Invariants in Commutative Algebra: combinatorial aspects and prime characteristic techniques

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The aim of the project is to explore various invariants of various objects in commutative algebra where either the Frobenius endomorphism (prime characteristic) or additional combinatorial structure gives one a possible handle.Specifically, the project will initially aim to describe (1) the attached primes and secondary decompositions of local cohomology modules and (2) generating roots of local cohomology modules with support in binomial edge ideals in prime characteristic.