Topology Seminar: Rudradip Biswas (Warwick)
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Title: Cantor Dynamical Systems, Bratteli Diagrams, and Their Associated Full GroupsAbstract: If a countable group G acts on a Cantor set X, one can enlarge G to a (still countable) group F(G) by adding homeomorphisms of X that act locally as elements of G. This group, known as the full group of the dynamical system […]
Title: A Comparison of Two Supercharacter TheoriesAbstract: In 2008, P. Diaconis and I.M. Isaacs introduced a generalization of classical character theory, which they called supercharacter theory. Let X be a partitioning of the irreducible characters of a finite group G such that the trivial character is in its own block of this partition. Let Y […]
Title: Two-row Delta Springer varietiesAbstract: I will discuss the geometry and topology of a certain family of so-called Delta Springer varieties from an explicit, diagrammatic point of view. These singular varieties were introduced by Griffin—Levinson—Woo in 2021 in order to give a geometric realization of an expression that appears in the t = 0 case of […]
Title: Monoidal complete Segal spaces. Abstract: Viewing a monoid as a category with a single object allows us to encode the binary operation using the properties of composition and associativity inherent in any category. In this talk, we use this idea to explore the relationship between (∞,1)-categories with a monoidal structure and (∞,2)-categories with one […]
Title: Poisson geometry and Azumaya loci of cluster algebrasAbstract: Roughly speaking, cluster algebra is a commutative algebra obtained from taking the intersection of Laurent polynomial rings associated a "seed". When a cluster algebra satisfies some compatibility condition, M. Gekhtman, M. Shapiro, and A. Vainshtein showed that one can connect a Poisson bracket to the cluster algebra. In […]
Title: Spectral algebraic geometry and topological modular formsAbstract: An important area of study in homotopy theory is the study of elliptic cohomology. In this talk we briefly review the context of elliptic cohomology and its interpretation in terms of spectral algebraic geometry. Furthermore, we construct the Deligne-Mumford compactification of the stack of oriented elliptic curves. If time […]
Title: Motives in geometric representation theoryAbstract: The spherical and Iwahori-Hecke algebras of a reductive group are of great importance in the Langlands program. They are categorified by equivariant sheaves on the affine Grassmannian and affine flag variety respectively, as introduced in the previous talk. Similarly, the Satake and Bernstein isomorphisms are categorified by the Satake equivalence and […]