List of topics I want to present in a mathematically palatable language.
Life processes and information systems: from the cell to large language models (LLMs).Viruses: information storage, transmission, and evolution.Information warfare, organic poisons, infections, and immune systems.The central dogma (Crick): principal information flow in the cell; information reduction under protein folding.Metastability, catalysis, and signaling: signaling in cells, plants, animals, and humans.Information reduction and energy dissipation in epigenesis / development: the emergence of a chick from an egg.Information flows in animal nervous systems and the human brain: (broken) symmetries in olfaction, proprioception, somatosensation, vision, and audition.Modularity of circuitry in cells and in the brain.Poincaré–Sturtevant stochastic representations of geometry; object-dominated life-related (visual and non-visual) signals vs. stochastic continuity of abiotic signals.Stochastic generative combinatorics in languages.Information spaces and Kanerva’s sparse distributed memory (SDM) model.Artificial neural networks, information geometry, and orthogonal symmetries in LLMs.A mathematical perspective on learning, knowledge, and understanding.

 
List of topics I want to present in a mathematically palatable language.
Life processes and information systems: from the cell to large language models (LLMs).Viruses: information storage, transmission, and evolution.Information warfare, organic poisons, infections, and immune systems.The central dogma (Crick): principal information flow in the cell; information reduction under protein folding.Metastability, catalysis, and signaling: signaling in cells, plants, animals, and humans.Information reduction and energy dissipation in epigenesis / development: the emergence of a chick from an egg.Information flows in animal nervous systems and the human brain: (broken) symmetries in olfaction, proprioception, somatosensation, vision, and audition.Modularity of circuitry in cells and in the brain.Poincaré–Sturtevant stochastic representations of geometry; object-dominated life-related (visual and non-visual) signals vs. stochastic continuity of abiotic signals.Stochastic generative combinatorics in languages.Information spaces and Kanerva’s sparse distributed memory (SDM) model.Artificial neural networks, information geometry, and orthogonal symmetries in LLMs.A mathematical perspective on learning, knowledge, and understanding.

Most modern algorithms for computation of conformal blocks in numerical bootstrap applications are based on Zamolodchikov-like recursion relations. These relations come from the idea that conformal blocks have poles in the exchanged scaling dimension, associated to appearance of null states in the corresponding parabolic Verma module. In odd dimensions the pole is simple, the residue is another conformal block, and the recursion relation is well understood. However, in even dimensions double poles can appear, and the structure of the recursion relation is an open problem. In this talk, I will describe the surprisingly subtle solution of this problem in four dimensions. In particular, I will explain that the natural setting for this question is the principal block of the deformed parabolic BGG category O, which can be efficiently studied using Morita theory.  Based on work in progress with Colum Flynn.
 
