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. 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.
Quantum Theory, Groups and Representations: An Introduction
This is a textbook covering quantum mechanics and quantum field
theory from the point of view of representation theory. It was
published November 2017 by Springer which has a webpage for
the book, and a Springer
Link page for the book (from which your institution may
provide ability to buy a MyCopy softcover version for $24.99).
A page with errata is here.
Essentially the same content is available from my website here,
and I have retained copyright for the book content. If you're
in the mood to write a review of the book, the Amazon page is here.
Some blog entries about the book are here.
Not Even Wrong
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.
GR6402: Modern Geometry (Fall 2017)
GU4032: Fourier Analysis (Spring 2017)
G4344: Lie Groups and Representations (Spring 2016)
V1102: Calculus II (Fall 2015)
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)
Mathematics V1101: Calculus I (Fall 2010)
Mathematics V1102: Calculus II (Spring 2009)
Mathematics V1102: Calculus II (Fall 2008)
G4343-4: Lie Groups and Representations (Fall 2007-Spring 2008)
G4344: Lie Groups and Representations (Spring 2007)
Calculus IV (Fall 2005)
Geometry (Fall 2004-Spring 2005)
G6434: Quantum Field Theory and Geometry (Fall 2003)
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. It now (mid-2017) contains over 1600 postings
that may be of some sort of interest.
I wrote a few articles in 2016 for Heidelberg Laureate Forum blog,
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.
Without a Theory
Inference, Vol. 3, No. 3, November 2017.
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.
from introductory talks on quantum mechanics and representation
theory at LaGuardia Community College, November 1, 2017 and
Queensborough Community College, November 15, 2017.
from a colloquium talk in the physics and astronomy department at
Rochester, March 7, 2018.
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, profiles, etc.
with John Horgan 2006.
at Scienceline, December 28, 2006.
conversation with Sabine Hossenfelder, July 9. 2008.
conversation with Craig Callendar, September 10, 2009.
Speaking. April 2010.
Big Think. June 6,
Admiral of the String Theory Wars, Nautilus, May 7, 2015.
Not Even Wrong, Physics World podcast, September 2016.
String Theory Is Still Not Even Wrong, Scientific American
blog, April 27,2017.
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.
Goldilocks Enigma, New Humanist, September-October 2006.
Review of Paul Davies' The Goldilocks Enigma.
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.
Fun 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
Faith and Fantasy in the New Physics, MAA Reviews, September
15, 2016. Review of Roger Penrose's Fashion, Faith and
Fantasy in the New Physics
for God at the Center of the Big Bang, Wall Street Journal,
February 17, 2017. Review of Zeeya Merali's A Big Bang in a
for the "Perfect" Theory, Physics World, May 2017.
Review of Frank Close's Theories of Everything
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?