L6

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.

A number of moduli problems are, via Hodge theory, closely related to 
ball quotients. In this situation there is often a choice of possible 
compactifications such as the GIT compactification´and its Kirwan 
blow-up or the Baily-Borel compactification and the toroidal 
compactificatikon. The relationship between these compactifications is 
subtle and often geometrically interesting. In this talk I will discuss 
several cases, including cubic surfaces and threefolds and 
Deligne-Mostow varieties. This discussion links several areas such as 
birational geometry, moduli spaces of pointed curves, modular forms and 
derived geometry. This talk is based on joint work with S. 
Casalaina-Martin, S. Grushevsky, S. Kondo, R. Laza and Y. Maeda.