Mathematical and Theoretical Physics Seminar 数学与理论物理研讨会

All times are in China Standard Time (UTC+8). You can subscribe to the seminar schedule via this link. Posters of all talks can be found in this link.

1. 2026, November 14 Saturday 10:00–11:00 Upcoming Event

   Unifying spacetime approaches to quantum mechanics

   Nahuel Diaz

   Los Alamos National Laboratory

   Venue

   Online

   Tencent Meeting

   180-706-582 (password: 1927)

   Abstract

   Recent efforts to formulate quantum mechanics in a way that treats space and time on a more equal footing have led to a variety of spacetime-oriented approaches. In this talk, I will introduce spacetime states, the central objects of the recently developed framework of spacetime quantum mechanics, and show how several existing proposals can be understood as different manifestations of a common underlying structure. In particular, path integrals, quantum states over time, pseudo-density matrices, the Page and Wootters mechanism, superdensity operators, and timelike-entanglement proposals arise from spacetime states through particular evaluations, reductions, or maps. I will emphasize how this perspective clarifies the information encoded by different temporal-state constructions, including their connections to unequal-time correlation functions and Kirkwood-Dirac quasiprobabilities. I will also briefly discuss applications to temporal entanglement, tensor networks, out-of-time-ordered correlators, and relativistic quantum field theory.

2. 2026, November 04 Wednesday 15:00–16:00 Upcoming Event

   Generalized Cluster States and Strip 2-Algebras

   Shuhei Ohyama

   RIKEN

   Venue

   Online

   Tencent Meeting

   137-769-365 (password: 1927)

   Abstract

   This talk will discuss 2d cluster states with non-invertible symmetries and strip 2-algebras.

3. 2026, October 30 Friday 10:00–11:00

   Quantum Correlations Across Space and Time

   James Fullwood

   Hainan University

   Venue

   Central South University, Xiaoxiang Campus, Physics Building 541

   Tencent Meeting

   907-200-806 (password: 1927)

   Abstract

   This talk explores the fundamental distinctions between bipartite quantum correlations across spacelike and timelike separated measurements. While spacelike separated measurements yield local probabilities that remain independent of one another, sequential measurements are governed by the Lüders-von Neumann distribution, which introduces measurement back-action. This measurement dependence creates a temporal asymmetry that provides a clear arrow of time not present in spatial correlations. To mathematically encode these temporal expectation values, the pseudo-density matrix (PDM) formalism is introduced. Unlike standard density matrices that are strictly positive semi-definite, PDMs can admit negative eigenvalues, which act as a witness to quantum correlations that imply causation.

   Recording
4. 2026, October 14 Wednesday 15:00–16:00

   Quantum Stochastic Processes with Kirkwood-Dirac Quasiprobabilities

   Kelvin Onggadinata

   Nanyang Technological University, School of Physical and Mathematical Sciences (SPMS)

   Venue

   Online

   Tencent Meeting

   933-971-036 (password: 1927)

   Abstract

   Classical stochastic processes — multi-time joint probability distributions over outcomes — are powerful and ubiquitous tools for modelling owing to their ability to capture full statistics and temporal correlations. In this work, we look into an alternative description of a quantum stochastic process obtained from a multi-time quantum process with measurements at each discrete time using Kirkwood-Dirac (KD) quasiprobability, which we refer to as the KD-process. We show that the KD-process can well characterize whether a stochastic process is classical/quantum and Markovian/non-Markovian. In particular, we demonstrate consistency with the classification of non-coherence-detecting-and-generating (NCGD) and non-discord-generating-and-detecting (NDGD) dynamics as classical processes. Moreover, we show through several examples that the KD-process recovers the underlying classical stochastic process, whereas the standard approach characterized as quantum -- thus drawing a tighter bound at the classical-quantum boundary. We discuss the classical simulability of the KD-process using a Monte Carlo sampling method, and identify space complexity and sampling complexity as the additional resources for the simulation. We find that sampling complexity grows with the nonpositivity of the KD-process, and that Markov processes enable Markov chain sampling, which can significantly reduce the space complexity. Lastly, we demonstrate an application of the KD-process as a tool to examine the probabilistic evolutions of quantum computing. Using Grover's algorithm as a case study, the KD-process reveals a Markovian structure with striking resemblance to the classical unstructured search algorithm, and that sampling complexity grows sub-exponentially with the search size — signifying the hardness of classically simulating quantum computation even when the computational speedup is only quadratic.

