nLab Urs Schreiber



Urs Schreiber


animated logo of CQTS


I work in
the Mathematics Division of Science
of New York University in Abu Dhabi
in the group of Prof. Hisham Sati leading the
Research Center for Quantum and Topological Systems
(see at CQTS for latest activity).



I am researching mathematical and fundamental physics (e.g. on Hypothesis H and Quantum Systems).

For latest talk notes see here.

selected talks


recent monograph:

Cover blurb: This book presents a novel development of fundamental and fascinating aspects of algebraic topology and mathematical physics: “extra-ordinary” and further generalized cohomology theories enhanced to “twisted” and differential-geometric form with focus on their rational approximation by generalized Chern character maps and on the resulting charge quantization laws in higher n n -form gauge field theories appearing in string theory and in the classification of topological quantum materials.

Motivation for the conceptual re-development is the observation, laid out in the introductory chapter, that famous and famously elusive effects in strongly interacting (“non-perturbative”) physics demand “non-abelian” generalization of much of established generalized cohomology theory. But the relevant higher non-abelian cohomology theory (”higher gerbes“) has an esoteric reputation and has remained underdeveloped.

The book’s theme is that variously generalized cohomology theories are best viewed through their classifying spaces – possibly but not necessarily infinite-loop spaces – from which perspective the character map is really an incarnation of the fundamental theorem of rational homotopy theory, thereby uniformly subsuming not only the classical Chern character and a multitude of scattered variants that have been proposed, but now seamlessly applying in the previously elusive generality of (twisted, differential and) non-abelian cohomology.

In laying out this result with plenty of examples, we provide modernized introduction and review of fundamental classical topics: 1. abstract homotopy theory via model categories, 2. generalized cohomology in homotopical incarnation, 3. dg-algebraic rational homotopy theory, whose fundamental theorem we re-cast as a (twisted) non-abelian de Rham theorem which naturally induces the (twisted) non-abelian character map.

research wiki

nLab banner

I enjoy putting math/phys information into context.
For that purpose I had started (in Nov 2008)

with edit logs and discussion being had on:

For more on the nnLab, see:

more web logs

For logs of further activity see:

while n n Lab-edits are announced

For links to technical discussions about math and physics see my pages:


See behind the links for detailed lecture notes that I wrote:

datelecture notes
winter \,\, 2017Mathematical Quantum Field Theory
summer 2017Topological K-Theory
summer 2017Topology
winter \,\, 2016Super Cartan Geometry
summer 2016Complex oriented cohomology theory
summer 2016Stable Homotopy Theory
summer 2015Structure Theory for Higher WZW Terms
summer 2015Higher Cartan Geometry
summer 2014Homological Algebra

A list of further teaching in the past is here.


I used to write an irregular column at PhysicsForums Insights. Articles in the series include these:

on pre-quantum field theory

on perturbative quantum field theory

on string theory

copyright statement

To the extent that it matters, my contributions to the nLab are copyrighted according to CC BY-SA 3.0.

category: people

Last revised on June 20, 2024 at 13:30:09. See the history of this page for a list of all contributions to it.