Depending on nutrient availability, cells switch between two different modes: growth, which requires secretion, and conservation, which requires autophagy, a cellular recycling pathway. The mechanisms underlying the switch between these two modes are not clear. We propose that the evolutionary-conserved Ypt1/Rab1 GTPase, which is essential for the beginning of secretion and macro-autophagy pathways from yeast to human, coordinate this switch by functioning in two different “GTPase Modules” that include “pathway-specific” upstream activators and downstream effectors.     

Séminaire d’Analyse
We construct critical trajectories in kinetic geometry, i.e. curves in (t,x,v) that are tangential to the transport and v-gradient, connecting any two given points, respecting the underlying kinetic scaling, and matching scaling properties of the stochastic trajectories near the starting point. The construction is based on solving the laws of motions with a forcing made up of desynchronised logarithmic oscillations. These critical trajectories provide an  »almost exponential map » that allows to prove several functional analytic estimates. In particular they allow to extend to the kinetic setting the universal estimate for the logarithm of positive supersolutions by Moser 1971, and deduce optimal (weak) Harnack inequalities. This is a joint work with Helge Dietert, Lukas Niebel and Rico Zacher. 
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Séminaire d’Analyse
In this talk we will review the progress on the probabilistic theory of PDEs (random data, additive and multiplicative noise etc.) in recent years. Breakthrough has been made in the subcritical regime, first in parabolic settings, and then in dispersive settings, which also leads to better understanding of a number of important models. However, a number of challenges still exist. This talk is based on joint works with Bjoern Bringmann, Andrea Nahmod, and Haitian Yue.
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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 
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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