It is known that minion homomorphisms give very natural complexity reductions between (P)CSPs (Barto, Bulín, Opršal, Krokhin, 2019). We will explore how to translate these techniques into the valued CSP situation. Convex geometry will make an appearance.
Minion homomorphisms and valued CSP
Mar. 11, 2021 11am (Zoom)
Noncomm Geometry
Stefano D'Alesio (ETH Zurich)
X
In this pre-talk I will discuss some basic notions in noncommutative (affine) geometry, using representation schemes of associative unital algebras. According to the Kontsevich-Rosenberg's principle a noncommutative geometric structure of some kind on an algebra should induce the corresponding commutative structure on its representation schemes. We are particularly interested in noncommutative Poisson structures, and I will talk about the following two approaches: 1. W. Crawley-Boevey's Poisson structures. They are Lie algebra structures of some kind on the zeroth Hochschild homology of an algebra (generalising the Necklace Lie algebra structure on the space of cyclic paths in a quiver) and they induce Poisson structures on the moduli spaces of representations. 2. M. Van den Bergh's double Poisson structures. They are double brackets which are double derivations in both arguments and satisfy a double version of antisymmetry and the Jacobi identity. They are needed to induce Poisson structures on the full representation schemes, rather than only on the moduli space of representations.
Representation schemes and noncommutative Poisson geometry
Mar. 11, 2021 1pm (Zoom (vir…
Rep Theory
Kang Lu (University of Denver)
X
Skew representations (corresponding to skew Young diagrams) of Yangian and quantum affine algebra of type A were introduced by Cherednik and extensively studied by Nazarov and Tarasov. In this talk, we will discuss some known results about skew representations of super Yangian of type A such as Jacobi-Trudi identities, Drinfeld functor, irreducibility conditions of tensor products, and extended T-systems. We also discuss some open problems related to tame modules of super Yangian. Some essential differences comparing to the even case will be discussed as well.
In 1954 René Thom wrote a Ph.D. thesis that revolutionalized algebraic topology. One of the main theorems in his thesis solves the geometric problem of classifying manifolds up to bordism by exhibiting an equivalence to a problem in stable homotopy theory. Thom's method makes use of what are now called 'Thom spectra', objects that have since become central in stable homotopy theory. In this talk, we will introduce the notions of bordism and spectra, and then describe the constructions that interpolate between the geometric and homotopic problems.
Minion homomorphisms and valued CSP