Scientific Series

A large amount of effort has recently been put into understanding the barren plateau phenomenon. In this perspective talk, we face the increasingly loud elephant in the room and ask a question that has been hinted at by many but not explicitly addressed: Can the structure that allows one to avoid barren plateaus also be leveraged to efficiently simulate the loss classically? We present a case-by-case argument that commonly used models with provable absence of barren plateaus are also in a sense classically simulable, provided that one can collect some classical data from quantum devices during an initial data acquisition phase. This follows from the observation that barren plateaus result from a curse of dimensionality, and that current approaches for solving them end up encoding the problem into some small, classically simulable, subspaces. We end by discussing caveats in our arguments including the limitations of average case arguments, the role of smart initializations, models that fall outside our assumptions, the potential for provably superpolynomial advantages and the possibility that, once larger devices become available, parametrized quantum circuits could heuristically outperform our analytic expectations.

Astrophysical compact objects, neutron stars, and black holes are powerful sources of non-thermal electromagnetic emission spanning many orders of magnitude in photon energy, from radio waves to multi-TeV gamma rays. Despite multiple groundbreaking observational discoveries done in recent years, our understanding of the dynamics of relativistic plasmas that produce these emission signatures remains limited. In this talk, I will describe a few successful examples of modeling the observed light coming from these remarkable astrophysical laboratories using various numerical approaches. I will focus on advances in understanding coherent radio emission of rotating neutron stars, pulsars, and multi-wavelength flares from accreting black holes. 

In this talk, I will present a sewing-factorization theorem for conformal blocks in arbitrary genus associated to a (possibly nonrational) $C_2$-cofinite VOA $V$. This result gives a higher genus analog of Huang-Lepowsky-Zhang's tensor product theory. Moreover, I will explain the relation between our result and pseudotraces, and confirm some of the conjectures by Gainuditnov-Runkel. The relationship between our result and coends will also be discussed. The talk is based on an ongoing project (arXiv: 2305.10180, 2411.07707) joint with Bin Gui.

In this talk, I will describe how ideas from geometry and combinatorics can help us understand the mathematical and physical properties of cosmological integrals. From efficiently deriving canonical differential equations to a systematic method for finding a minimal basis for the physical subspace. Time permitting, I will also comment on how geometry and combinatorics control the zeros of cosmological integrands.