This talk is rescheduled and will take place on 21 January 2025
The McCullough-Miller space is a contractible simplicial complex that admits an action of the pure symmetric (outer) automorphisms of the free group, with stabilizers that are free abelian. This space has been used to derive several cohomological properties of these groups, such as computing their cohomology ring and proving that they are duality groups. In this talk, we will generalize the construction to right-angled Artin groups (RAAGs), and use it to obtain some interesting cohomological results about the pure symmetric (outer) automorphisms of RAAGs.
A topological quantum field theory (TQFT) is a functor from a category of bordisms to a category of vector spaces. Classifying low-dimensional TQFTs often involves considering presentations of bordism categories in terms of generators and relations. In this talk, we will introduce these concepts and outline a program for obtaining such presentations using Morse–Cerf theory.
Introduction to flat space holography in three dimensions and Carrollian CFT2, with selected results on correlation functions, thermal entropy, entanglement entropy and an outlook to Bondi news in 3d.
The fundamental group of a hyperbolic surface has an infinite number of rank k subgroups. What does it mean, therefore, to pick a 'random' subgroup of this type? In this talk, I will introduce a method for counting subgroups and discuss how counting allows us to study the properties of a random subgroup and its associated cover.
We will explore the connection between Celestial and Euclidean Anti-de Sitter (EAdS) holography in the massive scalar case. Specifically, exploiting the so-called hyperbolic foliation of Minkowski space-time, we will show that each contribution to massive Celestial correlators can be reformulated as a linear combination of contributions to corresponding massive Witten correlators in EAdS. This result will be demonstrated explicitly both for contact diagrams and for the four-point particle exchange diagram, and it extends to all orders in perturbation theory by leveraging the bootstrapping properties of the Celestial CFT (CCFT). Within this framework, the Kantorovic-Lebedev transform plays a central role. This transform will allow us to make broader considerations regarding non-perturbative properties of a CCFT.
Given a singularity with a crepant resolution, a symmetry of the derived
category of coherent sheaves on the resolution may often be constructed
using the formalism of spherical functors. I will introduce this, and
new work (arXiv:2409.19555) on general constructions of such symmetries
for hypersurface singularities. This builds on previous results with
Segal, and is inspired by work of Bodzenta-Bondal.
Joint work with Paul Hacking (U Mass Amherst). We first explain how to
prove homological mirror symmetry for a maximal normal crossing
Calabi-Yau surface Y with split mixed Hodge structure. This includes the
case when Y is a type III K3 surface, in which case this is used to
prove a conjecture of Lekili-Ueda. We then explain how to build on this
to prove an HMS statement for K3 surfaces. On the symplectic side, we
have any K3 surface (X, ω) with ω integral Kaehler; on the algebraic
side, we get a K3 surface Y with Picard rank 19. The talk will aim to be
accessible to audience members with a wide range of mirror symmetric
backgrounds.