Pi Day - School of Maths 2026

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Across
  1. 4. Hotel always has room.
  2. 5. The set everyone meets before they know what a set really is.
  3. 8. Conjectures relating regulators, K-theory, and special values of L-functions.
  4. 13. Conjecture predicting a bound relating sums and products of coprime integers.
  5. 14. Combinatorial paradoxes and dynamical systems.
  6. 15. Logarithm pioneer whose tables saved astronomers centuries of calculation.
  7. 17. Spectral sequence computing derived functors of a composite functor.
  8. 22. Conjecture describing the location of nontrivial zeros of the zeta function.
  9. 23. The closed unit ball of the dual space of a normed vector space is compact in the weak topology.
  10. 24. Hypothetical objects intended to unify cohomology theories of algebraic varieties.
  11. 25. Cohomology theory obtained from differential forms on manifolds.
  12. 26. Combinatorial theorem guaranteeing monotone subsequences.
  13. 27. Circles and randomness conspire.
  14. 29. Ordinals that lead to contradiction.
  15. 30. Group characters and matrices.
  16. 31. Category-theoretic generalization of a topological space used in algebraic geometry.
Down
  1. 1. Measure-theoretic theorem allowing interchange of integrals.
  2. 2. Fundamental equivalence used in perfectoid geometry.
  3. 3. Paradoxical decomposition of a sphere using group actions.
  4. 4. Polynomials orthogonal under Gaussian weight, used in probabilistic expansions, quantum mechanics, and spectral PDE methods.
  5. 6. Property of Banach spaces where the canonical embedding into the double dual is surjective.
  6. 7. Property of a function whose derivative changes sign infinitely often near a point.
  7. 9. Grand unifying program linking automorphic forms with Galois representations.
  8. 10. Axioms defining natural numbers.
  9. 11. Limit of scaled random walks converging to Brownian motion.
  10. 12. The theorem relating elliptic curves over ℚ to modular forms.
  11. 16. Non-Archimedean analytic spaces generalizing rigid analytic geometry.
  12. 18. Algebraic structure with associative multiplication and identity.
  13. 19. Property where future evolution depends only on present state.
  14. 20. Function that keeps coming back to haunt complex analysts.
  15. 21. p-adic analytic study of cyclotomic fields, class groups, and growth of invariants over infinite towers of number fields.
  16. 28. Cohomology theory used to study algebraic varieties over arbitrary fields.