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What can be said about a system of polynomial equations over a finite field if its number of solutions deviates from that of a random system? Answer: Roughly, one of the polynomials (or a linear combination thereof) can be written in terms of “few”...

Pretannakian categories, that is k-linear abelian categories with finite dimensional Hom groups, given with a commutative and associative tensor product, with a unit object (such that End(1)=k) and duals, can be viewed as generalizations of linear...

Play Reading is a popular activity that brings the IAS community together to read plays. The group meets at 7:00 pm on several evenings this...

Every word in a free group induces a probability distribution on every finite group by substituting the letters of w by uniformly random elements of the group. The connection between such distributions on the symmetric group and the poset of...