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Seed Seminar of Mathematics and Physics
Spring ’26: TQFT and Knot Theory 
Non-rational 2d CFTs are defined as unitary CFTs with c > 1, a normalizable vacuum, a discrete spectrum, a modular invariant torus partition function, and no conserved currents beside those of the Virasoro identity module.
Perturbative results and lattice simulations suggest that a large class of these non-rational CFTs can be engineered as critical points of RG flows that couple N copies of unitary Virasoro minimal models, while preserving a non-invertible categorical symmetry of the form Fib⊠N ⋊ SN.
In this talk I will give a pedagogical introduction to fusion categories and their tube algebra representations in terms of defect lines. I will then discuss how to extend the modular conformal bootstrap approach to study 2d CFTs with Fib⊠N ⋊ SN non-invertible categorical symmetry and present some preliminary numerical results for this analysis.Based on 2602.06117 with Balt van Rees and a WIP with Junchen Rong, Francesco Russo and Balt van Rees.
More information: https://seedseminar.apps.math.cnrs.fr/program/#may-27-2026
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Seed Seminar of Mathematics and Physics
Spring ’26: TQFT and Knot Theory 
Coloured Jones and Alexander polynomials are quantum invariants originating in representation theory and their geometric information is an important open problem in quantum topology. We present a new topological perspective that unifies these invariants through the topology of configuration spaces. First, for a fixed N, we define new link invariants: “N th Unified Jones invariant” and “N th Unified Alexander invariant” globalising all coloured Jones and ADO link polynomials of (multi)-colours bounded by N. Asymptotically, Habiro defined his universal knot invariant globalising coloured Jones polynomials by introducing the Habiro ring. For the link case, such globalisation remained open for both sequences of invariants.
We answer this problem coming from representation theory using topological tools. On the representation theory side we define extensions of Habiro type rings. On the topological side, we construct a universal Jones link invariant and a universal Alexander link invariant. Putting these together, our universal invariants of geometrical nature take values in the extended Habiro rings that we construct.
More information: https://seedseminar.apps.math.cnrs.fr/program/#may-27-2026
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Seed Seminar of Mathematics and Physics
Spring ’26: TQFT and Knot Theory 
Quantum Computation is a new paradigm for computation in which data is stored in quantum systems, processed via physical manipulations (unitary gates) of these systems and finally read out using measurements. Theoretically, this gives an exponential speed-up over classical computing for important problems including simulations of quantum many body physics. Recent years have witnessed an acceleration in the development of hardware for quantum computers. One challenge is to make these robust against noise, i.e. unwarranted interactions with the computer’s environment, which may cause computational errors. There are known schemes to overcome this problem and achieve universal fault-tolerant quantum computing.
One of the most powerful software schemes for fault-tolerant quantum computing is through so-called topological quantum error correction. This is deeply connected to topological quantum field theories (TQFT), which are quantum field theories that are invariant under diffeomorphisms of space-time. There is also an ongoing effort to build hardware based on topological phases of matter (described by TQFT in the low-energy regime), as such a computer would be topologically protected – i.e. there is a low probability that noise from the environment will alter the topology of the system/processes and thereby introduce errors.
In this talk, I will survey some of the deep connections between TQFT and Quantum Computing. I will also present details of an ongoing project, which aims to use quantum computing to approximate the Witten-Reshetikhin-Turaev TQFT partition function of a general closed three-manifold with the goal of probing central conjectures in quantum topology. This project is further motivated by a BQP-completeness essentially result due to Freedman, Larsen, Kitaev and Wang, which asserts that any problem which can be efficiently solved by a quantum computer can be reduced (with polynomial overhead) to the computation of the WRT-TQFT partition function.
This project is joint with the following colleagues at Centre for Quantum Mathematics at University of Southern Denmark: J.E. Andersen, S. Hindson, G.K. Potter and K. Wernli.
More information: https://seedseminar.apps.math.cnrs.fr/program/#may-13-2026
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Seed Seminar of Mathematics and Physics
Spring ’26: TQFT and Knot Theory 
I will present ongoing joint work with J. E. Andersen and W. E. Mistegård on a general procedure for expressing WRT invariants of 3-manifolds as finite-dimensional integrals. This technique is based on the universal R-matrix construction and features Faddeev’s quantum dilogarithm in a central way. Natural follow-up questions (in the direction of Witten’s asymptotic expansion conjecture) about the semiclassical behaviour of these integrals will then be touched upon, which will involve a discussion of Yoon’s generalised potential function of a link diagram.
More information: https://seedseminar.apps.math.cnrs.fr/program/#april-29-2026
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Seed Seminar of Mathematics and Physics
Spring ’26: TQFT and Knot Theory 
The symmetry topological field theory (SymTFT) has emerged in the past years as a powerful framework for analyzing generalized symmetries. In this talk, I will review how we can use it to characterize the gapped infrared phases of two-dimensional quantum field theories with an internal symmetry, described in general by a fusion category. I will then discuss extensions of this framework that incorporate space-time symmetries, with a particular focus on time-reversal.
More information: https://seedseminar.apps.math.cnrs.fr/program/#april-29-2026
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Séminaire Amplitudes et Gravitation sur l’Yvette (IHES/IPhT)
Long-range interactions, mediated for instance by photons and/or gravitons, force exclusive S-matrix elements to vanish in D = 4 flat space-time, due to infrared divergences. This poses a challenge to programs, such as positivity and S-matrix bootstrap, that directly rely on the properties of 2-to-2 amplitudes. In this talk, I will introduce stripped amplitudes as IR-finite, analytic, crossing-symmetric and Regge-behaved avatars of standard amplitudes, associated with a physical detector scale $Lambda$. In the regime in which the latter is taken exponentially small than all other scales, they also satisfy a form of unitarity, allowing to derive IR-finite positivity bounds on EFTs, in presence of long-range interactions.
 
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Séminaire Amplitudes et Gravitation sur l’Yvette (IHES/IPhT)
The effective-one-body (EOB) approach is a powerful formalism that maps the two-body problem in general relativity into the motion of a single body in an effective metric. EOB-based models are nowadays providing fast and accurate gravitational wave (GW) templates for comparable-mass coalescing compact binaries, namely the sources observed by the currently operating GW detectors. Third-generation detectors will instead allow us to detect signals from different sources, among which are black hole binaries with a larger mass ratio, which require a dedicated modelling. After briefly introducing the EOB formalism, I will discuss past and ongoing efforts in adapting an EOB waveform model in order to efficiently describe the evolution of large-mass-ratio binaries.
 
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Studying quantum field theories (QFTs) in anti-de Sitter (AdS) space naturally leads to boundary correlation functions that satisfy all the axioms of the conformal bootstrap. Upon taking the radius of the AdS space to infinity, one expects to recover flat space physics. We use this idea to extract bounds on the flat space S-matrix by taking the appropriate limit of numerical conformal bootstrap bounds.
 
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Energy plays a ubiquitous role in physics, and many physical classical field theories obey pointwise energy conditions. However, for QFTs, the study of energy is both richer and more precarious. In this talk, I will derive new families of quantum null energy inequalities (QNEIs), i.e. bounds on integrated null energy, in QFTs in both two and higher dimensions. These are state-independent lower bounds on localised integrals of the stress tensor, and the first of this kind for interacting theories in higher dimensions. These results are new, fundamental constraints on null energy in all quantum field theories. The proofs will include ingredients from field theory and quantum information: the quantum null energy condition (QNEC), strong subadditivity of von Neumann entropies, defect operator expansions, and the vacuum modular Hamiltonians of null intervals and strips.
 
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