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Gregory W. Moore |
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Directory information
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Position: |
Faculty |
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Research group: |
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Email address: |
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Telephone: |
(732) 445-4375 |
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Dept. Fax: |
(732) 445-4343 |
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Office: |
Serin E362 |
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Mailing address: |
Greg Moore |
Teaching
Research Activities
My work places particular emphasis on the
underlying mathematical structures and applications to and from modern
mathematics.
Specific research interests include:
- The
theory of branes and generalized abelian gauge theories in supergravity.
This involves interesting topological issues related to generalized differential cohomology theories, especially K-theory.
There are also interesting relations to the theory of self-dual fields, anomaly cancellation, and noncommutative geometry. - Effective low energy supergravity theories in string compactification and the computation of nonperturbative stringy effects in effective supergravities.
- D-branes on Calabi-Yau manifolds and BPS state counting. Relations to Borcherds products, automorphic forms, black-hole entropy, and wall-crossing.
- Applications of the theory of automorphic forms to conformal field theory, string compactification, black hole entropy counting, and the AdS/CFT correspondence.
- Potential connections to
number theory. For example - I pointed out in 1998 that the attractor mechanism
of supersymmetric black holes singles out Calabi-Yau varieties with relations to complex multiplication. - Conformal field theories. Rational conformal field theories, especially applications to the theory of anyons and nonabelions.
- Topological field theories, and applications to invariants of manifolds.
- String field theory.
- String cosmology and time-dependence in string theory
- Does the alleged ``landscape of N=1 effective four-dimensional string vacua'' really exist?
Expository, Historical, and Philosophical
- ``What is a brane?'' . Published in: Notices of the American Mathematical Society, Vol. 52, No. 2, pp.214-215.
- ``How many black holes fit on the head of a pin?'', coauthored with Frederik Denef. Published in: Int.J.Mod.Phys. D17 (2008) 679-684, Gen.Rel.Grav. 39 (2007) 1539-1544 .
- ``The Impact of D-branes on Mathematics''. I wrote this trying to collect my thoughts before appearing on a panel at JOEFEST at the KITP, February 2014 .
- ``Response to the 2014 Eisenbud Prize''. I wrote this since the AMS requested a response.
- ``Some Comments on Physical Mathematics''. I wrote this to try to collect my thoughts, preparing a talk for the 2014 Heineman Prize. It is an expansion on the previous essay. The talk is here .
- ``Physical Mathematics and the Future''. This is the essay which is meant to accompany my ``vision talk'' in the summary section of Strings 2014 in Princeton. It is a further expansion of the previous essay (without the review of N=2 supersymmetric theories). The video of the accompanying talk is available from the conference website here and also from YouTube here .
- An essay, submitted as a Snowmass whitepaper on physical mathematics, is in the same spirit as the previous item, but is a bit more technical, co-authored with I. Bah, D. Freed, N. Nekrasov, S. Razamat, and S. Schaefer-Nameki is on the e-Print ArXiv as 2203.05078. It will eventually be accompanied by a much longer companion paper with ample references.
Publications
(Almost all publications after August 1991 are available on the
e-print arXiv .)
- Anomalous Inequivalence of Phenomenological Theories, (with A. Manohar), Nucl. Phys. {\bf B243}(1984)55.
- Anomalies
and Odd Dimensions, (with L. Alvarez-Gaum\'e
and S. Della Pietra) Ann. Phys. (1985)288 - Anomalies
in Nonlinear Sigma Models, (with P. Nelson),
Phys. Rev. Lett. {\bf 53}(1984)1519 - Constraints
on a Two-Higgs Interpretation of the
$\zeta(8.3)$, (with H. Georgi and A. Manohar), Phys. Lett.
{\bf 149B}(1984)234 - The
Aeteology of Sigma Model Anomalies, (with P. Nelson)
Comm. Math. Phys. {\bf 100}(1985)83 - A
Comment on Sigma Model Anomalies, (with A. Manohar and
P. Nelson) Phys. Lett. {\bf 152B}(1985)68 - Measure
for Moduli, (with P. Nelson), Nucl. Phys.
{\bf B266}(1986)58 - An
Off-Shell Propagator for String Theory, (with
A. Cohen, P. Nelson, and J. Polchinski), Nucl. Phys.
{\bf B267}(1986)143 - An
Invariant String Propagator (with A. Cohen, P. Nelson,
and J. Polchinski) in {\it Unified String Theories}, D. Gross and
M. Green eds., World Scientific (1986) - Strings
and supermoduli (with P.~Nelson, and J.~Polchinski)
Phys.~Lett. {\bf B169} (1986) 47; {\bf201B} (1988) 579(E) - Heterotic
geometry, (with P. Nelson), Nucl. Phys.
