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Tokyo Probability Seminar
Seminar information archive ～05/24｜Next seminar｜Future seminars 05/25～
| Date, time & place | Monday 16:00 - 17:30 126Room #126 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Makiko Sasada, Shuta Nakajima, Masato Hoshino |
2025/04/14
16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Masato Hoshino (Science Tokyo)
On the proofs of BPHZ theorem and future progress
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Masato Hoshino (Science Tokyo)
On the proofs of BPHZ theorem and future progress
[ Abstract ]
Hairer’s theory of regularity structures (2014) provides a robust framework to guarantee the renormalizability of stochastic partial differential equations (SPDEs). This theory is established in several steps, among which the final and most technically involved step is the proof of the so-called "BPHZ theorem." There are two main approaches to this proof: a graph-theoretic approach developed by Chandra and Hairer (2016+), and a Malliavin calculus-based inductive approach introduced by Linares, Otto, Tempelmayr, and Tsatsoulis (2024). As for Gaussian noises, the latter is simpler and more inductive. While the language used by Otto and his coauthors is different from that of regularity structures, similar arguments have been formulated in the language of regularity structures by Hairer and Steele (2024) and Bailleul and Hoshino (2023+) by different approaches. In this talk, I will first give an overview of the theory of regularity structures, then compare the outlines of the proofs of BPHZ theorem. If time permits, I will also discuss some current researches and future problems.
Hairer’s theory of regularity structures (2014) provides a robust framework to guarantee the renormalizability of stochastic partial differential equations (SPDEs). This theory is established in several steps, among which the final and most technically involved step is the proof of the so-called "BPHZ theorem." There are two main approaches to this proof: a graph-theoretic approach developed by Chandra and Hairer (2016+), and a Malliavin calculus-based inductive approach introduced by Linares, Otto, Tempelmayr, and Tsatsoulis (2024). As for Gaussian noises, the latter is simpler and more inductive. While the language used by Otto and his coauthors is different from that of regularity structures, similar arguments have been formulated in the language of regularity structures by Hairer and Steele (2024) and Bailleul and Hoshino (2023+) by different approaches. In this talk, I will first give an overview of the theory of regularity structures, then compare the outlines of the proofs of BPHZ theorem. If time permits, I will also discuss some current researches and future problems.
