▶Japanese
Post to SNS
- Home
- > School of Science
- > Graduate major in Mathematics
- > Special lectures on advanced topics in Mathematics K
- School of Science
-
School of Engineering
- Undergraduate major in Mechanical Engineering
- Undergraduate major in Systems and Control Engineering
- Undergraduate major in Electrical and Electronic Engineering
- Undergraduate major in Information and Communications Engineering
- Undergraduate major in Industrial Engineering and Economics
- Common courses
- School of Materials and Chemical Technology
- School of Computing
- School of Life Science and Technology
- School of Environment and Society
- 工学院，物質理工学院，環境・社会理工学院共通科目
- Liberal arts and basic science courses
- First-Year Courses
- School of Science
- School of Engineering
- School of Materials and Chemical Technology
- School of Computing
- School of Life Science and Technology
-
School of Environment and Society
- Department of Architecture and Building Engineering
- Department of Civil and Environmental Engineering
- Department of Transdisciplinary Science and Engineering
- Department of Social and Human Sciences
- Department of Innovation Science
- Graduate major in Technology and Innovation Management
- Common courses
- Liberal arts and basic science courses
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Ninomiya Syoiti
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- Day/Period(Room No.)
- Intensive (本館2階201数学系セミナー室)
- Group
- -
- Course number
- MTH.E535
- Credits
- 2
- Academic year
- 2023
- Offered quarter
- 2Q
- Syllabus updated
- 2023/6/5
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
-
Course description and aims
The main subject of this course is the theory of regularity structures. First, we recall the basics of the rough path theory and introduce its application to stochastic differential equations. Next we introduce the basics of regularity structures as an extension of the rough path theory. Finally we also introduce its application to renormalizations of singular stochastic partial differential equations (SPDEs).
While the theory of regular structures is powerful enough to apply to many singular SPDEs, it is written in a lot of abstract notions and is not easy to comprehend. In this course, we explain basic concepts such as rough paths, Hopf algebras, and renormalizations which are necessary to understand the regularity structures.
Student learning outcomes
・Be familiar with renormalizations of singular SPDEs
・Understand the essentials of the rough path theory and regularity structures
・Be familiar with algebraic notions required for regularity structures
・Understand applications of regularity structures to singular SPDEs
Keywords
Singular SPDE, regularity structure, rough path, branched rough path, model, modelled distribution, reconstruction, rooted decorated tree, BPHZ model
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
This is a standard lecture course. There will be some assignments.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | "The following topics will be covered in this order : -- singular SPDEs -- rough path theory -- branched rough path theory -- a relation between Hopf algebra and branched rough paths -- abstract of the theory of regularity structures -- regularity structures, model, modelled distribution -- reconstruction theorem -- renormalization of models -- renormalization of SPDEs -- BPHZ model -- convergence of BPHZ models" | Details will be provided during each class session． |
Textbook(s)
None required
Reference books, course materials, etc.
"M. Hairer, ""A theory of regularity structures"", Invent, Math. 198 (2014), 269–504.
Y. Bruned, M. Hairer and L. Zambotti, ""Algebraic renormalisation of regularity structures"", Invent. Math, 215 (2019), 1039–1156."
Assessment criteria and methods
Assignments (100%).
Related courses
- None
Prerequisites (i.e., required knowledge, skills, courses, etc.)
None Required
