Scientific Series

Our ability to model cosmological observations has reached an awesome level, a tour de force of observational innovation, sophisticated statistical inference, and delicate numerical computation. There’s little doubt that the Standard Cosmological Model will stand the test of time. But what has it told us and what is still missing? What are the prospects for learning particle physics and condensed matter from cosmology? And what can the path we’ve taken to reach this point tell us about where it might lead?

The elliptic genus is a powerful deformation invariant of 1+1D SQFTs: if it is nonzero, then it protects the SQFT from admitting a deformation to one with spontaneous supersymmetry breaking. I will describe a "secondary" invariant, defined in terms of mock modularity, that goes beyond the elliptic genus, protecting SQFTs with vanishing elliptic genus. The existence of this invariant supports the hypothesis that the space of minimally supersymmetric 1+1D SQFTs provides a geometric model for universal elliptic cohomology. Based on joint works with D. Gaiotto and E. Witten.

Primordial SU(2) gauge fields and axions can contribute to the physics of
inflation. In this class of models, both the gauge field and axion acquire
a VEV, which is P and CP breaking and enriches the phenomenology of
particles with spin. Their multifaceted phenomenology and unique
observational signatures, e.g., chiral primordial gravitational waves and
gravitational leptogenesis, turned this class of models to a hot topic of
research in the past nine years. In this talk, first, I will briefly
review the different realizations of this setup. Next, I will tell you
about the three different types of particles produced by the SU(2) gauge field,
i.e., scalar, fermion, and spin-2 particles and their observable
signatures. In particular, the new spin-2 field produces
chiral gravitational waves, which can be detected with LiteBIRD, CMB-S4,
adv LISA, and BBO. Last but not least, I will tell you about the fermion
generation during inflation, dark and visible, as yet another generous
opportunity offered by the primordial SU(2)!

Connections between representation categories of quantum groups and vertex operator algebras (VOAs) have been studied since the 1990s starting with the pioneering work of Kazhdan and Lusztig. Recently, connections have been found between unrolled quantum groups and certain families of VOAs. In this talk, I will introduce unrolled quantum groups and describe their connections to the Singlet, Triplet, and Bp vertex operator algebras.

Factorization algebras provide a flexible language for describing the observables of a perturbative QFT, as shown in joint work with Kevin Costello. In joint work with Eugene Rabinovich and Brian Williams, we extend those constructions to a manifold with boundary for a special class of theories that includes, as an example, a perturbative version of the correspondence between chiral U(1) currents on a Riemann surface and abelian Chern-Simons theory on a bulk 3-manifold. Given time, I'll sketch a systematic higher dimensional version for higher abelian CS theory on an oriented smooth manifold of dimension 4n+3 with boundary a complex manifold of complex dimension 2n+1. (This talk will be very informal.)

I will start with an introduction into the framework of perturbative algebraic quantum field theory (pAQFT), which is a mathematically rigorous approach to perturbative QFT. In its original formulation, it is based on the Haag-Kastler axiomatic framework, where locality is a fundamental principle. In my talk I will discuss how it can be extended to treat also non-local observables, with potential applications to effective quantum gravity

Thus far, the non-linear regime of structure formation is only accessible through expensive numerical N-body simulations since the conventional ana-
lytic treatment of cosmic density fluctuations via the hydrodynamical equations runs into severe problems even in a mildly non-linear regime. I will give an overview of Kinetic Field Theory, a novel analytic approach to cosmic large-scale structure formation, which provides a density fluctuation power spectrum that agrees well with state of the art N-body simulations up to k = 10h Mpc−1. I will point out how Kinetic Field Theory avoids the difficulties of standard perturbation theory by construction and allows to proceed deeply into the non-linear regime of density fluctuations. I will give a summary of the most important results and recent developments for cosmic structure formation and briefly show applications of Kinetic Field Theory outside of cosmology, stressing the opportunities this method provides for the study of the physics behind structure formation. I will then focus my discussion on how the form of the interaction potential influences the formation of cosmic structures in the highly non-linear regime and the implications it bears on the NFW density profile of dark matter halos.

