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Schedule, Notes/Handouts & Videos

Stochastic Quantization (SLMath) July 01, 2024 - July 12, 2024

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Jul 01, 2024
Monday
09:15 AM - 09:30 AM
  Introduction to SLMath
09:30 AM - 10:45 AM
  From quantum mechanics to measures
Hao Shen (University of Wisconsin-Madison), Lorenzo Zambotti (Sorbonne Université)
10:45 AM - 11:15 AM
  Break
11:15 AM - 12:30 PM
  Euclidean quantum field theory and Gaussian free field
Hao Shen (University of Wisconsin-Madison), Lorenzo Zambotti (Sorbonne Université)
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  TA Session: "Fourier analysis"
Sky Cao (Massachusetts Institute of Technology)
03:00 PM - 03:10 PM
  Group Photo
03:10 PM - 03:30 PM
  Afternoon Tea
03:30 PM - 04:30 PM
  TA Session: "Tightness of probability measures"
Evan Sorensen (Columbia University)
Jul 02, 2024
Tuesday
09:30 AM - 10:45 AM
  Langevin dynamic on finite lattice
Hao Shen (University of Wisconsin-Madison), Lorenzo Zambotti (Sorbonne Université)
10:45 AM - 11:15 AM
  Break
11:15 AM - 12:30 PM
  Stationary coupling, existence of infinite volume limit
Hao Shen (University of Wisconsin-Madison), Lorenzo Zambotti (Sorbonne Université)
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  TA Session: "Littlewood-Paley theory, Part I"
Sarah-Jean Meyer (University of Oxford)
03:00 PM - 03:30 PM
  Afternoon Tea
03:30 PM - 04:30 PM
  TA Session: "Hermite polynomials"
Sky Cao (Massachusetts Institute of Technology)
Jul 03, 2024
Wednesday
09:30 AM - 10:45 AM
  Convergence to equilibrium / uniqueness of infinite volume limit
Hao Shen (University of Wisconsin-Madison), Lorenzo Zambotti (Sorbonne Université)
10:45 AM - 11:15 AM
  Break
11:30 AM - 02:00 PM
  Lunch
02:00 PM - 03:15 PM
  Integration by parts, Wick theorem, Introduction to small scale limit
Hao Shen (University of Wisconsin-Madison), Lorenzo Zambotti (Sorbonne Université)
03:15 PM - 03:45 PM
  Afternoon Tea
03:45 PM - 04:45 PM
  TA Session: "Wiener chaos & practice with Wick’s theorem"
Evan Sorensen (Columbia University)
Jul 04, 2024
Thursday
All Day
  SLMath Closed
Jul 05, 2024
Friday
09:30 AM - 10:45 AM
  Small scale limit - probabilistic estimates
Hao Shen (University of Wisconsin-Madison), Lorenzo Zambotti (Sorbonne Université)
10:45 AM - 11:15 AM
  Break
11:15 AM - 12:30 PM
  Small scale limit - PDE estimates
Hao Shen (University of Wisconsin-Madison), Lorenzo Zambotti (Sorbonne Université)
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  TA Session: "Littlewood-Paley theory, Part II"
Sarah-Jean Meyer (University of Oxford)
03:00 PM - 03:30 PM
  Afternoon Tea
03:30 PM - 04:30 PM
  TA Session: "Estimates on some stochastic terms"
Evan Sorensen (Columbia University)
Jul 08, 2024
Monday
09:30 AM - 10:45 AM
  $\Phi^4_2$ without cutoffs, computations with stochastic terms (like the cube)
Massimiliano Gubinelli (University of Oxford)
10:45 AM - 11:15 AM
  Break
11:15 AM - 12:30 PM
  Perturbation theory for $\Phi^4_2$, Part I
Hao Shen (University of Wisconsin-Madison)
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  TA Session: "Paraproducts "
Sarah-Jean Meyer (University of Oxford)
03:00 PM - 03:30 PM
  Afternoon Tea
03:30 PM - 04:30 PM
  TA Session: "Weighted $L^p$ estimates for $\Phi^4_2$"
Sky Cao (Massachusetts Institute of Technology)
Jul 09, 2024
Tuesday
09:30 AM - 10:45 AM
  Perturbation theory for $\Phi^4_2$, Part II
Hao Shen (University of Wisconsin-Madison)
10:45 AM - 11:15 AM
  Break
11:15 AM - 12:30 PM
  $\Phi^4_3$, paracontrolled energy estimates
Massimiliano Gubinelli (University of Oxford)
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  TA Session: "Lattice Schauder estimates"
Sky Cao (Massachusetts Institute of Technology)
03:00 PM - 03:30 PM
  Afternoon Tea
03:30 PM - 04:30 PM
  TA Session: "Weighted Besov spaces"
Sarah-Jean Meyer (University of Oxford)
Jul 10, 2024
Wednesday
09:30 AM - 10:45 AM
  $\Phi^4_3$, the second renormalization and commutator lemmas
Massimiliano Gubinelli (University of Oxford)
10:45 AM - 11:15 AM
  Break
11:15 AM - 12:30 PM
  Subgaussian tails for $\Phi^4_2$
Hao Shen (University of Wisconsin-Madison)
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  TA Session: "Wavelet representation and the localization operators"
Sarah-Jean Meyer (University of Oxford)
03:00 PM - 03:30 PM
  Afternoon Tea
03:30 PM - 04:30 PM
  TA Session: "$L^\infty$ estimates and coming down from infinity for $\Phi^4_2$"
Sky Cao (Massachusetts Institute of Technology)
Jul 11, 2024
Thursday
09:30 AM - 10:45 AM
  The Abelian Higgs model in two dimensions, local theory
Hao Shen (University of Wisconsin-Madison)
10:45 AM - 11:15 AM
  Break
11:15 AM - 12:30 PM
  $\Phi^4_3$, tightness, infinite volume limit and some properties of the measure#
Massimiliano Gubinelli (University of Oxford)
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  TA Session: "The Abelian Higgs model in two dimensions, global theory"
Sky Cao (Massachusetts Institute of Technology)
03:00 PM - 03:30 PM
  Afternoon Tea
03:30 PM - 04:30 PM
  TA Session: "Approximate duality and commutator lemma"
Sarah-Jean Meyer (University of Oxford)
Jul 12, 2024
Friday
09:30 AM - 10:45 AM
  An invitation to nonabelian gauge theories
Hao Shen (University of Wisconsin-Madison)
10:45 AM - 11:15 AM
  Break
11:15 AM - 12:30 PM
  Stochastic estimates in $\Phi^4_3$
Massimiliano Gubinelli (University of Oxford)
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
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