Scientific Series

In this broad-audience talk, I will discuss the basics of gravitational wave theory and the major achievements in the field following the direct observation of the first gravitational wave signal in 2015. Then, I will discuss how gravitational wave data are used to test the validity of general relativity and motivate my current research on the subject.

Although there are good reasons to believe that quantum states are sometimes relativized to observers, there are difficulties for the view that quantum states can only be relativized to conscious macroscopic observers, and also for the view that quantum states can be relativized to any physical system. In this talk, I will argue for an alternative `emergence' approach such that we can indeed write down a description relative to any physical system, but the full formalism of quantum theory emerges only in the limit as the reference system becomes large. If this is true, it poses a challenge for attempts to understand the emergence of the classical regime from the quantum world, since our standard quantum descriptions may presuppose a classical system to which they are relativized. I will describe how this idea might give new insight into Extended Wigner's Friend paradoxes and the measurement problem, and then sketch some ideas for how we might generalize beyond quantum mechanics to characterize descriptions relative to other kinds of reference systems.

Given a vertex operator algebra V, one can define sheaves of conformal blocks on moduli spaces of curves following constructions of Ben-Zvi--Frenkel and Damiolini--Gibney--Tarasca. When V is strongly rational, these sheaves are vector bundles equipped with a projectively flat connection. In this talk, I will explain how these bundles satisfy the compatibility conditions required to form a modular functor. A key consequence of this result is that the category C_V of admissible V-modules is a modular fusion category. This provides a purely algebro-geometric construction of the tensor product on C_V, which is expected to agree with the tensor product defined by Huang and Lepowsky using analytic methods. Time permitting, I will discuss open questions concerning extensions beyond the rational setting. This is joint work with Lukas Woike.

Small naked singularities—those not shielded by a macroscopic event horizon—are ubiquitous in classical General Relativity. Their existence constitutes apparent violations of the weak cosmic censorship conjecture, which asserts that physically reasonable solutions should appear regular to asymptotic observers. In this talk, we will show how the inclusion of stringy and quantum effects resolves these pathologies by uplifting naked singularities into fully regular configurations. Focusing on critical gravitational collapse as a concrete example, we demonstrate that a proper quantum treatment replaces naked singularity formation with black hole formation. This suggests that cosmic censorship is not fundamentally a property of classical General Relativity, but rather emerges only once quantum gravitational effects are taken into account.

Since the 1980s, simulation of quantum many-body systems has been a leading candidate for practical quantum advantage. Yet computing thermal equilibrium properties, a central pillar of this vision, still lacks an end-to-end algorithmic solution. Today, I will present a general-purpose algorithmic and analytic framework for preparing quantum thermal states as a quantum analog of Markov chain Monte Carlo (MCMC) methods, and as a workable model of nature’s system-bath interaction.

In recent years, non-onsite symmetry representations on the
lattice have enabled new insights in both anomalous and non-invertible
symmetries.  In (1+1)D, these can be represented as matrix product
operators (MPO), a type of tensor network that captures the correlated
action on neighbouring sites.  In this talk, I will present the
underlying mathematical structures that govern these symmetries, and
show that these MPOs provide the lattice representation theory of
generalised symmetries in (1+1)D.  Time permitting, I will discuss some
applications of these ideas, in particular how they can be leveraged to
improve computational performance in state of the art in tensor network
algorithms.

Based on arXiv:2509.03600, arXiv:2408.06334

In this talk, I will argue that the universal structure of the corner algebra offers a new perspective on quantum gravity, in which the representation theory of this algebra plays a role as fundamental as that of the Poincaré algebra in quantum field theory. I will discuss the representation theory of the (quantum) universal and extended corner symmetries in a simplified model of spherically symmetric spacetimes, where the corner reduces to a point and the algebra correspondingly simplifies. Furthermore, I will propose a purely algebraic procedure for gluing regions in the quantum theory, compute the entanglement entropy, and derive the entropy–area law for a class of specific coherent states.

Achieving superpolynomial speedups for optimization has long been a central goal for quantum algorithms. I will discuss Decoded Quantum Interferometry (DQI), a quantum algorithm descended from Regev's reduction, that uses the quantum Fourier transform to reduce optimization problems to decoding problems. For approximating optimal polynomial fits over finite fields, DQI achieves a superpolynomial speedup over known classical algorithms. The speedup arises because the problem’s algebraic structure is reflected in the decoding problem, which can be solved efficiently. Whether DQI can also attain quantum advantage for algebraically unstructured optimization problems such as max-k-XORSAT remains an open question. One reason for optimism is that the sparsity of the clause structure in max-k-XORSAT is reflected in the dual decoding problem, which is for LDPC codes. I will describe some current lines of attack on this open question, as well as generalizations of DQI for preparing Gibbs states of Hamiltonians. This talk will target a broad audience without assuming deep background in quantum algorithms.

Decoded Quantum Interferometry (DQI) has been recently proposed as a new quantum algorithm for optimization. Hamiltonian Decoded Quantum Interferometry (HDQI), an extension of DQI, adapts this paradigm to Hamiltonian optimization and Gibbs state preparation. In this work, I will introduce HDQI for general Pauli Hamiltonians and discuss its application to the approximation of Gibbs states.

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.