Scattering amplitudes of massive spin-2 particles generically grow with energy and lead to violations of perturbative unitarity. One way to partially soften such amplitudes is with the infinite towers of particles present in Kaluza-Klein theories. In this talk I will discuss in detail this mechanism of unitarization for general dimensional reductions of pure gravity and show that it leads to some interesting constraints on the eigenfunctions and eigenvalues of the scalar Laplacian on closed manifolds. A consequence of these constraints is that there exists an upper bound on the gaps between Kaluza-Klein excitations of the graviton, which applies also to Calabi-Yau compactifications of string theory.   

Merging compact objects encode a vast deal of information about their progenitor stellar systems, such as the types of galactic environments they were born in, the intricacies of stellar evolution the persisted throughout their lives, and the physics of the supernovae that marked their deaths. In this talk, I will highlight multiple open questions that can be illuminated through a combination of compact objects observations (via gravitational waves and/or electromagnetic radiation) and computational modeling of environments that lead to the formation of black holes and neutron stars. I first focus on how the growing catalog of black hole mergers observed by the LIGO/Virgo network can place constraints on binary black hole formation scenarios, both by uncovering gravitational-wave sources that have features specific to a subset of formation scenarios (such as spins that are anti-aligned from the orbital angular momentum, high masses that occupy the pair instability mass gap, and distinguishable eccentricities at merger) and through pairing Bayesian hierarchical inference with state-of-the-art astrophysical models. Next, I will show how various uncertain aspects of binary stellar evolution and supernova physics can be constrained by phenomena attributed to merging neutron stars, such as enigmatic r-process enrichment in globular clusters and the association between short gamma-ray bursts and their host galaxies.

At the heart of the quantum measurement problem lies the ambiguity about exactly when to use the unitary evolution of the quantum state and when to use the state-update in dynamics of quantum mechanical systems. In the Wigner’s friend gedankenexperiment, different observers (one of whom is observed by the other) describe one and the same interaction differently. One – the friend – uses the state-update rule and the other – Wigner – chooses unitary evolution. This can lead to paradoxical situations in which Wigner and his friend assign different probabilities to the outcomes of subsequent measurements. In my talk, I will apply the Page-Wootters mechanism (PWM) as a timeless description of the Wigner's friend-like scenario. This description assigns one timeless state to the entire experimental scenario from which it is possible to derive probabilities without the need to involve the evolution of the quantum state during – and in-between – measurements. I will consider several rules for assigning two-time conditional probabilities within the PWM. All of these reduce to standard (“textbook”) rules for non-Wigner’s friend scenarios. However, when applied to the Wigner’s friend setup, they differ. Each rule potentially resolves the probability-assignment paradox in a different way. Moreover, one rule imposes that a joint probability distribution for the measurement outcomes of Wigner and his friend is well-defined only when Wigner’s measurement does not disturb the friend’s memory, in agreement with the recent “no-go theorem for observer-independent facts

(with Veronika Baumann, Flavio Del Santo, Alexander R. H. Smith, Flaminia Giacomini, and Esteban Castro-Ruiz)

In order to satisfy the Reeh-Schlieder theorem, I study the infinite-dimensional Hilbert spaces using von Neumann algebras. I will first present the theorem that the entanglement wedge reconstruction and the equivalence of relative entropies between the boundary and the bulk (JLMS) are exactly identical. Then I will demonstrate the entanglement wedge reconstruction with a tensor network model of von Neumann algebra with type II1 factor, which guarantees the equivalence between the boundary and the bulk. I will further sketch that this toy model can be generalized to provide more general von Neumann algebras, including the case of a type III1 factor. This can give further insights to understanding quantum gravity from an algebraic perspective.

We will investigate a common property of the measurements used in measurement-based quantum computing paradigms. We will show how this relates to the notion of equiangular planes. We will ask when a continuous collection of such planes can give a universal model. Surprisingly, in a sense that will be made precise, octonionic lines turn out to be the unique answer. This research is motivated by the challenge to construct a measurement-based model that exploits chemical protection given by the symmetries of certain molecules.  A joint work with Michael Freedman and Zhenghan Wang.