The Constraint Satisfaction Problem (CSP) over a structure with a finite relational signature is the problem of deciding whether a given finite input structure with the same signature as has a homomorphism to . According to the famous result of Bulatov and Zhuk we know that CSPs over finite template structures exhibit a complexity dichotomy: they are all in or -complete. Generalizing this theorem to infinite structures has been a topic of active research in the past few decades. A currently standing conjecture in this direction is by Bodirsky and Pinsker which states that the same complexity dichotomy holds for first-order reducts of finitely bounded homogeneous structures. In my talk I am exploring some ideas on how this conjecture could be attacked under some strong model theoretical assumptions such as -stability or first-order interpretability in the pure set. This approach often requires a detailed understanding of structures arising in this context which also leads to some questions in model theory that could be of independent interest.
This is joint work with Manuel Bodirsky and Paolo Marimon.
W-superalgebras are a large class of vertex algebras obtained from affine Lie algebras. Due to their duality, hook-type W-superalgebras have captured a lot of attention in the last decade. I will explain the duality in their representation theory and the phenomenon appearing at the level of characters.
Duality of hook-type W-superalgebras and characters Sponsored by the Meyer Fund
Model theoretical tameness and CSPs