L5

The Farrell--Jones conjecture predicts that the algebraic K-theory of a group ring is isomorphic to a certain equivariant homology theory, and there are also versions for L-theory and Waldhausen's A-theory. In principle, this provides a way to calculate these K-groups, and has many applications. These include classifying manifolds admitting a given fundamental group and a positive resolution of the Borel conjecture.

I will discuss work with Yassine Guerch and Sam Hughes on the Farrell--Jones conjecture for extensions of relatively hyperbolic groups, as well as an application to their automorphism groups in the one-ended case. The methods are from geometric group theory: we go via the theory of JSJ decompositions to produce acylindrical actions on trees.

When tensor products of N minimal models accumulate at central charge N, they also admit relevant operators arbitrarily close to marginality. This raises the tantalizing possibility that they can be use to reach purely Virasoro symmetric CFTs where the breaking of extended chiral symmetry can be seen in a controlled way. This talk will give an overview of the theories where this appears to be the case, according to a brute force check at low lying spins. We will also encounter an interesting non-example where the same type of analysis can be used to give a simpler proof of integrability.

We’ll begin by introducing homotopy algebras (assuming no background) and their intimate connection to quantum field theory, with a briefly summary of some applications: scattering amplitude recursion relations, colour-kinematics duality, and generalised asymptotic observables. We’ll then introduce (deformed) Alexandrov–Kontsevich–Schwarz–Zaboronsky theories as the paradigmatic example of this framework, before developing their applications to gravity in two, three and four dimensions.   

Rank-based models for equity markets are reduced-form models where the asset dynamics depend on the rank that asset occupies in the investment universe. Such models are able to capture certain stylized macroscopic properties of equity markets, such as stability of the capital distribution curve and collision rates of stock rank switches. However, when calibrated to real equity data the models possess undesirable features such as an "Atlas stock" effect; namely the smallest security has an unrealistically large drift. Recently, Campbell and Wong (2024) identified that listings and delistings (i.e. entrances and exists) of securities in the market are important drivers for the stability of the capital distribution curve. In this work we develop a framework for ranked-based models with listings and delistings and calibrate them to data. By incorporating listings and delistings the calibration procedure no longer leads to an "Atlas stock" behaviour. Moreover, by studying an appropriate "local model", focusing on a specific target rank, we are able to connect collisions rates with a notion of particle density, which is more stable and easier to estimate from data than the collision rates. The calibration results are supported by novel theoretical developments such as a new master formula for functional generation of portfolios in this setting. This talk is based on joint work in progress with Martin Larsson and Licheng Zhang.  

This paper shows that a simple sale contract with a collection of options implements the full-information first-best allocation in a variety of continuous-time dynamic adverse selection settings with news. Our model includes as special cases most models in the literature. The implementation result holds regardless of whether news is public (i.e., contractible) or privately observed by the buyer, and it does not require deep pockets on either side of the market. It is an implication of our implementation result that, irrespective of the assumptions on the game played, no agent waits for news to trade in such models. The options here do not play a hedging role and are, thus, not priced using a no-arbitrage argument. Rather, they are priced using a game-theoretic approach.

The fundamental group of a complex variety is finitely presented. The talk will survey algebraic variants (in fact, distant corollaries) of this fact, in the context of variants of the etale fundamental group. We will then zoom in on "tame" etale fundamental groups of p-adic analytic spaces. Our main result is that it is (topologically) finitely generated (for a quasi-compact and quasi-separated rigid space over an algebraically closed field).  The proof uses logarithmic geometry beyond its usual scope of finitely generated monoids to (eventually) reduce the problem to the more classical one of finite generation of tame fundamental groups of algebraic varieties over the residue field. This is joint work with Katharina Hübner, Marcin Lara, and Jakob Stix.

I will discuss the recent progress in the numerical bootstrap of the 3d Ising CFT using the correlation functions of stress-energy tensor and the relevant scalars. This numerical bootstrap setup gives excellent results which are two orders of magnitude more accurate than the previous world's best. However, it also presents many significant technical challenges. Therefore, in addition to describing in detail the numerical results of this work, I will also explain the state-of-the art numerical bootstrap methods that made this study possible. Based on arXiv:2411.15300 and work in progress.

Gauging is a systematic way to construct a model with non-invertible symmetry from a model with ordinary group-like symmetry. In 2+1d dimensions or higher, one can generalize the standard gauging procedure by stacking a symmetry-enriched topological order before gauging the symmetry. This generalized gauging procedure allows us to realize a large class of non-invertible symmetries. In this talk, I will describe the generalized gauging of finite group symmetries in 2+1d lattice models. This talk will be based on my ongoing work with L. Bhardwaj, S.-J. Huang, S. Schäfer-Nameki, and A. Tiwari.

Celestial Holography posits the existence of a holographic description of gravitational theories in asymptotically flat space-times. To date, top-down constructions of such dualities involve a combination of twisted holography and twistor theory. The gravitational theory is the closed string B model living in a suitable twistor space, while the dual is a chiral 2d gauge theory living on a stack of D1 branes wrapping a twistor line. I’ll talk about a variant of these models that yields a theory of self-dual Einstein gravity (via the Plebanski equations) in four dimensions. This is based on work in progress with Roland Bittleston, Kevin Costello & Atul Sharma.