| Description |
In this first edition of the ICTP Associates Seminars, Apoorva Khare from Indian Institute of Science will discuss Majorization Inequalities. Zoom registration: https://zoom.us/meeting/register/Xv13idM5SOaBdAfQTLtr1A#/registration Abstract: I would gently introduce inequalities connecting symmetric polynomials and majorization. These have been studied by Maclaurin and Newton (1700s), Schlomilch (1800s), Gantmacher, Muirhead, Schur (1900s), and in ancient Greece. I will then mention (perhaps the first) weak majorization result, shown in joint work with Tao (2021). This involves Schur polynomials, and parallels results by Cuttler–Greene–Skandera and Sra (2010s). Time permitting, I will explain recent work with Chen and Sahi, where we subsume several of these inequalities by a "master" majorization inequality: using Jack or Macdonald polynomials. This is conjectural, and we prove it for 2 variables. These seminars are a way of sharing the work and experiences of ICTP Associates. The seminars have a personal part and a scientific part. The speaker will talk a bit on his/her personal trajectory first, and then later gently introduce a research theme of his/her choice. |
ICTP Associates Seminars: The History of Majorization Inequalities - from Newton to Macdonald
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