Other Fields — Open Conjectures

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Conjectures from fields not covered by the other pages.

Computational Complexity

# Conjecture Eponym(s) Comments
1 Quantum PCP conjecture —  
2 Unique games conjecture —  

Dynamical Systems & Ergodic Theory

# Conjecture Field Eponym(s) Comments
1 Berry–Tabor conjecture Geodesic flow Michael Berry, Michael Tabor  
2 Quantum unique ergodicity conjecture Dynamical systems — 2004: Elon Lindenstrauss, for arithmetic hyperbolic surfaces. 2008: Kannan Soundararajan & Roman Holowinsky, for holomorphic forms of increasing weight for Hecke eigenforms on noncompact arithmetic surfaces.
3 Sarnak conjecture Topological entropy Peter Sarnak  
4 Weinstein conjecture Periodic orbits Alan Weinstein  

Polynomials

# Conjecture Eponym(s) Comments
1 Casas-Alvero conjecture Eduardo Casas-Alvero  
2 Jacobian conjecture Carl Gustav Jacob Jacobi Named by way of the Jacobian determinant

Diophantine Approximation

# Conjecture Eponym(s) Comments
1 Littlewood conjecture John Edensor Littlewood ⇐ Margulis conjecture

Monodromy & Differential Equations

# Conjecture Field Eponym(s) Comments
1 Deligne conjecture Monodromy Pierre Deligne  
2 Grothendieck–Katz p-curvature conjecture Differential equations Alexander Grothendieck, Nick Katz  

Other

# Conjecture Field Eponym(s) Comments
1 Birkhoff conjecture Integrable systems George David Birkhoff  
2 Chowla conjecture Möbius function Sarvadaman Chowla ⇒ Sarnak conjecture
3 Ibragimov–Iosifescu conjecture Probability theory Ildar Ibragimov, Marius Iosifescu For φ-mixing sequences
4 Kung–Traub conjecture Iterative methods H. T. Kung, Joseph F. Traub  
5 Pierce–Birkhoff conjecture Real algebraic geometry Richard S. Pierce, Garrett Birkhoff  

References

  • Arora, S. & Barak, B. Computational Complexity: A Modern Approach. Cambridge University Press, 2009.
  • Katok, A. & Hasselblatt, B. Introduction to the Modern Theory of Dynamical Systems. Cambridge University Press, 1995.

See also the centralized bibliography for general references.