Talks

Over the three lectures and the tutorial, I want to explore some problems in enumerative algebra that can be understood by associating lattices to semistandard Young tableaux. I will introduce a family of rational functions called Hall--Littlewood--Schubert series (HLS series), which was recently introduced by Christopher Voll and myself. The enumerative problems we discuss will be solved by judicious substitutions of the variables of the HLS series.

Dark photons and axions are exciting candidates for dark matter, which may be observable through their couplings to electromagnetism or electrons. While many experimental programs have been developed to explore the wide range of parameter space over which these candidates may exist, the mass range corresponding to frequencies below a kHz has been seldom probed by laboratory experiments. In this talk, I will discuss two ongoing efforts to probe this region of parameter space. Both rely on the ability of dark-photon or axion dark matter to source an oscillating magnetic field signal inside an experimental apparatus. In the first case, this magnetic field signal is detected by observing its effect on magnetically levitated (Maglev) systems. The oscillating magnetic field signal sourced by dark matter can drive translational motion of a levitated superconductor or rotational motion of a levitated ferromagnet. As mechanical resonators, Maglev systems are naturally sensitive to lower frequencies, making them well-suited detectors for sub-kHz dark matter candidates. In the second case, we instead consider Earth as the experimental apparatus. That is, we search directly for the oscillating magnetic field signal using unshielded magnetometers located across the Earth's surface. Not only does the signal strength receive an enhancement from the large size of the Earth, but it is also correlated between independent measurements at different locations. I will discuss the search for this signal in existing publicly available magnetometer data maintained by the SuperMAG collaboration, as well as an independent experimental effort, known as SNIPE Hunt, to measure this signal in the field. I will show that both Maglev systems and unshielded magnetometers have the potential to set the leading laboratory constraints on dark-photon and axion dark matter in the sub-kHz regime.

Improving cosmological constraints from galaxy clustering presents several challenges, particularly in extracting information beyond the power spectrum due to the complexities involved in higher-order n-point function analysis. In this talk, I will introduce novel inference techniques that allow us to go beyond the state-of-the-art, not only by utilizing the galaxy trispectrum, a task that remains computationally infeasible with traditional methods, but also by accessing the full information encoded in the galaxy density field for the first time in cosmological analysis. I will present simulation-based inference (SBI), a powerful deep learning technique that enables cosmological inference directly from summary statistics in simulations, bypassing the need for explicit analytical likelihoods or covariance matrices. This is achieved using LEFTfield, a Lagrangian forward model based on the Effective Field Theory of Large Scale Structure (EFTofLSS) and the bias expansion, ensuring robustness on large scales. Furthermore, LEFTfield enables field-level Bayesian inference (FBI), where a field-level likelihood is used to directly analyze the full galaxy density field rather than relying on compressed statistics. I will conclude by exploring the question of how much cosmological information can be extracted at the field level through a comparison of σ8 constraints obtained from FBI, which directly uses the 3D galaxy density field, and those obtained from n-point functions via SBI.

What does it mean to specify a subregion in a diffeomorphism invariant fashion? This subtle question lies at the heart of many deep problems in quantum gravity. In this talk, we will explore a program of research aimed at answering this question. The two principal characters of the presentation are the extended phase space and the crossed product algebra. The former furnishes a symplectic structure which properly accounts for all of the degrees of freedom necessary to invariantly specify a subregion in gauge theory and gravity, while the latter serves as a quantization of this space into an operator algebra which formalizes the observables of the associated quantum theory. The extended phase space and the crossed product were originally motivated by the problems of the non-invariance/non-integrability of symmetry actions in naive subregion phase spaces, and the non-factorizability/divergence of entanglement entropy in naive subregion operator algebras. The introduction of these structures resolves these issues, while the correspondence between them unifies these resolutions. To illustrate the power of our framework, we demonstrate how the modular crossed product of semiclassical quantum gravity can be reproduced via this approach. We then provide some remarks on how this construction may be augmented in the non-perturbative regime, leading to the notion of a `fuzzy subregion'. We conclude with remarks on currently ongoing and future work, which includes applications to asymptotic and corner symmetries, quantum reference frames, generalized entropy, and the definition of quantum diamonds.

The series of three short lectures provides an introduction to the subject of subgroup growth and related directions of research in asymptotic group theory. For instance, we will discuss polynomial subgroup growth and look at subgroup zeta functions of finitely generated nilpotent groups. We also cover methods from the theory of compact p-adic Lie groups, which have applications to subgroup growth and representation growth.

Higgs branches in theories with 8 supercharges change as one tunes the gauge coupling to critical values.  This talk will focus on six dimensional (0,1) supersymmetric theories in studying the different phenomena associated with such a change. Based on a Type IIA brane system, involving NS5 branes, D6 branes and D8 branes, one can derive a "magnetic quiver” which enables the construction of the Higgs branch using a “magnetic construction” or as a more commonly known object “3d N=4 Coulomb branch”.  Interestingly enough, the magnetic construction opens a window to a new set of Higgs branches which were not available using the well studied method of hyperkähler quotient.  It turns out that exceptional global symmetries are fairly common in the magnetic construction, and few examples will be shown. In all such cases there are strongly coupled theories where Lagrangian description fails, and the magnetic construction is helpful in finding properties of the theory.  Each Higgs branch can be characterized by a phase diagram which describes the different sets of massless fields around vacua. We will use such diagrams to study how Higgs branches change.  If time permits we will show an interesting exceptional sequence consisting of SU(3) — G2 — SO(7).