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京东 11.11 红包
Igor Krichever:two-torus到spheres的共形调和映射和elliptic CM system——1
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https://www.youtube.com/watch?v=IS1aQ4t5pE4 Informal Mathematical Physics Seminar Igor Krichever, "Conformal harmonic maps of two-torus to spheres and elliptic CM system", part 1 The theory of harmonic maps of Riemann surfaces to spheres or symmetric spaces is a classical problem of differential geometry. In the talk an exact construction of conformal harmonic maps from two-torus to the spheres of any dimension will be presented. They are high dimensional analogs of instanton maps of two-torus to two sphere. A key step in the construction is unexpected connection with the theory of elliptic Calogero-Moser system. The talk is based on joint work in progress of the author with N.Nekrasov Igor Krichever, Nikita Nekrasov——《Novikov-Veselov Symmetries of the Two-Dimensional O(N) Sigma Model》:https://doi.org/10.48550/arXiv.2106.14201 We show that Novikov-Veselov hierarchy provides a complete family of commuting symmetries of two-dimensional O(N) sigma model. In the first part of the paper we use these symmetries to prove that the Fermi spectral curve for the double-periodic sigma model is algebraic. Thus, our previous construction of the complexified harmonic maps in the case of irreducible Fermi curves is complete. In the second part of the paper we generalize our construction to the case of reducible Fermi curves and show that it gives the conformal harmonic maps to even-dimensional spheres. Remarkably, the solutions are parameterized by spectral curves of turning points of the elliptic Calogero-Moser system. Igor Krichever Homepage:http://www.math.columbia.edu/~krichev/index.html ICM2022 Igor Krichever——可积系统理论中的代数几何方法和Riemann-Schottky type problems:BV1rx4y197kz Igor Krichever——《Characterizing Jacobians of algebraic curves with involution》:https://doi.org/10.48550/arXiv.2109.13161 Igor Krichever——《Abelian pole systems and Riemann-Schottky type systems》:https://doi.org/10.48550/arXiv.2202.04585
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