Talks

I will present recent work (to appear soon) on the homological mirror symmetry about the universal centralizers $J_G$, for any complex semisimple Lie group $G$. The A-side is a partially wrapped Fukaya category of $J_G$, and the B-side is the category of coherent sheaves on the categorical quotient of a dual maximal torus by the Weyl group action (with some modification if $G$ has a nontrivial center).

In her live Perimeter Public Lecture webcast on November 4, 2020, physicist Catherine Beauchemin used contemporary examples from COVID-19 and influenza to explain eroding public trust in health research – and why a dose of physics may be just the prescription we need. Beauchemin is a Professor of Physics at Ryerson University and a Deputy Program Director in the RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program in Japan.

The Fermi-Hubbard model is of fundamental importance in condensed-matter physics, yet is extremely challenging to solve numerically. Finding the ground state of the Hubbard model using variational methods has been predicted to be one of the first applications of near-term quantum computers. In this talk, I will discuss recent work which carried out a detailed analysis and optimisation of the complexity of variational quantum algorithms for finding the ground state of the Hubbard model, including extensive numerical experiments for systems with up to 12 sites. The depth complexities we find are substantially lower than previous work. If our numerical results on small lattice sizes are representative of the somewhat larger lattices accessible to near-term quantum hardware, they suggest that optimising over quantum circuits with a gate depth less than a thousand could be sufficient to solve instances of the Hubbard model beyond the capacity of classical exact diagonalisation. I will also discuss a proof-of-principle implementation on Rigetti quantum computing hardware.

The talk is based on joint work with Chris Cade, Lana Mineh and Stasja Stanisic ( arXiv:1912.06007 , arXiv:2006.01179 ).

Gravitational waves provide a unique way to study the universe. From the initial direct detection of coalescing black holes in 2015, to the ground-breaking multimessenger observations of coalescing neutron stars in 2017, and continuing with the now routine detection of merging stellar remnants, gravitational wave astronomy has quickly matured into a key aspect of modern physics. After briefly discussing what we've begun to learn from the new gravitational-wave transient catalog published by the LIGO, Virgo, and KAGRA collaborations (GWTC-2), I will discuss novel tests of fundamental physics GWs enable. In particular, I will focus on our current understanding of matter effects during the inspiral of compact binaries and matter at supranuclear densities, including possible phase transitions, through tests of neutron star structure. Detailed knowledge of dynamical interactions between coalescing stars, observations of extreme relativistic astrophysical systems, terrestrial experiments, and nuclear theory provide complementary views of fundamental physics. I will show how combining aspects from all these will improve our understanding of dense matter through the example of how we can determine whether newly observed objects are neutron stars or black holes.

The standard model of cosmology is built upon on a series of propositions on how the early, intermediate, and late epochs of the Universe behave. In particular, it predicts that dark energy and dark matter currently pervades the cosmos. Understanding the properties of the dark sector is plausibly the biggest challenge in theoretical physics. There is, however, a broad assumption in cosmology that the Universe on its earlier stages is fully understood and that discrepancies between the standard model of cosmology and current data are suggestive of distinct dark energy properties. Uncertainties on the validity of this hypothesis are not usually taken into account when forecasting survey capabilities, even though our investigations might be obfuscated if the intermediate and early Universe did behave abnormally. In this colloquium, I propose a program to investigate dark energy and earlier aspects of our Universe simultaneously, through space missions in the 2020s in combination with ground-based observatories. This program will help guide the strategy for the future LSST and WFIRST supernovae and weak lensing surveys. My investigations on how properties of the early and intermediate Universe affect inferences on dark energy (and vice-versa) will also support community understanding of how future missions can be employed to test some of the core hypotheses of the standard model of cosmology.

Flat bands in Moire superlattices are emerging as a fascinating new playground for correlated electron physics. I will present the results of several studies inspired by these developments. First, I will address the question of whether superconductivity is possible even in the limit of a perfectly flat band. Then, I will discuss transport properties of a spin-polarized superconductor in the limit of zero spin-orbit coupling, where the topological structure of the order parameter space allows for a new dissipation mechanism not known from conventional superconductors. If time allows, I will also discuss the interpretation of new measurements of the electronic compressibility in twisted bilayer graphene, indicating a cascade of symmetry-breaking transitions as a function of the density of carriers in the system. 

References:

https://arxiv.org/abs/2006.10073

https://arxiv.org/abs/1912.08848

https://arxiv.org/abs/1912.06150

Neutrino oscillations have been probed during the last few decades using multiple neutrino sources and experimental set-ups. In recent years, very large volume neutrino telescopes have started contributing to the field. These large and sparsely instrumented detectors observe atmospheric neutrinos for combinations of baselines and energies inaccessible to other experiments. IceCube, the largest neutrino telescope in operation, has used this to measure standard oscillations and place limits on exotic proposals, such as sterile neutrinos. In this talk, I will go over the newest results from IceCube as well as the improvements expected thanks to a new detector upgrade to be deployed in the near future.

The compatibility-hypergraph approach to contextuality (CA) and the contextuality-by-default approach (CbD) are usually presented as products of entirely different views on how physical measurements and measurement contexts should be understood: the latter is based on the idea that a physical measurement has to be seen by a collection of random variables, one for each context containing that measurement, while the imposition of the non-disturbance condition as a physical requirement in the former precludes such interpretation of measurements. The aim of our work is to present both approaches as entirely compatible ones and to introduce in the compatibility-hypergraph approach ideas which arises from contextuality-by-default. We

introduce in CA the non-degeneracy condition, which is the analogous of consistent connectedness (an important concept from CbD), and prove that this condition is, in general, weaker than non-disturbance. The set of non-degenerate behaviours defines a polytope, therefore one can characterize non-degeneracy using a finite set of linear inequalities. We introduce extended contextuality for behaviours and prove that a behaviour is non-contextual in the standard sense if and only if it is non-degenerate and non-contextual in the extended sense. Finally, we use extended scenarios and behaviours to shed new light on our results.