Explicit deformation of Galois representations.
Galois groups of tamely ramified -extensions
Very little is known regarding the Galois group of the maximal -extension unramified outside a finite set of primes of a number field in the case that the primes above are not in . We describe methods to compute this group when it is finite and conjectural properties of it when it is infinite.
Violations of the Ingleton inequality and revising the four-atom conjecture
The entropy region is a fundamental object of study in mathematics, statistics, and information theory. On the one hand, it involves pure group theory, governing inequalities satisfied by subgroup indices, whereas on the other hand, computing network coding capacities amounts to a convex optimization over this region. In the case of four random variables, the points in the region that satisfy the Ingleton inequality (corresponding to abelian groups and to linear network codes) form a well-understood...
Spaces of constant rank matrices over .
Pro- groups and towers of rational homology spheres.
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