Laboratoire Analyse, Géométrie et Applications

CNRSParis Citelogo-UP13-2

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Lundi 27 mars à 14h en Amphi Euler
- L’exposé sera suivi à 15 heures du Thé du Laga en Amphi Euler -


Prof. Hiroshi MATANO (Tokyo U.) www.s.u-tokyo.ac.jp/en/people/matano_hiroshi/

Title: « Dynamics of order-preserving systems with mass conservation »

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Abstract : In this talk, I will discuss the dynamics of order-preserving systems having a certain mass conservation property. The base space $X$ is an ordered metric space and we consider a semi-dynamical system generated by a continuous map $F: X \to X$ which is order preserving and compact. We further assume that there exists a strictly monotone map $M: X \to {\bf R}$ such that $M(F(u))=M(u)$ (mass conservation property).Among other things we show that any bounded orbit converges to a fixed point (convergence theorem) and that the existence of one fixed point implies the existence of a continuum of fixed points that are totally ordered (structure theorem). This latter result, when applied to a linear problem for which 0 is always a fixed point, implies automatically the existence of positive fixed points. These theorems extend earlier related results considerably, with a notably simpler proof.I will mention a number of applications of the above results including mathematical models for transportation by molecular motors with time-periodic or autonomous coefficients, chemical reversible reaction models and two-component competition-diffusion systems.
This talk is based on a joint work with Toshiko Ogiwara and Danielle Hilhorst.

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Colloquium du LAGA
Jeudi 19 janvier 15h30 - 16h30, Amphi Euler
Suivi du Thé du Laga en B407.

Prof. Lars Hesselholt (Nagoya/Copenhague)

Title: Topological Hochschild homology and the Hasse-Weil zeta function

Abstract: In the nineties, Deninger gave a detailed description of a
conjectural cohomological interpretation of the (completed) Hasse-Weil zeta
function of a regular scheme proper over the ring of rational integers. He
envisioned the cohomology theory to take values in countably infinite
dimensional complex vector spaces and the zeta function to emerge as the
regularized determinant of the infinitesimal generator of a Frobenius flow.
In this talk, I will explain that for a scheme smooth and proper over a
finite field, the desired cohomology theory naturally appears from the Tate
cohomology of the action by the circle group on the topological Hochschild
homology of the scheme in question.