Soumyajit Saha, Malik Tuerkoen and I have just uploaded our paper “Concavity Properties of solutions of Elliptic Equations under Conformal Deformations” to the Arxiv. This paper studies the solutions for two types of elliptic PDEs and shows that they satisfy certain concavity properties. The main theme of the paper is to generalize away from the… Read More Log-Concavity and Conformal Gauges
After posting the recent video on factoring polynomials, I got a lot of really helpful feedback. In particular, Jeff Suzuki left a comment mentioning his lecture series on the history of mathematics. He has a number of videos on history of the cubic and quartic equation (which start here) and discuss how these formulas were… Read More Recent Finds 3: Fact-checking the history of polynomials
The third Summer of Math Exposition (#SoME3) hosted by Grant Sanderson (3blue1brown) wrapped up this week. Over the past two years, I’ve learned a lot from many of the videos that people produce and it’s been really great to see all the high-quality explanations of math topics. So I am looking forward to seeing what… Read More Recent finds 2: SoME3 and the need for math research exposition
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
Following John Baez’s long running series, I thought I would start writing about math I stumble upon. The first edition discusses a new Youtube series on the Riemann hypothesis and the field with one element.… Read More Recent finds 1: A series on the Riemann Hypothesis
Malik Tuerkoen, Guofang Wei and I have just uploaded our paper “Modulus of Concavity and Fundamental Gap Estimates on Surfaces” to the Arxiv. This paper studies the fundamental gap problem on surfaces with positive curvature and obtains bounds on the gap whose leading order term is sharp. More precisely, we show the following. Main Theorem:… Read More Modulus of Concavity and Fundamental Gap Estimates on Surfaces
A few weeks ago, I uploaded the preprint Curvature-Torsion Entropy for Twisted Curves under Curve Shortening Flow to the Arxiv, which has been accepted in the Bulletin of the Australian Math Society. This paper studies curve shortening flow, which is the geometric flow defined by the equation where is a smooth curve in , is… Read More Twisted Curves and Curve Shortening Flow
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
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