{\bf B274} (1986) 509 - An
$O(16)\times O(16)$ Heterotic String, (with L. Alvarez-Gaum\'e,
P. Ginsparg, and C. Vafa) Phys. Lett. {\bf 171B}(1986)155 - Theta Functions,
Modular Invariance, and Strings,
(with L. Alvarez-Gaum\'e, and C. Vafa), Comm. Math. Phys.
{\bf 106}(1986)1 - Semi-Off-Shell
String Amplitudes (with A. Cohen,
P. Nelson, and J. Polchinski), Nucl. Phys. {\bf B281}(1986)127 - Modular
forms and Two-Loop String Physics, Phys. Lett.
{\bf 176B}(1986)369 - Bosonization
in Arbitrary Genus, (with L. Alvarez-Gaum\'e,
J. B. Bost, P. Nelson, and C. Vafa) Phys. Lett. {\bf 178B}(1986)41 - Bosonization
on higher genus Riemann surfaces,
(with L.~Alvarez-Gaum\'e, J.~B.~Bost, P. Nelson, and C.~Vafa),
Commun. Math. Phys. {\bf112} (1987) 503 - Modular
forms and the cosmological constant,
(with J. Harris, P. Nelson, and I. Singer)
Phys.\ Lett.\ {\bf178B} (1986) 167; {\bf201B} (1988) 579(E) - Modular
Forms and Multiloop String Physics, in
{\it Proceedings of the VIIIth International Congress on
Mathematical Physics} at Marseille.
M. Mebkhout, ed. World Scientific, 1987, pp. 776-783 - Atkin-Lehner Symmetry, Nucl. Phys. {\bf B293}(1987)139
- Vanishing
Vacuum Energies for Nonsupersymmetric Strings,
in {\it Nonperturbative Quantum Field Theory} (Cargese lectures),
G. Mack,
G. `t Hooft, A. Jaffe, P. Mitter, and R. Stora, eds.
Plenum. - Quasicrystalline
Compactification, (with J. Harvey and
C. Vafa) Nucl. Phys. {\bf B304}(1988)269 - Some
Remarks on Two-Loop Superstring Calculations,
(with A. Morozov), Nucl. Phys. {\bf B306}(1988)387 -
Some
global issues in string
perturbation theory, " (with J. J. Atick, and A. Sen),
Nucl. Phys. B308(1988)1-101 - Rationality
in Conformal Field Theory, (with
G. Anderson), Comm. Math. Phys. {\bf 117}(1988)441 -
Catoptric
tadpoles, (with J. J. Atick, and A. Sen)
Nucl. Phys. B307(1988)221 - Strings
in the Operator Formalism, (with L. Alvarez-Gaum\'e,
C. Gomez, and C. Vafa), Nucl. Phys. {\bf 303}(1988)455 - Polynomial
Equations for Rational Conformal Field
Theories, (with N. Seiberg),
Phys. Lett. {\bf 212B}(1988)451 - Naturality
in Conformal Field Theory,
(with N. Seiberg), Nucl. Phys. {\bf B313}(1989)16 - Classical
and Quantum Conformal Field Theory,
(with N. Seiberg), Commun. Math. Phys. {\bf 123}(1989)177 - Taming
the Conformal Zoo,
(with N. Seiberg), Phys. Lett. {\bf 220B}(1989)422 - A
Comment on Quantum Group Symmetry in Conformal Field
Theory, (with N. Reshetikhin), Nucl. Phys. {\bf B328}(1989)557 - Remarks
on the Canonical Quantization of the Chern-Simons-
Witten Theory, (with S. Elitzur, A. Schwimmer, and N. Seiberg),
Nucl. Phys. {\bf B326}(1989)108 - Rational
Conformal Field Theory and Group Theory,
(with N. Seiberg), in the proceedings of the
Schloss Ringberg conference, April 1989 - Lectures on Rational Conformal Field Theory,
(with N. Seiberg), in {\it Strings '89},Proceedings
of the
3-14 April 1989, M. Green, et. al. Eds. World
Scientific, 1990. - The
Ising model, the Yang-Lee edge singularity, and
2D quantum gravity, (with \v C. Crnkovi\'c and P. Ginsparg),
Phys. Lett. {\bf 237B}(1990)196 -
Nonabelions
in the fractional quantum hall effect, (with N. Read),
Nucl. Phys. 360B(1991)362 - Geometry
of the String Equations, Commun. Math. Physics.
