Talks

W-algebras are a family of vertex algebras obtained as Hamiltonian reductions of affine vertex algebras parametrized by nilpotent orbits. The W-algebras associated with regular nilpotent orbits enjoy the Feigin-Frenkel duality. More recently, Gaiotto and Rap\v{c}\'ak generalize this result to hook-type W-algebras with the triality for vertex algebras at the corner. In this talk, I will present the correspondence of representation categories for the hook-type W-superalgebras and how to gain general W-algebras in type A from hook-type W-algebras. The talk is based on joint works with my collaborators.

---

Zoom link https://pitp.zoom.us/j/92163414611?pwd=a1A5NHUrbEpxUUVuS3pEd1VYQk5kdz09

Network nonlocality, and more specifically, triangle network nonlocality, is a basic feature of modern causal modelling when going beyond Bell scenarios. However, despite the apparent simplicity of the problems one may formulate, relatively little is known due to the hardness of certifying nonlocality in networks. In this talk, I will describe a motivating example of a quantum triangle distribution, the Elegant Joint Measurement due to Nicolas Gisin, that is strongly believed to be nonlocal even in the presence of experimental noise. I will then present the ongoing effort to produce a computer-assisted proof of nonlocality for this distribution, thereby developing a toolkit to tackle general nonlocality problems. This effort is based on the inflation technique for causal inference, but taken to higher levels than what was generally considered tractable. This is made possible by a number of optimization techniques, involving symmetry reductions, branch-and-bound optimization, and most importantly, the use of a Frank-Wolfe algorithm to bypass the need to call a standard linear program solver.

---

Zoom link https://pitp.zoom.us/j/97499052021?pwd=R1EyU2pmc1hFSzJ1UEpJQ1h0RnQzdz09

Atmospheric characterisation of habitable-zone exoplanets is a major frontier of exoplanet science. The detection of atmospheric signatures of habitable Earth-like exoplanets is challenging due to their small planet-star size contrast and thin atmospheres with high mean molecular weight. Recently, a new class of habitable sub-Neptune exoplanets, called Hycean worlds, have been proposed, which are expected to be temperate ocean-covered worlds with H2-rich atmospheres. Their large sizes and extended atmospheres, compared to rocky planets of the same mass, make Hycean worlds significantly more accessible to atmospheric spectroscopy. Several temperate Sub-Neptunes have been identified in recent studies as candidate Hycean worlds orbiting nearby M dwarfs that make them highly conducive for transmission spectroscopy with JWST. Recently, we reported the first JWST spectrum of a possible Hycean world, K2-18 b, with detections of multiple carbon-bearing molecules in its atmosphere. In this talk, we will present constraints on the atmospheric composition of K2-18 b and on the temperature structure, clouds/hazes, atmospheric extent, chemical disequilibrium and the possibility of a habitable ocean underneath the atmosphere. We will discuss new observational and theoretical developments in the characterisation of candidate Hycean worlds, and their potential for habitability. Our findings demonstrate the unprecedented potential of JWST for characterising Hycean worlds, and temperate sub-Neptunes in general, and open a new era of atmospheric characterisation of habitable-zone exoplanets with JWST.

---

Zoom link https://pitp.zoom.us/j/98012554989?pwd=b0pCYkIvYmd2Y2hueUExQXBNVG8vZz09

Abstract TBA

---

Zoom link https://pitp.zoom.us/j/97897878725?pwd=dHZNUEc5cVlkU2ZNdU14bEhIRmFPZz09

Inflation remains one of the enigmas in fundamental physics. While it is difficult to distinguish different inflation models, information contained in primordial non-Gaussianity (PNG) offers a route to break the degeneracy. In galaxy surveys, the local type PNG is usually probed by measuring the scale-dependent bias in the galaxy power spectrum on large scales, where cosmic variance and systematics are also large. Other types of PNG need bispectrum, which is computationally challenging and is contaminated by gravity. I will introduce a new approach to measuring PNG by using the reconstructed density field, a density field reversed to the initial conditions from late time. With the reconstructed density field, we can fit a new template at the field level, or compute a near optimal bispectrum estimator, to constrain PNG. By reconstructing the initial conditions, we remove the nonlinearity induced by gravity, which is a source of confusion when measuring PNG. Near optimal bispectrum estimator mitigates computational challenges. This new approach shows strong constraining power, offers an alternative way to the existing method with different systematics, and also follows organically the procedure of baryon acoustic oscillation (BAO) analysis in large galaxy surveys. I will present a reconstruction method using convolutional neural networks that significantly improves the performance of traditional reconstruction algorithms in the matter density field, which is crucial for more effectively probing PNG. This pipeline can enable new observational constraints on PNG from the ongoing Dark Energy Spectroscopic Instrument (DESI) and Euclid surveys, as well as from upcoming surveys, such as that of the Nancy Grace Roman Space Telescope.

---

Zoom link https://pitp.zoom.us/j/92361466496?pwd=ZlljUGlKaTVlSFZIV21NUHNGY2RRUT09