Home /  Stochastic Quantization (SLMath)

Summer Graduate School

Stochastic Quantization (SLMath) July 01, 2024 - July 12, 2024
Parent Program: --
Location: SLMath: Eisenbud Auditorium
Organizers Massimiliano Gubinelli (University of Oxford), Martina Hofmanova (Universität Bielefeld), LEAD Hao Shen (University of Wisconsin-Madison), Lorenzo Zambotti (Sorbonne Université)
Lecturer(s)

Show List of Lecturers

Teaching Assistants(s)

Show List of Teaching Assistants

Description
Wordcloud

This summer school will familiarize students with the basic problems of the mathematical theory of Euclidean quantum fields. The lectures will introduce some of its prominent models and analyze them via the so called “stochastic quantization” methods, involving recently developed stochastic and PDE techniques. This is an area which is highly interdisciplinary combining ideas ranging from the theory of partial differential equations, to stochastic analysis, to mathematical physics. Our goal is to bring together students who are perhaps familiar with some but not all of these subjects and teach them how to integrate these different tools to solve cutting-edge problems of Euclidean quantum field theory.

School Structure

The organizers plan to introduce gradually the basic tools and ideas needed in this area of research, which will cover at least the first 3/4 of the school.  The remaining time will be left to discuss other models and more recent developments. There will be two or three lectures per day, 1.5 hours each, plus one or two 1.5 hours long TA/problem session.

Bibliography

Prerequisites

A basic knowledge of finite-dimensional probability and of Brownian motion (without stochastic calculus), of basic functional analysis and basic PDE theory: linear equations, Fourier transform, Sobolev spaces on R^d. This the ideal background but it is not strictly necessary: we are well aware that the participants will come from a wide range of knowledge and abilities, so we will work to bring them to a common ground. A few weeks before the school we plan to assign recommended readings that would help the participants get better prepared, for instance, reading material along the line of Section 2.2.1 and 2.3.1 of “Partial Differential Equations” by Evans, and Chapter 2 of “Stochastic Differential Equations: An Introduction with Applications” by Oksendal.

Recommended Readings

For eligibility and how to apply, see the Summer Graduate Schools homepage.

Keywords and Mathematics Subject Classification (MSC)
Tags/Keywords
  • Euclidean quantum field theory

  • stochastic (partial) differential equations

  • paracontrolled distributions

  • a priori estimates

  • renormalization theory

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Funding & Logistics Show All Collapse

Show Directions to Venue

Show Visa/Immigration

Schedule, Notes/Handouts & Videos
Show Schedule, Notes/Handouts & Videos
Show All Collapse
Jul 01, 2024
Monday
09:15 AM - 09:30 AM
  Introduction to SLMath
09:30 AM - 10:45 AM
  Lecture 1
10:45 AM - 11:15 AM
  Break
11:15 AM - 12:30 PM
  Lecture 2
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  TA Session
03:00 PM - 03:30 PM
  Afternoon Tea
03:30 PM - 04:30 PM
  TA Session
04:30 PM - 04:45 PM
  Group Photo
Jul 02, 2024
Tuesday
09:30 AM - 10:45 AM
  Lecture 1
10:45 AM - 11:15 AM
  Break
11:15 AM - 12:30 PM
  Lecture 2
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  TA Session
03:00 PM - 03:30 PM
  Afternoon Tea
03:30 PM - 04:30 PM
  TA Session
Jul 03, 2024
Wednesday
09:30 AM - 10:45 AM
  Lecture 1
10:45 AM - 11:15 AM
  Break
11:30 AM - 02:00 PM
  Picnic Lunch
02:00 PM - 03:15 PM
  Lecture 2
03:15 PM - 03:45 PM
  Afternoon Tea
03:45 PM - 04:45 PM
  TA Session
Jul 04, 2024
Thursday
All Day
  SLMath Closed
Jul 05, 2024
Friday
09:30 AM - 10:45 AM
  Lecture 1
10:45 AM - 11:15 AM
  Break
11:15 AM - 12:30 PM
  Lecture 2
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  TA Session
03:00 PM - 03:30 PM
  Afternoon Tea
03:30 PM - 04:30 PM
  TA Session
Jul 08, 2024
Monday
09:30 AM - 10:45 AM
  Lecture 1
10:45 AM - 11:15 AM
  Break
11:15 AM - 12:30 PM
  Lecture 2
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  TA Session
03:00 PM - 03:30 PM
  Afternoon Tea
03:30 PM - 04:30 PM
  TA Session
Jul 09, 2024
Tuesday
09:30 AM - 10:45 AM
  Lecture 1
10:45 AM - 11:15 AM
  Break
11:15 AM - 12:30 PM
  Lecture 2
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  TA Session
03:00 PM - 03:30 PM
  Afternoon Tea
03:30 PM - 04:30 PM
  TA Session
Jul 10, 2024
Wednesday
09:30 AM - 10:45 AM
  Lecture 1
10:45 AM - 11:15 AM
  Break
11:15 AM - 12:30 PM
  Lecture 2
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  TA Session
03:00 PM - 03:30 PM
  Afternoon Tea
03:30 PM - 04:30 PM
  TA Session
Jul 11, 2024
Thursday
09:30 AM - 10:45 AM
  Lecture 1
10:45 AM - 11:15 AM
  Break
11:15 AM - 12:30 PM
  Lecture 2
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  TA Session
03:00 PM - 03:30 PM
  Afternoon Tea
03:30 PM - 04:30 PM
  TA Session
Jul 12, 2024
Friday
09:30 AM - 10:45 AM
  Lecture 1
10:45 AM - 11:15 AM
  Break
11:15 AM - 12:30 PM
  Lecture 2
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Participant Survey
03:00 PM - 03:30 PM
  Afternoon Tea
03:30 PM - 04:00 PM
  TA Session or Free Discussion