{\bf 133}(1990) 261-304 - Physical
Solutions for Unitary-Matrix Models
(with M. Douglas and C. Crnkovic), Nucl. Phys. {\bf B360}(1991)507 - Simplex Equations and Their Solutions, (with
Commun. Math. Phys. {\bf 138}(1991)259 - Matrix Models of 2D Gravity and Isomonodromic Deformation,
in Common Trends in Mathematics and Quantum Field
Theories, T. Eguchi et. al., eds. Prog. Theor. Phys. Suppl.
102; Also, in the Proceedings of the
1990 Carg\'ese Workshop on Random Surfaces, Quantum Gravity and
Strings, with slightly improved version. - Multicritical Multi-Cut Matrix Models, (with \v C.
Crnkovi\'c),
Phys. Lett. {\bf B257}(1991)322 - Double-Scaled Field Theory at c=1, Nucl.Phys.B368:557-590,1992,
- Boundary
Operators in 2D Gravity, (with E. Martinec and
- From Loops to States in 2D Quantum Gravity, (with
and M. Staudacher), Nucl. Phys. B362 (1991)665 - Loop
Equations and the Topological Phase of Multi-Cut Matrix
Models, (with \v C. Crnkovi\'c and M. Douglas), hep-th/9108014;
Int.J.Mod.Phys.A7:7693-7711,1992 - From
Loops to Fields in 2D Quantum Gravity (with
Int. Jour. Mod. Phys. {\bf 7A}(1992)2601. - Exact S-Matrix for 2D String Theory, (with R.
Plesser and S.
Ramgoolam),
hepth/9111035; Nucl.Phys.B377:143-190,1992 - Gravitational Phase Transitions and the Sine-Gordon Model A version with the figures is here.
- Classical
Scattering in 1+1 Dimensional String Theory, (with R.
Plesser), hepth/9203060; Phys.Rev.D46:1730-1736,1992 - Fractional
quantum Hall effect and nonabelian statistics, (with
N. Read), hepth/9111035;
to appear in Proceedings of 4th Yukawa International Symposium - The
partition function of 2d string theory, (with R. Dijkgraaf and
R. Plesser), hepth/9208031; Nucl.Phys.B394:356-382,1993 - Lectures
on 2D Gravity and 2D String Theory, (with P. Ginsparg),
hepth/9304011; in {\it Recent Directions in Particle Theory}, J. Harvey
and J. Polchinski,
eds., World Scientific, 1993 - Finite in All Directions, hepth/9305139
- Symmetries
and Symmetry-Breaking in String Theory,
hepth/9308052; in {\it International Workshop on
Supersymmetry and Unification of Fundamental
Forces}, P. Nath, ed, World Scientific 1993 - Symmetries of
the bosonic string $S$-matrix,
hep-th/9310026 - Large N 2D
Yang-Mills Theory and Topological
String Theory,
http://arxiv.org/abs/hep-th/9402107. Commun.Math.Phys.185:543-619,1997 -
Chaotic Coupling Constants, (with J. Horne)
Nucl.Phys.B432:109-126,1994 - Addendum to: ``Symmetries of the
Bosonic String S-Matrix,
http://arxiv.org/abs/hep-th/9404025. Nucl.Phys.B432:109-126,1994
Some Talks
- A talk entitled ``Life After RCFT,'' delivered at the Soviet-American Workshop On String Theory, Princeton University, Oct. 30 - Nov. 2, 1989. This was perhaps the second-most disastrous talk of my career (so far). It included an announcement of my work with Nick Read, introducing the ``Pfaffian state'' of the fractional quantum Hall effect and suggesting that that state would support nonabelions. The slides can be viewed here
- Lectures
at the Les Houches Meeting on Number Theory, Geometry, and
Physics. Les Houches, March 9-21, 2003. -
Localized
tachyon flows and Hirzebruch-Jung spaces, at the conference
``Avant Strings,'' Institut des Hautes Etudes Scientifiques, -
On
the quantization of Page charges, at the conference
``Avant Strings,'' Institut des Hautes Etudes Scientifiques, - Anomalies, Gauss Laws, and Page charges, at the
conference
``Strings 2004,'' - Testing some Black Hole/Topological String conjectures,
Institute
for Advanced Study, April 11, 2005 - Lie Algebras, BPS States, and String Duality,
Summer workshop on
Groups and Algebras in M-theory, Rutgers Math Department, May 31, 2005 - Black
holes and Arithmetic, Talk delivered at the Mathematicshe
Arbeitstagung,
Max Planck Institute, - Remarks
on the Hamiltonian Formulation of Some
Generalized Abelian Gauge Theories, Talk delivered at the workshop,
Geometric Topology and Connections with
Quantum Field Theory, - Noncommutativity of Electric and Magnetic Fluxes,
String Theory, June 22, 2005, - Electric and Magnetic Flux Do Not Commute,
Aspen Workshop in Superstring
Cosmology, Aspen, Co, August 9, 2005 - Mathematics Aspects of Fluxes,,
KITP Workshop on Mathematics of String Theory,
Cosmology, Santa Barbara, October 11, 2005 - An uncertainty principle for fluxes, with applications to self-dual fields, , CUNY, June 28, 2006 (26th International Colloquium on Group Theoretical Methods in Physics)
- Split Polar Attractors , Harvard, September 29, 2006
- Wall-crossing and an entropy enigma , Strings 2007, Madrid, June 28,2007. For question period see this link.
