Graph coloring is a classic hard algorithmic problem. In promise graph coloring, we ask if at least an approximation is feasible: given a graph promised to be 3-colorable, say, can we efficiently find a 100-coloring? To prove that even this relaxed problem is hard, we study polymorphisms (think: algebraic relations between solutions). It turns out that in some cases, basic topological tools give a very direct understanding of those polymorphisms, seeing them as continuous maps from toruses to spheres. Joint work with Andrei Krokhin, Jakub Opršal, Stanislav Živný.
Topology in promise constraint satisfaction
Feb. 04, 2021 1pm (Zoom (vir…
Rep Theory
Christoph Keller (University of Arizona)
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Physicists are interested in holographic families of VOAs. These are families of VOAs that on the one hand have dim V_n `small' for `small' n, and on the other hand have some kind of large central charge limit. I will discuss the motivation behind these requirements and the connection to extremal VOAs. I will then discuss some attempts at constructing such families, namely permutation orbifold VOAs and lattice orbifold VOAs. This talk is based on joint work with Thomas Gemuenden.
If I told you that there is an abundance of geometry lurking in the prime ideals of a ring, then you probably wouldn't believe me. In this talk, I'll (hopefully) convince you otherwise. I'll introduce the (underlying set of) affine schemes from a geometric point of view, starting with motivation from classical algebraic geometry, and after looking at the hidden geometry of rings, we'll take a look at why this perspective is "better" than the classical view.