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Shmuel Weinberger

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Andrew MacLeish Distinguished Service Professor of Mathematics

**How to reach me**

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**Research**

Most of my research concerns geometry and topology, broadly defined. I have been interested in manifolds, their range of possible metrics and their group actions, and in stratified spaces, homology manifolds, and their invariants, the large scale geometry of discrete groups and other natural large scale metric spaces such as spaces of Riemannian metrics. I am currently interested in spaces of discontinuous functions, processes on large networks, and their scientific applications. In short, my focus these days is on quantitative and applied topology.

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**Links to selected talks**

(This is experimental; talks are often written in a hurry and should be used for information and inspiration, not as completely reliable sources of fact or scholarship.)

Quantitative and Applied Topology: 2012 Clifford Lectures Hopefully more information to come soon.

Disordered solids and the dynamics of manifolds of bounded geometry, 2011 talk at ETH (Applied Algebraic Topology)

Group actions on aspherical manifolds, 2011 talk at Dubrovnik Topology Conference (handwritten)

Persistent homology of data, function spaces, and landscapes, 2010 Benter lecture at the Hong Kong City University

2008 AAAS talk on data

Taming 3-manifolds by Positive Scalar Curvature, 2009 talk at Vanderbilt

2008 talk on the work of Sylvain Cappell (at the Courant celebration of his birthday)

Playing the Novikov game, 2008 Hardy lecture in Edinburgh

Entropy, function spaces, complexity and variational problems, 2008 Hardy lecture in London

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**Links to coauthors**

Robert Adler

Victor Bangert

Arthur Bartels

Jonathan Block

Omer Bobrowski

Matthew Strom Borman

John Bryant

Sylvain Cappell

Greg Chambers

Stanley Chang

Jim Davis

Mike Davis

Sasha Dranishnikov

Benson Farb

Michael Farber

Steve Ferry

Erik Guentner

Jean-Claude Hausmann

Nigel Higson

Bruce Hughes

Tadeusz Januszkiewicz

Misha Katz

Alex Lubotzky

Wolfgang Lueck

Fedor Manin

Washington Mio

Alex Nabutovsky

Partha Niyogi

Piotr Nowak

Erik Pederson

John Roe

Jonathan Rosenberg

Stephane Sabourau

Julius Shaneson

Steven Shnider

Steve Smale

Larry Taylor

Mathai Varghese

Bruce Williams

Zhizheng Xie

Min Yan

Guoliang Yu

**Links to seminars**

Algebraic Topology Seminar

Geometry-Topology Seminar

**Links to (former) students**

Min Yan

Stanley Chang

David Chase

Heather Johnston

Kevin Whyte

Stanley Chang

Ben Wieland

Courtney Thatcher

Jim Fowler

Robert Young

Katharine Turner

Grigori Avramidi

Fedor Manin

**Links for students and others**

L^2 cohomology 2021

Modeling 2020

Logic and Geometry 2020

Algebraic Topology

Second steps in topology

Network course additional readings

Quantitative Topology Readings (2010 +2019)

Differential Topology 2010

Readings for "Applied Algebraic Topology". (2009)

Readings for "Topology of Manifolds" (2008)

Readings for "Aspherical Manifolds" (2007)

Some of my favorite geometric arguments/theorems.

Fundamental group and Covering Spaces: the facts.

Degrees and intersections

Introduction to Mathematics (Numbers and Stuff)