Studies on exact WKB analysis, topological recursion and Painleve equation

2022 Fiscal Year Final Research Report

• Project/Area Number: 20K14323
• Research Category: Grant-in-Aid for Early-Career Scientists
• Allocation Type: Multi-year Fund
• Review Section: Basic Section 12010:Basic analysis-related
• Research Institution: The University of Tokyo
• Principal Investigator: IWAKI Kohei 東京大学, 大学院数理科学研究科, 准教授 (00750598)
• Project Period (FY): 2020-04-01 – 2023-03-31
• Keywords: 完全WKB解析 / 位相的漸化式 / パンルヴェ方程式

Outline of Final Research Achievements

We investigated a relationship among the exact WKB analysis, topological recursion and Painleve equation, based on the theory of quantum curves. We succeeded in constructing a solution to the BPS Riemann-Hilbert problem via the topological recursion (joint work with Omar Kidwai). We also studied a relation between the irregular conformal block and accessory parameter to test the irregular-version of Zamolodchikov's conjecture (joint work with Hajime Nagoya).

Free Research Field

微分方程式、可積分系、特殊函数

Academic Significance and Societal Importance of the Research Achievements

本研究は、背景の全く異なる数学的対象の間に新たな関係性を構築することを目標としたものである。周期と可積分性の間の関係性に関して、背後にある数学的構造の解明に向けて、様々な知見を得ることができた。