Jérémie Unterberger
I am currently assistant professor at the maths institute IECL (Institut Elie Cartan de Lorraine), in the Probability and Statistics team.
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My research interests include constructive field theory (rigorous renormalization techniques), mathematical physics, statistical physics, stochastic calculus, random matrix theory, and
Darwinian evolution theory.
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Projects:
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â—‹ ERC AbioEvo (2020-25) : conditions for the
emergence of evolution during abiogenesis
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â—‹ METALORIGIN (2023, financement INSU): le métal des météorites, moteur de l’évolution abiotique de
la matière organique complexe des surfaces planétaires primitives
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Former projects:
â—‹ ANR SINGULAR (2017-2021) on singular stochastic PDEs and renormalization
â—‹ GDR RENORM on algebraic, analytic and geometric aspects of renormalization
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Selection of significant articles:
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â—‹ Autocatalysis in kinetic chemical networks and origin of life:
Stoechiometric and dynamical autocatalysis for diluted chemical reaction networks, J. Math. Biol. (2002) pdf
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â—‹ Large-scale fluctuations for a generalized random matrix dynamics:
Global fluctuations for log-gas dynamics, Stoch. Proc. Appl. (2018) pdf
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â—‹ Large-scale diffusive limit of KPZ equation through constructive renormalization techniques:
The scaling limit of the KPZ equation in dimension 3 and higher, J. Stat. Phys. (2018). pdf
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â—‹ with J. Magnen: singular stochastic calculus by renormalization techniques,
From constructive field theory to fractional stochastic calculus. (II) Constructive proof of convergence for the Lévy area
of fractional Brownian motion with Hurst index $\alpha\in(1/8,1/4)$, Ann. H. Poincaré (2011). pdf
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â—‹ Fourier-normal ordering "para-product" technique for arbitrary rough paths (Comm. Math. Phys, 2010),
Hölder-continuous rough paths by Fourier normal ordering. pdf
â—‹ and the Springer book (in collaboration with C. Roger, foreword by M. Henkel) :
The Schrödinger-Virasoro algebra. Mathematical structure and dynamical Schrödinger symmetries
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