Let X be a regular, proper, flat and generically smooth scheme over the spectrum of a (strict) DVR S.
Bloch conjectured a formula which relates algebraic differential forms of X with the total dimension of the l-adic vanishing cohomology of X/S.
In this talk I’ll describe a proof of this formula using methods from non-commutative and derived algebraic geometry.
This is a joint work with Dario Beraldo.
 
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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.

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 
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 
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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