Mathematics Branches, Topics, and Sub-Topics

A structured visual guide to the major mathematical areas and their relationships.

Search by code, branch, topic, subtopic, or a keyword from the descriptions.

60Lxx Rough analysis and related topics

This subtopic introduces the core ideas in rough analysis and related topics, including foundational concepts, standard methods, and the main questions used to organize the area. Typical uses include building mathematical background, framing related research problems, and supporting applications in neighboring fields where these concepts provide useful structure.

Specific topics

60L10 Signatures and the log-signature map

Overview

Signatures and the log-signature map. This topic studies rough analysis and related frameworks for highly irregular signals and paths beyond classical smooth stochastic calculus.

Related Wikipedia Page

Wikipedia: Rough path

Useful Links

Key Ideas

  • analysis of irregular paths
  • enhanced path structures
  • nonclassical integration frameworks

Typical Uses

Used to define and analyze differential equations driven by rough or distributional signals.

Applications

  • Stochastic PDE theory
  • Machine learning with path signatures
  • Robust stochastic modeling

References

Recommended Textbooks

60L20 Rough paths

Overview

Rough paths. This topic studies rough analysis and related frameworks for highly irregular signals and paths beyond classical smooth stochastic calculus.

Related Wikipedia Page

Wikipedia: Rough path

Useful Links

Key Ideas

  • analysis of irregular paths
  • enhanced path structures
  • nonclassical integration frameworks

Typical Uses

Used to define and analyze differential equations driven by rough or distributional signals.

Applications

  • Stochastic PDE theory
  • Machine learning with path signatures
  • Robust stochastic modeling

References

Recommended Textbooks

60L30 Regularity structures

Overview

Regularity structures. This topic studies rough analysis and related frameworks for highly irregular signals and paths beyond classical smooth stochastic calculus.

Related Wikipedia Page

Wikipedia: Rough path

Useful Links

Key Ideas

  • analysis of irregular paths
  • enhanced path structures
  • nonclassical integration frameworks

Typical Uses

Used to define and analyze differential equations driven by rough or distributional signals.

Applications

  • Stochastic PDE theory
  • Machine learning with path signatures
  • Robust stochastic modeling

References

Recommended Textbooks

60L40 Stochastic partial differential equations and regularity structures

Overview

Stochastic partial differential equations and regularity structures. This topic studies rough analysis and related frameworks for highly irregular signals and paths beyond classical smooth stochastic calculus.

Related Wikipedia Page

Wikipedia: Rough path

Useful Links

Key Ideas

  • analysis of irregular paths
  • enhanced path structures
  • nonclassical integration frameworks

Typical Uses

Used to define and analyze differential equations driven by rough or distributional signals.

Applications

  • Stochastic PDE theory
  • Machine learning with path signatures
  • Robust stochastic modeling

References

Recommended Textbooks

60L50 Stochastic analysis, rough paths

Overview

Stochastic analysis, rough paths. This topic studies rough analysis and related frameworks for highly irregular signals and paths beyond classical smooth stochastic calculus.

Related Wikipedia Page

Wikipedia: Rough path

Useful Links

Key Ideas

  • analysis of irregular paths
  • enhanced path structures
  • nonclassical integration frameworks

Typical Uses

Used to define and analyze differential equations driven by rough or distributional signals.

Applications

  • Stochastic PDE theory
  • Machine learning with path signatures
  • Robust stochastic modeling

References

Recommended Textbooks

60L70 Algebra and geometry of rough paths

Overview

Algebra and geometry of rough paths. This topic studies rough analysis and related frameworks for highly irregular signals and paths beyond classical smooth stochastic calculus.

Related Wikipedia Page

Wikipedia: Rough path

Useful Links

Key Ideas

  • analysis of irregular paths
  • enhanced path structures
  • nonclassical integration frameworks

Typical Uses

Used to define and analyze differential equations driven by rough or distributional signals.

Applications

  • Stochastic PDE theory
  • Machine learning with path signatures
  • Robust stochastic modeling

References

Recommended Textbooks

60L90 Applications of rough paths

Overview

Applications of rough paths. This topic studies rough analysis and related frameworks for highly irregular signals and paths beyond classical smooth stochastic calculus.

Related Wikipedia Page

Wikipedia: Rough path

Useful Links

Key Ideas

  • analysis of irregular paths
  • enhanced path structures
  • nonclassical integration frameworks

Typical Uses

Used to define and analyze differential equations driven by rough or distributional signals.

Applications

  • Stochastic PDE theory
  • Machine learning with path signatures
  • Robust stochastic modeling

References

Recommended Textbooks

60L99 None of the above

Overview

None of the above. This topic studies rough analysis and related frameworks for highly irregular signals and paths beyond classical smooth stochastic calculus.

Related Wikipedia Page

Wikipedia: Rough path

Useful Links

Key Ideas

  • analysis of irregular paths
  • enhanced path structures
  • nonclassical integration frameworks

Typical Uses

Used to define and analyze differential equations driven by rough or distributional signals.

Applications

  • Stochastic PDE theory
  • Machine learning with path signatures
  • Robust stochastic modeling

References

Recommended Textbooks