   Recording
5. 2026, July 24 Friday 10:00–12:00

   A Bootstrap Approach to Fermion Condensation

   Zijie Wan 万梓杰

   Nankai University, Chern Institute of Mathematics

   Venue

   中南大学潇湘校区物理楼541

   Abstract

   Anyon condensation provides a powerful framework for understanding phase transitions between topological orders. While a systematic bootstrap analysis for bosonic anyon condensation has been well established (Kong 2014), a rigorous mathematical treatment of fermion condensation remains underdeveloped. In this talk, we apply a bootstrap approach to $2d$ condensation from a bosonic topological order (described by $\mathcal{C}$, a unitary modular tensor category (UMTC)) to a fermionic topological order (described by $\mathcal{D}$, a UMTC over $\text{sRep}(\mathbb{Z}_2^f)$). We show that the local excitations in $\mathcal{D}$ — a local boson and a local fermion — correspond to a direct sum $A = A_0 \oplus A_1$ in $\mathcal{C}$, which forms a connected supercommutative symmetric normalized-special super $*$-Frobenius algebra with $\dim A_0 = \dim A_1$. We call this a fermionic $2d$-condensable algebra. Then we use bootstrap method to analyze the properties of the condensed phase $\CD$ and the domain wall $\CE$ between these two topological phases. We also discuss the bulk-to-wall maps and compare with the familiar bosonic condensation scenario.

6. 2026, July 17 Friday 10:00–12:00

   From DHR Sectors to DHR Bimodules: Superselection Theory for Infinite Quantum Spin Chains

   Mei-Hui Xiao 肖美慧

   Sun Yat-sen University, School of Physics and Astronomy

   Venue

   中南大学潇湘校区物理楼541

   Tencent Meeting

   734-565-112 (password: 1927)

   Abstract

   Traditional descriptions of internal symmetry begin with a field algebra, a symmetry group, and a Hilbert-space representation. The observable algebra is then obtained as the fixed-point algebra, and the Hilbert space decomposes into charge sectors associated with irreducible representations of the symmetry group. In contrast, DHR superselection theory adopts a bottom-up perspective: it starts from the net of local observable algebras and describes charges as localized and transportable representations that agree with the vacuum representation outside bounded regions.For infinite quantum lattice systems, the usual representation-theoretic formulation remains dependent on a distinguished ground-state representation. DHR bimodule theory replaces states by unital completely positive maps and Hilbert-space representations by bimodule. Applied to the identity channel of the quasi-local algebra, this construction produces a canonical, state-independent C*-tensor category of localizable bimodules. In this talk, I will review the basic structure of DHR theory, introduce DHR bimodules and their localization condition, and explain the role of weak algebraic Haag duality in constructing a braiding. I will conclude with fusion spin chains associated with a unitary fusion category, whose DHR bimodule category is braided equivalent to the Drinfeld center.

   Recording
7. 2026, April 17 Friday 10:00–11:00 am

   Generalized symmetries and their application in topological phases of matter

   Weiguang Cao 曹伟光

   University of Southern Denmark, Centre for Quantum Mathematics

   Venue

   中南大学潇湘校区物理楼541

   Tencent Meeting

   730-795-041 (password: 1927)

   Abstract

   Recently, the notion of symmetry has been generalized, including high form, subsystem, and noninvertible symmetries. These novel symmetries have extended our understanding of topological phases of matter. In this talk, I will review the recent development on generalized symmetry, with a focus on noninvertible symmetry and the phases protected by it. I will present a general method to classy a broad class of noninvertible symmetry protected topological phases (NISPTs), together with concrete lattice realizations. Finally I will show that NISPT is a natural platform to exhibit the connection between noninvertibility and entanglement.

   Recording

No seminars listed for this year.

1. 2026

   Almost-idempotent quantum channels and approximate C*-algebras

   Alexei Kitaev

   Preprint · arXiv:2405.02434

2. 2026

   An operator algebraic approach to fusion category symmetry on the lattice

   David E. Evans, Corey Jones

   Preprint · arXiv:2507.05185