Organizing Committee
 Jonathan Kelner
Massachusetts Institute of Technology  Yiannis Koutis
University of Puerto Rico  Gary Miller
Carnegie Mellon University
Abstract
Spectral graph theory, which studies how the eigenvalues and eigenvectors of the graph Laplacian (and other related matrices) interact with the combinatorial structure of a graph, is a classical tool in both the theory and practice of algorithm design. The success of this approach has been rooted in the efficiency with which eigenvalues and eigenvectors can be computed, and in the surprisingly large number of ways that a graph's properties are connected to the Laplacian's spectrumparticularly to the value of its second smallest eigenvalue, λ2.
However, while the eigenvalues and eigenvectors of the Laplacian capture a striking amount of the structure of the graph, they certainly do not capture all of it. Recent work in the field suggests that we have only scratched the surface of what can be done if we are willing to broaden our investigation to include more general linearalgebraic properties of the matrices we associate to graphs.
A particularly fruitful example of this has been the study of Laplacian linear systems, where the interplay between linear algebra and graph theory has led to progress in both fields. On the one hand, researchers have used the combinatorial structure of the corresponding graphs to facilitate the solution of these linear systems, resulting in solvers that run in nearlylinear time. On the other hand, one can use these linear systems to describe the behavior of electrical flows on a graph, which has provided a powerful new primitive for algorithmic graph theory. This interaction has already led to improved algorithmic results for many of the basic problems in algorithmic graph theory, including finding maximum flows and minimum cuts, solving traveling salesman problems, sampling random trees, sparsifying graphs, computing multicommodity flows, and approximately solving a wide range of general clustering and partitioning problems. In addition, researchers have recently shown how to exploit a wide range of other algebraic properties of matrices associated to graphs, such as the threshold rank, cut norm, sensitivity to perturbation, or hypercontractivity of the eigenspaces, to achieve impressive algorithmic results.
In this workshop, we will bring researchers together to study and advance this new emerging frontier in algorithmic graph theory.
Confirmed Speakers & Participants

Rediet Abebe
Cornell University

Monther Alfuraidan
King Fahd University of Petroleum and Minerals

Zeyuan AllenZhu
Microsoft AI

Anima Anandkumar
California Institute of Technology

John Augustine
Indian Institute of Technology

Chen Avin
BenGurion University of the Negev

Haim Avron
Tel Aviv University

Frank Bauer
Harvard University

Petra Berenbrink
University of Hamburg

Erik Boman
Sandia National Laboratories

Christian Borgs
Microsoft

Christos Boutsidis
Goldman Sachs

Yixin Cao
Hong Kong Polytechnic University

Jennifer Chayes
Microsoft

Michael Cohen
Massachusetts Institute of Technology

Mihai Cucuringu
University of Oxford and Alan Turing Institute

Thomas Dickerson
Brown University

Michela Egidi
Technische Unviersität Dortmund

Lledo EsquerraOrtells
Amazon

Pedro Felzenszwalb
Brown University

Kyle Fox
University of Illinois at UrbanaChampaign

Eli FoxEpstein
Brown University

Nathanaël François
TU Dortmund

David Gillman
New College of Florida

David Gleich
Purdue University

Mamikon Gulian
Brown University

Bruce Hendrickson
Sandia National Laboratories

Emilie Hogan
Pacific Northwest National Laboratory

Majid Janzamin
University of California, Irvine

Jonathan Kelner
Massachusetts Institute of Technology

Yvonne Kemper
National Institute of Standards and Technology

Franklin Kenter
Rice University

Richard Kenyon
Brown University

Philip Klein
Brown University

Caroline Klivans
Brown University

Alexandra Kolla
University of Illinois at UrbanaChampaign

Yiannis Koutis
University of Puerto Rico

Rasmus Kyng
Yale University

Matthew Langston
Reservoir Labs Inc

James Lee
University of Washington

Gabor Lippner
Harvard University

Shiping Liu
University of Durham

Aleksander Madry
EPFL

Ahmad Mahmoody
Brown University

William Martin
Worcester Polytechnic Institute

Claire Mathieu
Ecole Normale Suptrieure

Charalampos Mavroforakis
Boston University

Patrick McDonald
New College of Florida

David Meierfrankenfeld
Brown University

Francois Meyer
University of Colorado

Gary Miller
Carnegie Mellon University

Sobhan Naderi Parizi
Brown University

Krishna Nand
Brown University

Danupon Nanongkai
Nanyang Technological University

Lorenzo Orecchia
Massachusetts Institute of Technology

Shayan OveisGharan
Stanford University

Jakub Pachocki
Carnegie Mellon University

Gopal Pandurangan
Nanyang Technological University

Debmalya Panigrahi
Duke University

Richard Peng
Massachusetts Institute of Technology

Lam Pham
Yale University

Mason Porter
UCLA

Saad Quader
University of Connecticut

Sanjay Ramassamy
Brown University

Anup Rao
University of Washington, St. Louis

Ben Raphael
Brown University

Amanda Redlich
Bowdoin College

Igor Rivin
Temple University

Scott Roche
Northeastern University

Sushant Sachdeva
Yale University

Bernd Schroeder
Louisiana Tech University

Olivia Simpson
UC San Diego

Ali Sinop
Institute for Advanced Study

Jon Sjogren
Towson University

Nikhil Srivastava
UC Berkeley

He Sun
The University of Edinburgh

Christino Tamon
Clarkson University

Evimaria Terzi
Boston University

Charalampos Tsourakakis
Boston University and Harvard University

Lara Ruth Turner
University of Vienna

Eli Upfal
Brown University

Nisheeth Vishnoi
École Polytechnique Fédérale de Lausanne

Van Vu
Yale University

Shen Chen Xu
Carnegie Mellon University

Grigory Yaroslavtsev
Pennsylvania State University

Neal Young
University of California, Riverside

Luca Zanetti
Universität des Saarlandes

Hang Zhou
Ecole Normale Suptrieure

Yao Zhu
Purdue University