I'm currently a Senior Lecturer in the Mathematics department at
Columbia University, where I teach, do research, and am responsible
for the department Computer system. At various times, I've
also been our Calculus Director, coordinating Calculus
teaching. Now I am setting up and overseeing our use of
the WebAssign online homework system in some of the Calculus
classes. My current main project is a textbook
on quantum mechanics and representation theory, to be
published by Springer late 2017.
My academic background includes undergraduate and master's degrees
in physics from Harvard, a Ph.D. in particle theory from Princeton,
and postdocs in physics (ITP Stony Brook) and mathematics (MSRI
Berkeley). I've been at Columbia since 1989, starting here as
Ritt assistant professor.
GU4032: Fourier Analysis (Spring 2017)
G4344: Lie Groups and Representations (Spring 2016)
V1102: Calculus II
W4392: Introduction to Quantum Mechanics (Spring 2015)
W4391: Introduction to Quantum Mechanics (Fall 2014)
G4343: Lie Groups and Representations (Fall 2013)
W4392: Introduction to Quantum Mechanics (continuation)
W4391: Introduction to Quantum Mechanics (Fall 2012)
G4344: Lie Groups and Representations (Spring 2012)
G4343-4: Lie Groups and Representations (Fall 2007-Spring 2008)
G4344: Lie Groups and Representations (Spring 2007)
G6434: Quantum Field Theory and Geometry
Lie Groups and Representations (Spring 2003)
My general area of research interest is the relationship between
mathematics (especially representation theory) and fundamental
physics (especially quantum field theories like the Standard
Model). Recently I've been working more specifically on
understanding whether certain quantum field theories can usefully be
formulated in terms of a generalization of the notion of an
"automorphic representation", which is central to the Langlands
program in number theory.
Field Theory and Representation Theory: A Sketch
Posted at www.arxiv.org as hep-th/0206135
and Dirac Cohomology (draft version).
Since 2004 I've maintained
an active blog called Not Even
Wrong, which deals with topics in physics and
mathematics. At the end of 2011 it had 13,378 subscribers at
Google Reader. It now contains over 1000 postings that may be
of some sort of interest.
My book Not
Even Wrong was published in June 2006 in England by Jonathan
Cape, in the US in September 2006 by Basic Books. Translations
have appeared in French, Italian, Czech and Korean. I'm
maintaining web-pages for links
to reviews, and errata.
Quantum Theory, Groups and Representations: An Introduction
In progress, completion expected mid-2015.
Some Popular articles
Theory: An Evaluation
Posted at www.arxiv.org as physics/010251
courtesy of SciPosts.
theory even wrong?
Published in the March-April 2002 issue of American Scientist.
problem with physics
Cosmos Magazine, August 2007
Theory and the Crisis in Particle Physics
Based on a talk at the Gulbenkian Foundation Conference in Lisbon on
Is Science Nearing Its Limits?
25-26 October 2007. This appears in the conference proceedings
volume, available here.
Polish translation by Alica Slaba available here.
Scenario for Fundamental Physics
Edge 2013 question contribution, published in
Should we be Worried About?
Edge 2014 question contribution, published in
Idea Must Die: Scientific Ideas that are Blocking Progress
theory and post-empiricism
Scientia Salon, July 10, 2014
a Grand Unified Theory of Mathematics and Physics
Essay written for FQXI contest, February 20, 2015.
Ancient material from the earliest days of the string theory
to these articles, various outrages,
and a few voices of
Anyone interested in a bet?
For technical audiences
from a talk on Quantization and
Equivariant K-theory at the Wigner Conference in New York,
May 27, 2003.
talk on Quantum Field Theory and
Representation Theory at the Dartmouth Math department,
June 3, 2004.
from talks on Is String Theory
Testable?, March 8 (INFN Rome) and March 15 (INFN
from a talk on BRST and Dirac
Cohomology at Dartmouth, October 23, 2008.
from a talk on Quantum Mechanics and Representation Theory at Texas
Tech, November 21, 2013.
from a colloquium talk in the physics department at Rutgers,
February 3, 2016.
For popular audiences
from a talk to students at Collin College, March 24, 2010.
talk. Joint performance with Tommaso Dorigo at the
Antwerp Opera House on September 24, 2011.
What We Don't Know About Fundamental Physics, Talk at the
Blind Tiger on Bleecker Street, April 29, 2014, part of Raising the Bar.
Interviews, podcasts, etc.
with John Horgan 2006.
conversation with Sabine Hossenfelder, July 9. 2008.
conversation with Craig Callendar, September 10, 2009.
Speaking. April 2010.
Big Think. June 6,
I've written quite a few book reviews on the blog, the ones from the
past few years are easily accessible here.
Some reviews I've written for publication include:
with Quantum Weirdness, American Scientist, September-October
2005. Review of Giancarlo Ghirardi's Sneaking a Look at God's Cards.
Happens In the Dark, Wall Street Journal, January 31,
2011. Review of Richard Panek's The 4% Universe.
the End Is the Beginning, Wall Street Journal, May 27,
2011. Review of Roger Penrose's Cycles of Time.
with Fysiks, American Scientist, July-August 2011.
Review of David Kaiser's How the
Hippies Saved Physics.
Our Mathematical Universe, Wall Street Journal, January 17,
2014. Review of Max Tegmark's Our Mathematical Universe.
Also available here.
Half-Life of Physicists, Wall Street Journal, May 1,
2015. Review of Paul Halpern's Einstein's Dice and