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            <title xml:lang="en">Analysis for Bismut hypoelliptic Laplacian in the double asymptotic of large friction and low temperature</title>
            <title xml:lang="fr">Analyse du Laplacien hypoelliptique de Bismut dans la double asymptotique des grandes frictions et basses températures</title>
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                <title xml:lang="en">Analysis for Bismut hypoelliptic Laplacian in the double asymptotic of large friction and low temperature</title>
                <title xml:lang="fr">Analyse du Laplacien hypoelliptique de Bismut dans la double asymptotique des grandes frictions et basses températures</title>
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                <authority type="supervisor">Francis Nier</authority>
                <authority type="jury">Jérôme Le Rousseau [Président]</authority>
                <authority type="jury">Xiaonan Ma [Rapporteur]</authority>
                <authority type="jury">Laurent Michel [Rapporteur]</authority>
                <authority type="jury">Jean-Michel Bismut</authority>
                <authority type="jury">Yannick Bonthonneau</authority>
                <authority type="jury">Ursula Ludwig</authority>
                <authority type="jury">Caterina Valcu</authority>
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                <term xml:lang="en">Analysis on manifolds</term>
                <term xml:lang="en">Bismut's hypoelliptic Laplacian</term>
                <term xml:lang="en">Geometric Kramers-Fokker-Planck operators</term>
                <term xml:lang="fr">Analyse sur les variétés</term>
                <term xml:lang="fr">Laplacien hypoelliptique de Bismut</term>
                <term xml:lang="fr">Opérateurs de Kramers-F&gt;okker-Planck géométriques</term>
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              <p>In my thesis, we focus on the lower part of the spectrum of Bismut’s hypoelliptic Laplacian. To achieve this, we begin by revisiting a proof of the sub-elliptic inequality for geometric KramersFokker-Planck operators, a class of operators to which the hypoelliptic Laplacian belongs. In the second step, we establish the spectral convergence of Bismut’s hypoelliptic Laplacian to the Witten Laplacian in the low-temperature and high-friction limit. This convergence enables a comparison between the spectra of these two operators.</p>
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              <p>Dans ma thèse, on s’intéresse au bas du spectre du Laplacien hypoelliptique de Bismut. Pour y parvenir, on commence par refaire une démonstration de l’inégalité sous-elliptique pour les opérateurs de Kramers-Fokker-Planck géométriques, une classe d’opérateurs dont fait partie le Laplacien hypoelliptique. Dans un second temps, on établit la convergence spectrale du Laplacien hypoelliptique de Bismut vers le Laplacien de Witten dans la limite de basse température et de grande friction. Cette convergence permet la comparaison entre le spectre de ces deux opérateurs.</p>
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