Talks

This panel discussion brings together researchers to share insights on effective scholarly writing. Each panelist will highlight two well-written papers: one of their own and one by other authors. Through moderated questions and open audience discussion, panelists will discuss what makes these papers effective, strategies for structuring papers and communicating ideas, and common pitfalls to avoid in academic writing.

Quantum group and its application to knot polynomial was the theme of Witten-Reshtikhin-Turaev theory. The categorfication of quantum group and application to knot homology has been discovered and developed by Khovanov-Lauda, Rouquier, and Webster, in the form of KLRW algebra. With Mina Aganagic and collaborators, we developed a new approach using Fukaya category and relate to KLRW algebra. The geometric origin allows us to give a geometric construction for the categorified coproduct. The talk is based on past work and work in progress with Mina Aganagic, Vivek Shende, Elise LePage, Ivan Danilenko and Yixuan Li.

In this talk, we will provide an overview of recent developments in the quantization of Cylindrically symmetric spacetimes, which contain the Einstein-Rosen gravitational waves. This class of solutions leads to an integrable field theory, and its phase space can be expressed directly in terms of initial data living on a null generator. The corresponding Poisson algebra appears in the double null sheet formulation of full 3+1 gravity (Reisenberger, 2007), as essentially a Poisson subalgebra on each null generator. This suggests that the algebraic quantization introduced by Korotkin-Samtleben in the context of cylindrically symmetric gravity is relevant for the search for the full quantum theory. We will present some results concerning this quantum algebra, where two Wick-type algebraic structures emerge. Finally, we will discus the known quantization of the Einstein-Rosen waves with one polarization, due to Ashtekar-Pierri, as a subsector of the general two polarizations case.

Gravitational waves (GW) from compact binaries provide excellent opportunities for testing general relativity (GR) in the strong- and dynamical-field regime. So far, inspiral-based tests have mostly assumed smooth deviations from GR within a post-Newtonian description, thereby overlooking certain beyond-GR effects that can arise in well-motivated extensions including quantum gravity, dark energy, and dark matter. In this talk, I will present an example of such an overlooked effect arising from massive scalar fields nonminimally coupled to gravity, and discuss recent constraints on this scenario using GW observations. I will then introduce a recently developed AI-based approach that incorporates both smooth and nonsmooth deviations within a unified, theory-agnostic parametrization for inspiral tests of GR. 

Fermi surfaces have a number of fascinating properties, including a continuum of gapless excitations, a landscape of possible collective modes, universal super-area law entanglement, and relevant deformations that can produce non-Fermi liquid quantum critical metals. Their extreme gaplessness makes them difficult to tame with the conventional tools of QFT. Bosonization provides a potential nonperturbative approach by describing Fermi surface dynamics through a collective field living on a part of phase space. However, while such a field is sensible semiclassically, the challenge of treating it quantum mechanically has prevented bosonization from providing as powerful a tool as in one dimension. I will show that general Fermi surfaces can be exactly described by a particular large N limit of a U(N)_1 WZW model, with a tower of irrelevant corrections. This matrix-valued description encodes the noncommutative nature of phase space, and its (solvable) strongly coupled dynamics resolves the naive overcounting of degrees of freedom in the collective field without the need to cut the Fermi surface into patches.