Invariant Theory: Recent Progress and Applications

This is the homepage for “Invariant Theory: Recent Progress and Applications” – a one-day meeting taking place at Middlesex University on June 16th 2017. The meeting is supported by a scheme 1 (celebrating new appointments) grant from the London Mathematical Society.

Conference Program

12 - 1pmRegistration in quad foyer
1 - 2pmJonathan Elmer (Middlesex): CoinvariantsAbstract: The algebra of coinvariants of a finite group G acting on V is the quotient of the algebra of invariants k[V]^G by the ideal of k[V] generated by positive degree invariants. Unlike the algebra of invariants itself, it is fairly computable. The algebra of coinvariants sometimes contains information about the structure of the invariants. We'll explore this in the modular and non-modular cases. Partially based on joint work with Mufit Sezer.
2.15 - 3.15pmR. J. Shank (Kent): Finite Subgroups of FieldsAbstract: Suppose that F is field of prime characteristic p and E is a finite subgroup of the additive group (F,+). Then E is an elementary abelian p-group. We view two such subgroups, say E and E', to be equivalent if there is a unit c in F^* such that E=cE'. This equivalence relation is motivated by a problem in invariant theory. The equivalence classes can be separated using rational functions. I will discuss the problem of finding explicit separating sets. This is joint work with Eddy Campbell, Jianjun Chuai and David Wehlau; details can be found in arXiv:1610.03709.
3.15 - 3.45pmCoffee Break
3.45 - 4.45pmEmilie Dufresne (Nottingham): Mapping toric varieties into small dimensional spacesAbstract: A smooth d-dimensional projective variety X can always be embedded into 2d + 1-dimensional space. In contrast, a singular variety may require an arbitrary large ambient space. If we relax our requirement and ask only that the map is injective, then any d-dimensional projective (resp. affine) variety can be mapped injectively to 2d+1-dimensional projective space (resp. affine). A natural question then arises: what is the minimal m such that a variety can be mapped injectively to m-dimensional space? In this talk I discuss this question for the affine cones over normal toric varieties, with the most complete results being for the affine cones over Segre-Veronese varieties.
(joint work with Jack Jeffries)

5 - 6pmReception in quad mezzanine, followed by dinner

Some financial support is available for PhD students. If you are interested in attending, click here to go to our booking site.