Seminars

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ABSTRACT: In the 1980s, Witten used a Morse function f to construct a deformation Dt of the Hodge-deRham Laplacian D on skew-symmetric tensors (or differential forms) such that as t → ∞ the low eigensections of Dt concentrate near critical points of f and the low eigenspaces of D can be calculated in terms of local data at the critical points of f. Since then, Witten deformation has been extensively studied, and well-understood, yet calculating local data is generally a difficult problem. In a joint work with Kwangho Choi, we applied a Witten deformation argument to symmetric tensors to obtain a dimension bound on divergencefree Killing p-tensors via local data and explicitly calculated the local data for p = 2 using canonical commutation relations (CCR) – CCR is a synonym of “symplectic” in some contexts.