Let K be a complete discrete valuation field with the residue field K, charK = p > 0. If K is a perfect field, there exists a beautiful theory of ramification in algebraic extensions of K. Given a finite Galois extension L/K with the Galois group G, one can introduce a canonical filtration (Gi) in G with quite a natural behavior with respect to subextensions in L/K. Namely, if H is a normal sub...

The SU(3) gauge theory in 2+1 dimensions is simple enough from a numerical point of view, so that it is possible with present computers to make continuum extrapolations with controlled systematic errors. Of course, there are some obvious differences between SU(3) gauge theory in 2 + 1 and 3 + 1 dimensions. In 2 + 1 dimensions the coupling constant g has the dimension of a mass, and the theory i...

The SU(3) gauge theory in 2+1 dimensions is simple enough from a numerical point of view, so that it is possible with present computers to make continuum extrapolations with controlled systematic errors. Of course, there are some obvious differences between SU(3) gauge theory in 2 + 1 and 3 + 1 dimensions. In 2 + 1 dimensions the coupling constant g has the dimension of a mass, and the theory i...

In ancient t imes, wax seals impressed with signet r ings were aff ixed to documents as evidence of their authent ic i ty . A digi ta l counterpart is a message authent icat ion code f ixed f i rmly to each important document. We sketch an archite cture that accompl ishes this by using encapsulat ion of content with provenance metadata, cryptographic seal ing, and webs of t rust rooted in respe...