# Seminars & Colloquia Calendar

## Graph Powering and Spectral Robustness

#### Peter Ralli (Princeton)

Location: ** Hill 705**

Date & time: Monday, 28 October 2019 at 2:00PM - 3:00PM

** Abstract:** Given an original graph G and positive integer r, graph powering produces a graph connecting vertices from the original graph that are within distance r. I will discuss the use of graph powering for spectral clustering: in a sparse graph the spectrum of the adjacency matrix might be contaminated by non-informational top eigenvalues. It is shown that graph powering regularizes the graph and decontaminates its spectrum in the following sense: if the graph is drawn from the sparse Erd?s-Rényi ensemble, which has no spectral gap, it is shown that graph powering produces a `maximal' spectral gap, which is justified by establishing an Alon-Boppana result for powered graphs.

Joint works with E. Abbe, E. Boix, and C. Sandon.

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

Brooke Logan

Wujun Zhang Organizer's webpage

P. Gupta, X.Huang and J. Song Organizer's webpage

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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