Top Open Problems
Provisional editorial order for Top Open Problems: Millennium Prize Problems first, followed by assessed difficulty tiers; the unassessed remainder keeps its previous catalogue order. About rankings
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- Math-1701 Topology of planar Brownian trace
- Math-1702 Percolation dimension of planar Brownian trace
- Math-1703 Convergence of synchronous reflected-Brownian couplings
- Math-1704 Non-extinction of a Fleming–Viot particle model
- Math-1705 Concatenated bounded Brownian pieces
- Math-1706 Do peaks of random labelings repel each other?
- Math-1707 Stationary distributions in one dimension
- Math-1708 Stationary distributions in higher dimensions
- Math-1709 Exchangeability in the mean-zero exclusion process
- Math-1710 Negative association for asymmetric exclusion
- Math-1711 Random Eulerian excursion dichotomy on high-dimensional tori
- Math-1712 Second-longest Eulerian excursion on the two-dimensional torus
- Math-1713 Shortest Eulerian excursion on the Hamming cube
- Math-1714 Largest common subcladogram exponents
- Math-1715 Largest common suborder of two random two-dimensional orders
- Math-1716 Percolation of planar empires at unit merger rate
- Math-1717 Online minimum spanning tree constant
- Math-1718 Stationary law of a drift-jump particle process
- Math-1719 Near-one asymptotics for oriented-percolation flow
- Math-1720 Conjecture 0.1 — Is there an infinite expander?
- Math-1721 Nonamenable subgraphs of transitive graphs with exponential growth
- Math-1722 Nonamenable subgraphs under uniform exponential growth
- Math-1723 Cheeger constants of nets in transitive graphs
- Math-1724 Uniform expansion bounds for graph nets
- Math-1725 Grid-or-tree embeddings in superlinear Cayley graphs
- Math-1726 Roughly transitive graphs versus homogeneous spaces
- Math-1727 Minimum diameter realizing a prescribed local ball
- Math-1728 Isoperimetric dimension and nontrivial percolation threshold
- Math-1729 Self-avoiding loops on nonamenable transitive graphs
- Math-1730 Locality of connective constants
- Math-1731 Half-plane percolation for invariant FKG processes
- Math-1732 Binary trees in critical clusters of regular planar triangulations
- Math-1733 Invariant finite-energy percolation with internal threshold one
- Math-1734 Uniqueness of percolation on graphs roughly isometric to lattices
- Math-1735 Cheeger constant and the percolation nonuniqueness phase
- Math-1736 Rough-isometry invariance of percolation nonuniqueness
- Math-1737 Percolation nonuniqueness on products with the line
- Math-1738 Infinite-cluster intersections with vertical fibers
- Math-1739 From a large percolation component to a giant component on expanders
- Math-1740 Nonintersecting couplings of random walks in dimensions three and four
- Math-1741 Liouville property of infinite Ramanujan graphs
- Math-1742 Liouville property under rough isometry to nonamenable Cayley graphs
- Math-1743 Liouville extensions by an isometric integer action
- Math-1744 Limit shape in Poisson–Voronoi metrics over $\ell_p$ planes
- Math-1745 Near-critical percolation limit shapes
- Math-1746 Finite graphs whose every ball is an expander
- Math-1747 When is the uniqueness threshold below one?
- Math-1748 Uniqueness at the percolation uniqueness threshold
- Math-1749 Limit shape of first-passage percolation
- Math-1750 Sharp lower bounds for entropic subspace approximation