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Groupe de Travail EDP et Théorie Spectrale

Sharp spectral gap for degenerated Witten Laplacian

Lois Delande

( (Université de Bordeaux) )

Salle de Conférences

le 19 avril 2024 à 11:00

In this talk I am interested in formulas describing the low-lying eigenvalues of the Witten Laplacian ΔV=h2Δ+V2hV\Delta_V = -h^2\Delta + | V^{\prime} |^2 - h V^{\prime \prime}. The case where VV is a Morse function has been largely studied and here I try to obtain similar results when VV has some degeneracy. In the end of the presentation I will also give an example of new behaviors that were not observed in the Morse case.