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Séminaire Analyse

organisé par l'équipe Analyse

  • Exponential Sums Equations and Tropical Geometry

    — Francesco Paolo Gallinaro

    2 février 2023 - 11:00Salle de conférences IRMA

    The Exponential-Algebraic Closedness Conjecture, due to Zilber, predicts sufficient conditions for systems of equations involving polynomials and exponentials to be solvable in the complex numbers; it is formulated geometrically, asking about the intersections between complex algebraic varieties and (Cartesian powers of) the graph of the exponential function. The conjecture originated from model theory, and it would imply a strong tameness result for subsets of the complex numbers that are definable using polynomials and exponentials. In this talk, we will briefly recall the motivation of this question and then focus on the case of varieties which split as the product of a linear space and an algebraic subvariety of the multiplicative group. These varieties correspond to systems of exponential sums equations, and the proof that the conjecture holds in this case uses tropical geometry and the theory of toric varieties.

  • TBA

    — Alexandre Goyer

    9 février 2023 - 11:00Salle de conférences IRMA

  • Prime geodesic theorem and closed geodesics for surfaces of large genus

    — Yuhao Xue

    2 mars 2023 - 11:00Salle de conférences IRMA

    Let Mg be the moduli space of hyperbolic surfaces of genus g endowed with the Weil-Petersson metric. We show that as g → ∞, for a generic surface in Mg , the error term in the Prime Geodesic Theorem is bounded from above by g · ^{3/4+eps}. We also show that as g → ∞, on a generic hyperbolic surface in Mg most closed geodesics of length significantly less than √g are simple and non- separating, and most closed geodesics of length significantly greater than √g are not simple, which confirms a conjecture of Lipnowski-Wright.

  • TBA

    — Simon Becker

    9 mars 2023 - 11:00Salle de conférences IRMA

  • Adiabatic Deformations of Quantum Hall Droplets

    — Blagoje Oblak

    16 mars 2023 - 11:00Salle de conférences IRMA