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Project

Half of the monodromy conjecture.

The monodromy conjecture is a conjecture in singularity theory first formulated by Igusa in the padic setting, and later stated by Denef and Loeser for complex varieties. When studying the singularities of an object defined by polynomial equations we cannot simply look at pictures, because we usually work with high dimensional objects. Hence the study of these singularities is done though algebraic invariants associated to the singularity. The advantage of these invariants is, amongst other things, that some of them can be computed using a computer, thereby providing very quantitative information that can be used to compare complicated singularities. The monodromy conjecture relates some of these invariants with each other in a very surprising way. It concerns in particular the topological zeta function, Bernstein-Sato polynomials, and eigenvalues of monodromy.  We will work towards a variation of this conjecture and try to prove "half" of it. This means that we will not prove the full statement, but we will prove the conjecture after ignoring some complicating aspects. Ignoring these complicating aspects makes the conjecture more approachable, and would still yield a very surprising and interesting result. Recently new results on some of the singularity invariants appeared that make this "half" version a particularly natural stepping stone towards the full conjecture.
 

Date:1 Oct 2017 →  31 Jul 2022
Keywords:monodromy conjecture
Disciplines:Geometry
Project type:PhD project