# Seminars & Colloquia Calendar

## On the extension of the FKG inequality to n functions

#### Siddhartha Sahi - Princeton University

Location: ** Hill Center Room 705**

Date & time: Thursday, 04 November 2021 at 1:20PM - 2:20PM

The 1971 Fortuin-Kasteleyn-Ginibre (FKG) correlation inequality for two monotone functions on a distributive lattice is well known and has seen many applications in statistical mechanics, combinatorics, statistics, probability, and other fields of mathematics.

In 2008 the speaker conjectured an extended version of this inequality for all n>2 monotone functions on a distributive lattice. This reveals an intriguing connection with the representation theory of the symmetric group.

We give a proof of the conjecture for two special cases: for monotone functions on the unit square in R^k whose (upper) level sets are k-dimensional rectangles, and, more significantly, for {\it arbitrary} monotone functions on the unit square R^2. The general case for R^k, k>2 remains open.

This is joint work with Elliott Lieb.

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Quentin Dubroff Organizer's webpage

James Holland; Organizer website

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Yanyan Li, Zheng-Chao Han, Jian Song, Natasa Sesum Organizer's Webpage

Organizer: Luochen Zhao

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Lisa Carbone, Yi-Zhi Huang, James Lepowsky, Siddhartha Sahi Organizer's webpage

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Joel Lebowitz, Michael Kiessling

Yanyan Li, Haim Brezis Organizer's Webpage

Stephen D. Miller, John C. Miller, Alex V. Kontorovich, Alex Walker seminar website

Stephen D. Miller

Brooke Ogrodnik, Website

Organizers: Yanyan Li, Z.C. Han, Jian Song, Natasa Sesum

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Kristen Hendricks, Xiaochun Rong, Hongbin Sun, Chenxi Wu Organizer's page

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