# Seminars & Colloquia Calendar

## From Janson's inequality to hypergraph containers

#### Rajko Nenadov, Google Zurich

Location: ** Zoom**

Date & time: Friday, 03 December 2021 at 11:30AM - 12:30PM

Abstract:Start with a complete graph with n vertices, and choose m edges uniformly at random. This basic model of random graphs is known as the Erd?s–Rényi G(n,m) model. One of the fundamental questions is how does the probability that G(n,m) does not contain some chosen graph H change as m goes from 1 to ex(H, n), the largest number of edges in an H-free graph. A standard approach to this question is via Janson's inequality. Surprisingly, and in contrast to the binomial random graph model G(n,p), this approach does not always correctly determine the order of the logarithm of the probability when H is a bipartite graph. In particular, a recent result of Balogh, Morris, and Samotij shows that in this case the probability eventually becomes super-exponentially small in m, whereas Janson's inequality reaches a plateau at an exponential bound.

In the first part of the talk we discuss a new proof of this result and its connection to the celebrated K?R conjecture. In the second part we discuss applications of these results in Ramsey theory and the motivation for revisiting the problem. Finally, generalising the presented ideas, we give a strengthening of Janson's inequality in the spirit of the so-called hypergraph containers, one of the most influential results in probabilistic combinatorics in the last decade.

Chiara Damiolini, Ian Coley and Franco Rota -Charles Weibel Organizer's Page

Brooke Logan

Wujun Zhang Organizer's webpage

Ziming Shi, Sagun Chanillo, Xiaojun Huang, Chi Li, Jian Song Seminar website Old seminar website

Swastik Kopparty, Sepehr Assadi Seminar webpage

Jeffry Kahn, Bhargav Narayanan, Jinyoung Park Organizer's webpage

Brooke Ogrodnik, Website

Robert Dougherty-Bliss and Doron Zeilberger --> homepage

Paul Feehan, Daniel Ketover, Natasa Sesum Organizer's webpage

Lev Borisov, Emanuel Diaconescu, Angela Gibney, Nicolas Tarasca, and Chris Woodward Organizer's webpage

Jason Saied Seminar webpage

Brian Pinsky, Rashmika Goswami website

Quentin Dubroff Organizer's webpage

James Holland; Organizer website

Edna Jones Organizer's webpage

Brooke Ogrodnik website

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

Organizer: Luochen Zhao

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

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

Simon Thomas website

Kasper Larsen, Daniel Ocone and Kim Weston Organizer's page

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

Yael Davidov Seminar webpage

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

Fioralba Cakoni Seminar webpage

Ebru Toprak, Organizer

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