Over the weekend (August 12-14, 2023), Huitao Fang, Kefeng Liu, Hiroshi Matsuzoe and Jun Zhang organized the fourth edition of the Symposium on Information Geometry and Affine Differential Geometry (IGADG IV). While I was unable to travel to Chongqing to attend in person, I gave a remote lecture on Statistical Mirror Symmetry. It was particularly… Read More A talk on Statistical Mirror Symmetry
Last summer, Leonard Wong and Jun Zhang organized a probability workshop at the Annual Meeting of the Statistical Society of Canada and invited me to give a talk. Initially, I was a little apprehensive about giving a talk to an audience of statisticians. Kori is a statistician, and she tells me that the mathematical talks… Read More Hyperbolic Information Geometry
This is a continuation of the previous post on statistical mirror symmetry. In this post, I will explain the conjectural link between this theory and the theory of automorphic forms/algebraic geometry in a bit more detail. The main goal is to pose several questions which are quite puzzling to me but completely outside my wheelhouse… Read More Statistical Mirror Symmetry (and number theory?) Part II
Over the past several years, Jun Zhang and I have been working on a phenomena we call “statistical mirror symmetry.” In mathematics, mirror symmetry is a duality between Calabi-Yau manifolds, in which two such distinct manifolds have closely related geometry. This correspondence was originally discovered by physicists studying string theory, where they observed that distinct… Read More Statistical Mirror Symmetry (and number theory?) Part I
In the previous post on this topic, I wrote about the relationship between optimal transport and information geometry, based on a survey paper by Jun Zhang and myself. This week, I gave a talk at the a SIAM MDS Minisymposium on Optimal Transport for Data Science on Optimal Transport and Information Geometry for Data Science/Machine… Read More Optimal Transport and Information Geometry (a follow up)
Jun Zhang and I have just published a survey paper “When optimal transport meets information geometry” (also available on the arXiv), which is intended to give an overview of some ways in which these two fields interact. Information geometry and optimal transport provide two distinct ways to study probability measures “geometrically.” As suggested by the… Read More Information Geometry and Optimal Transport
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