The Clay Mathematics Institute is a global organisation dedicated to furthering the beauty, power and universality of mathematical thought.
Yang-Mills & the Mass Gap
Experiment and computer simulations suggest the existence of a “mass gap” in the solution to the quantum versions of the Yang-Mills equations. But no proof of this property is known.
Navier-Stokes Equation
This is the equation which governs the flow of fluids such as water and air. However, for many decades no proof was found answering the most basic questions one can ask: do solutions exist, and are they unique? Why ask for a proof? Because a proof gives not only certitude, but also understanding.
Poincaré Conjecture
In 1904 the French mathematician Henri Poincaré asked if the three dimensional sphere is characterized as the unique simply connected three manifold. This question, the Poincaré conjecture, was a special case of Thurston’s geometrization conjecture. Perelman’s proof tells us that every three manifold is built from a set of standard pieces, each with one of eight well-understood geometries.
NZMRI 2027: Combinatorics, Probability and Symmetry
Nelson, New Zealand
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Arizona Winter School
University of Arizona
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Groups St Andrews 2027
University of St Andrews
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Geometric Analysis and Functional Analysis (GAFA)
Mathematical Institute of the Kazakhstan Branch of Lomonosov Moscow State University
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