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Studies on exact WKB analysis, topological recursion and Painleve equation

Research Project

Project/Area Number 20K14323
Research Category

Grant-in-Aid for Early-Career Scientists

Allocation TypeMulti-year Fund
Review Section Basic Section 12010:Basic analysis-related
Research InstitutionThe 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
Project Status Completed (Fiscal Year 2022)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2022: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2021: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2020: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywords完全WKB解析 / 位相的漸化式 / パンルヴェ方程式 / BPS構造 / 共形ブロック / アクセサリー・パラメータ / WRT不変量 / Painleve方程式
Outline of Research at the Start

自然界の様々な現象を記述する微分方程式(函数方程式)に対する新たな研究手法の構築を目指す。量子力学に由来するWKB法を発展させた完全WKB解析という手法と、行列模型の研究手法である位相的漸化式を組み合わせることで、Painleve方程式と呼ばれる特別なクラスの微分方程式の研究に取り組む。

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).

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。

Report

(4 results)
  • 2022 Annual Research Report   Final Research Report ( PDF )
  • 2021 Research-status Report
  • 2020 Research-status Report
  • Research Products

    (23 results)

All 2023 2022 2021 2020 Other

All Int'l Joint Research (2 results) Journal Article (5 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 5 results,  Open Access: 4 results) Presentation (14 results) (of which Int'l Joint Research: 8 results,  Invited: 13 results) Funded Workshop (2 results)

  • [Int'l Joint Research] University of Birmingham(英国)

    • Related Report
      2022 Annual Research Report
  • [Int'l Joint Research] University of Tours(フランス)

    • Related Report
      2022 Annual Research Report
  • [Journal Article] Topological Recursion and Uncoupled BPS Structures II: Voros Symbols and the $$\tau $$-Function2023

    • Author(s)
      Iwaki Kohei、Kidwai Omar
    • Journal Title

      Communications in Mathematical Physics

      Volume: 399 Issue: 1 Pages: 519-572

    • DOI

      10.1007/s00220-022-04563-y

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Topological recursion and uncoupled BPS structures I: BPS spectrum and free energies2022

    • Author(s)
      Iwaki Kohei、Kidwai Omar
    • Journal Title

      Advances in Mathematics

      Volume: 398 Pages: 108191-108191

    • DOI

      10.1016/j.aim.2022.108191

    • Related Report
      2022 Annual Research Report 2021 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Voros Coefficients for the Hypergeometric Differential Equations and Eynard-Orantin’s Topological Recursion: Part I-For the Weber Equation2022

    • Author(s)
      Kohei Iwaki, Tatsuya Koike, Yumiko Takei
    • Journal Title

      Annales Henri Poincare

      Volume: 24 Issue: 4 Pages: 1305-1353

    • DOI

      10.1007/s00023-022-01235-4

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Witten-Reshetikhin-Turaev Function for a Knot in Seifert Manifolds2021

    • Author(s)
      Hiroyuki Fuji, Kohei Iwaki, Hitoshi Murakami and Yuji Terashima
    • Journal Title

      Communications in Mathematical Physics

      Volume: - Issue: 1 Pages: 225-251

    • DOI

      10.1007/s00220-021-03953-y

    • Related Report
      2021 Research-status Report 2020 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] 2-Parameter tau-Function for the First Painleve Equation: Topological Recursion and Direct Monodromy Problem via Exact WKB Analysis2020

    • Author(s)
      Kohei Iwaki
    • Journal Title

      Commun. Math. Phys.

      Volume: 未定 Issue: 2 Pages: 1047-1098

    • DOI

      10.1007/s00220-020-03769-2

    • Related Report
      2020 Research-status Report
    • Peer Reviewed
  • [Presentation] Series expansion of accessory parameters of confluent Heun equations with a ramified irregular singular point2023

    • Author(s)
      Kohei Iwaki
    • Organizer
      Workshop on Accessory Parameters
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Topological recursion for elliptic curves2023

    • Author(s)
      岩木耕平
    • Organizer
      位相的漸化式と正則 アノマリー方程式
    • Related Report
      2022 Annual Research Report
  • [Presentation] Voros coefficients for isomonodromy systems associated with Painleve equations and BPS invariants2022

    • Author(s)
      Kohei Iwaki
    • Organizer
      Prospects in microlocal analysis and asymptotic analysis
    • Related Report
      2022 Annual Research Report
    • Invited
  • [Presentation] Voros coefficients for isomonodromy systems associated with Painleve equations and BPS invariants2022

    • Author(s)
      Kohei Iwaki
    • Organizer
      Painleve Equations : From Classical to Modern Analysis
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Topological recursion, BPS structure and Painleve τ-function2022

    • Author(s)
      Kohei Iwaki
    • Organizer
      Workshop on Mirror symmetry and Related Topics
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Topological recursion, uncoupled BPS structures and exact WKB analysis2022

    • Author(s)
      Kohei Iwaki
    • Organizer
      Algebraic Geometry and Integrable Systems 2022
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Topological recursion, quantum curves and Painleve equations2021

    • Author(s)
      Kohei Iwaki
    • Organizer
      Applicable resurgent asymptotics: towards a universal theory, ARA Focus Week, Exact Quantisation/Exact WKB and Resurgence (online)
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Topological recursion, Painleve tau--function and exact WKB analysis2021

    • Author(s)
      Kohei Iwaki
    • Organizer
      Combinatorics of Moduli Spaces, Cluster Algebras and Topological Recursion (online)
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Topological recursion, uncoupled BPS structures and exact WKB2021

    • Author(s)
      Kohei Iwaki
    • Organizer
      BPS states, mirror symmetry and exact WKB (online)
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 完全 WKB 解析とその周辺2021

    • Author(s)
      岩木耕平
    • Organizer
      日本数学会関数方程式論分科会 特別講演
    • Related Report
      2021 Research-status Report
    • Invited
  • [Presentation] Topological recursion for hypergeometric type spectral curves2020

    • Author(s)
      岩木耕平
    • Organizer
      ミラー対称性の諸相2020
    • Related Report
      2020 Research-status Report
    • Invited
  • [Presentation] Topological recursion and uncoupled BPS structure arising from spectral curves of hypergeometric type2020

    • Author(s)
      Kohei Iwaki
    • Organizer
      Strings and QFTs for Eurasian time zone (online)
    • Related Report
      2020 Research-status Report
    • Invited
  • [Presentation] Topological recursion and uncoupled BPS structure arising from spectral curves of hypergeometric type2020

    • Author(s)
      Kohei Iwaki
    • Organizer
      SISSA's Integrable System and Mathematical Physics Seminar (online)
    • Related Report
      2020 Research-status Report
    • Invited
  • [Presentation] Topological recursion, exact WKB analysis and Painleve equation2020

    • Author(s)
      Kohei Iwaki
    • Organizer
      Integrable Systems 2020 (online)
    • Related Report
      2020 Research-status Report
    • Int'l Joint Research / Invited
  • [Funded Workshop] 位相的漸化式と正則アノマリー方程式2023

    • Related Report
      2022 Annual Research Report
  • [Funded Workshop] Painleve Equations : From Classical to Modern Analysis2022

    • Related Report
      2022 Annual Research Report

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Published: 2020-04-28   Modified: 2024-01-30  

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