré (first and second).
Network of interacting neurons with random synaptic weights
Publication
Available online: press here to view it.
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.