Scientific Series

Recent work by Davide Gaiotto and collaborators introduced a new type of parametric Feynman integrals to compute BRST anomalies in topological and holomorphic quantum field theories. The integrand of these integrals is a certain differential form in Schwinger parameters. In a new article together with Simone Hu, we showed that this "topological" differential form coincides with a "Pfaffian" differential form that had been used by Brown, Panzer, and Hu, to compute cohomology of the odd graph complex and of the linear group. In my talk, I will review some aspects of the graph complex and the role played by the Pfaffian form there, sketch the proof of equivalence, and comment on various observations on either side of the equivalence and their natural counterparts on the other side.

A review of asymptotic (more generally, boundary) symmetries will be given in the context of the Hamiltonian formulation. General features (such as the form of the symmetry generators and the structure of the algebra) as well as specific examples will be covered.  A particular attention will be paid to asymptotically flat spaces and the asymptotic BMS algebra, where nonlinear redefinitions will be shown to yield a supertranslation-invariant angular momentum.

I describe a new solution to the Higgs hierarchy problem based on a dynamical vacuum selection mechanism in a landscape which scans the Higgs mass. The Higgs potential only admits a stable minimum when its mass is less than a critical value, cosmologically crunching away patches with a heavier Higgs. This critical value is set by the instability scale where the Higgs quartic turns negative. I consider the phenomenology of two explicit models that address the hierarchy problem in this context.

The standard models of particle physics and cosmology predict the existence of a cosmological magnetic field. Estimates of the magnetic field strength and coherence scale are derived from MHD simulations and new MHD invariants. Such magnetic fields are consistent with upper and lower bounds obtained from various cosmological observations.

Discrepancies between Lorentzian and Euclidean calculations of quantum corrections to de Sitter horizon thermodynamics revealed the existence of ‘edge’ degrees of freedom on the horizon. In this talk, I will review these calculations and present updates on understanding the physics of such edge modes in both gauge theories and (higher-spin) gravity. For Einstein gravity, I will discuss a plausible interpretation involving an embedded spherical brane. Finally, I will comment on how these ideas extend to more general black hole spacetimes.

As the sensitivity of gravitational-wave detector networks increases, high-fidelity signal recovery from the most prominent events becomes possible. The strongest signals present both opportunities and challenges for determining the properties of their sources. Focusing on the problem of inferring the nuclear equation of state from neutron star mergers, I will discuss how systematic errors from waveform modeling have the potential to dominate the inference of matter properties in near-future observations. If properly addressed, loud signals may reveal subdominant effects on the source dynamics, providing novel opportunities to learn about neutron star matter beyond the equation of state. I will outline a data-driven approach to interpreting gravitational-wave observations with phenomenological signal corrections, including some first results from work at CSUF on binary black hole systems. I’ll also discuss methods for connecting unmodeled waveform effects to the energetics of the source system. Finally, I will relate these uncertainty quantification methods to goals for instrumental design, demonstrating how next-generation sensitivities will translate into improved scientific potential.

In this talk, I will discuss a birational realization of King's conjecture which is indeed true, and its connections with noncommutative algebraic geometry and mirror symmetry. In particular, I will also establish the A-side analog of this result using constructible sheaves and promote the celebrated Coherent-Constructible Correspondence to a global family. The talk is based on recent joint work https://arxiv.org/abs/2501.00130 and work in preparation with David Favero.

Cosmology is undergoing a data revolution. Surveys such as the imminent Legacy Survey of Space and Time (LSST) to be conducted by the Vera C. Rubin Observatory will deliver huge galaxy catalogues that provide critical tools for understanding the nature of dark matter and dark energy. However, in order to obtain accurate cosmological constraints from these enormous datasets, we need reliable ways of estimating galaxy properties using only photometry. I will present pop-cosmos: a forward modelling framework for photometric galaxy survey data, where galaxies are modelled as draws from a population prior distribution over redshift, mass, dust properties, metallicity, and star formation history. These properties are mapped to photometry using an emulator for stellar population synthesis, followed by the application of a learned model for a survey's noise properties. Application of selection cuts enables the generation of mock galaxy catalogues. This enables us to use simulation-based inference to solve the inverse problem of calibrating the population-level prior on a deep multiwavelength catalogue, COSMOS2020. We use a diffusion model as a flexible population-level prior, and optimise its parameters by minimising the Wasserstein distance between forward-simulated photometry and the real COSMOS2020 survey data. The resulting model can then be used to derive accurate redshift distributions for upcoming photometric surveys, to facilitate weak lensing and clustering science. I will show applications of this framework, demonstrating how we are able to extract redshift distributions, and make inferences about galaxy evolution. I will also discuss the use of pop-cosmos as a prior for performing inference on individual galaxies in a highly scaleable manner, as well as ongoing work to analyse data from the Kilo-Degree Survey (KiDS) in preparation for LSST.

Quasars - accreting super-massive black holes - are the most luminous non-transient sources known and can be seen at redshifts of z > 7, when the Universe was just ~5% of its current age.  This implies that black holes with masses of up to ~10^9 M_Sun formed less than 800 Myr after the Big Bang, impossible under the default paradigm of Eddington-limited accretion onto stellar mass black holes.  The greatest barrier to understanding the formation and growth of these objects is the lack of data: quasars are very rare at these distances/times with fewer than ten known with z > 7 at present.  I will report on recent observational developments in this field, with a particular focus on the early results from the Euclid mission, for which the Wide Survey has the necessary combination of area, wavelength coverage and depth to increase the number of known quasars by an order of magnitude and to push to redshifts z > 8 and beyond.

In 2010, Kontsevich and Soibelman defined Cohomological Hall Algebras for quivers and potential as a mathematical construction of the algebra of BPS states. These algebras are modeled on the cohomology of vanishing cycles, which makes these algebras particularly hard to study but often result in interesting algebraic structures. A deformation of a particular case of them gives rise to a positive half of Maulik-Okounkov Yangians. The goal of my talk is to give an introduction to these ideas and explain how for the case of tripled cyclic quiver with canonical cubic potential, this algebra turns out to be one-half of the universal enveloping algebra of the Lie algebra of matrix differential operators on the torus, while its deformation turn out be one half of an explicit integral form of the Affine Yangian of gl(n).

I will introduce the Entanglement Bootstrap, a program to extract and understand the universal information characterizing a state of matter, starting from the local entanglement structure of a single representative state. This universal information is usually packaged in the form of a quantum field theory; the program therefore provides a surprising new perspective on quantum field theory. I will discuss what we can learn about gapped topological phases and their associated topological field theories, and about quantum critical points and their associated conformal field theories.