Diophantine Problems in Thin Orbits

Alex Kontorovich
Yale University

There has been a recent surge of activity on long-standing naturally-arising problems in arithmetic, by reformulating them in terms of orbits of group or semi-group actions. These orbits turn out to be "thin" in an archimedean sense, but algebro-geometrically rich, allowing progress. Assuming no background, we will explain these problems, what one can prove, and some of the tools going into the proofs.

Presentation (PDF File)

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