EVENT DETAILS AND ABSTRACT

Title: Relative rank and applications
Speaker: Amichai Lampert
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Abstract:

The rank of a polynomial, also known as the h-invariant or strength, was introduced by Schmidt in 1985 in his work on the distribution of integer solutions to homogeneous polynomial equations in many variables. More recently it has found applications in additive combinatorics in the context of counting points on varieties over finite fields (2007) and in commutative algebra through the proof of Stillman's conjecture (2016). We introduce relative rank, a substantial generalization of rank which retains many of the good properties of rank. The advantage of relative rank is that it allows for vastly improved quantitative bounds in many results, polynomial rather than Ackermann type.