主持人：骆文斌 青年研究员
报告简介：
The essential minimum of a height function is the minimal value that the height function can attain at generic points. There are methods to compute upper and lower bounds for the essential minimum. In a joint work with Ricardo Menares, Binggang Qu, and Martin Sombra, we prove using linear programming techniques that the difference between the upper and lower bounds can be made arbitrarily small. Therefore, one can devise a theoretical algorithm to compute the essential minimum with arbitrary precision and thus the essential minimum is a "computable" real number. This result has applications in several classical problems like the integral Chebyshev constant of the unit interval, the spectrums of the Zhang-Zagier and the Faltings heights and the asymptotic of the length of the shortest vector in the lattice associated to the Grassmannian Gr(2,4).
主讲人简介：
José Ignacio Burgos Gil，西班牙马德里数学科学研究所Instituto de Ciencias Matemáticas (ICMAT）教授。研究领域算术几何中Arakelov几何，Motive和Regulator等方向。此外，在计算机视觉和量子化学中亦有贡献。主要成果发表在Invent. Math, Duke Math. J., Ann. Sci. Ecole Norm. S., Mathematics of Computation等期刊。
