Starts 21 May 2026 11:00
Ends 21 May 2026 12:00
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ICTP Associates Seminars: The History of Majorization Inequalities - from Newton to Macdonald
ICTP and online
Stasi Lecture Hall
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.
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.