- An Uncertainty Principle for Topological Sectors , Jurg Frohlich birthday Celebration, Zurich, July 2, 2007. If the powerpoint does not work a pdf version can be obtained here
- Wall-crossing formulae for BPS states and some applications
, Clay Mathematics Institute workshop on K3's and modular forms,
Cambridge, Mass, March 20, 2008 - Four lectures on modular forms and black hole entropy , Trieste Spring School on Superstrings, Trieste, March 25-April 4, 2008. Some tex lecture notes are here . PDF's of the handwritten notes, actually used in the lectures are Lecture I , Lecture II , Lecture III , and Lecture IV .
- Mathematical Foundations of Orientifolds , UCSB, July 18, 2008
- Four-dimensional wall-crossing from three-dimensional field theory , KITP Miniprogram on Langlands Duality, July 31, 2008.
- Wall-crossing formulae for BPS states and some applications , Zurich Prestrings, Zurich, August 11, 2008
- Four-dimensional wall-crossing from three-dimensional field theory , Zurich Prestrings, Zurich, August 12, 2008
- Mathematical Foundations of Orientifolds , Zurich Prestrings, Zurich, August 11, 2008
- Update on Wall-Crossing , Strings 2008, CERN, August 22, 2008. Video of the talk available here.
- Improved version of the Prestrings/KITP talk, Four-dimensional wall-crossing from three-dimensional field theory, 3rd New England String Meeting, Brown University, Oct. 24, 2008
- Extremal N=2, 2D CFT and Constraints of Modularity Institute for Advanced Study, Nov. 5, 2008
- Overview of the theory of Self-dual fields AMS Meeting, Washington DC, Jan. 8, 2009. A pdf version is available here
- Four-dimensional wall-crossing from three-dimensional field theory Simons Center Workshop, StonyBrook, Jan. 13, 2009
- Orientifolds, Twisted Cohomology, and Self-Duality A talk at the Conference on Perspectives in Mathematics and Physics in honor of I.M. Singer's 85th birhday, MIT, May 23, 2009. For further material see the talk by Dan Freed and the talk by Jacques Distler
- BPS States, Hitchin Systems, and the WKB Approximation Workshop on Mirror Symmetry, Hausdorff Center for Mathematics, Bonn, June 3, 2009
- Here is a minicourse (half of which) was given at the Galileo Galilei Institute and at Frascati, in June 2009. Lecture 1 covers basics of the BPS wall-crossing phenomenon. Lecture 2 reviews the work with D. Gaiotto and A. Neitzke on the relation of the KSWCF to hyperkahler geometry. Lecture 3 and Lecture 4 review the paper on the relation to Hitchin Systems and the WKB approximation.
- The RR charge of an orientifold, Michigan Conference on Topology and Physics, Ann Arbor, Feb. 7, 2010 and Oberwolfach workshop, June 8,2010
- Say ``halo!'' to new walls and new indices, Strings2010, Texas A& M, March 15, 2010. Video of the talk in Monday, Session 3 is available here
- Line Operators in N=2 Gauge Theories, Simons Center Workshop on Quantum Teichmuller Theory, SUNY, Stonybrook, March 30, 2010. The paper is available here
- PiTP Lectures on Wall-Crossing, PiTP School at the Institute for Advanced Study, July 27-29, 2010. These are pedagogical notes on Wall-Crossing in four-dimensional N=2 theories. Video available here .
- Minicourse of three lectures on Generalized Abelian Gauge Theories, Self-Duality, and Differential Cohomology, at the Simons Center Workshop on Differential Cohomology, Simons Center for Geometry and Physics, Stonybrook, Jan. 11-14, 2011. Here are Lecture Notes . Video available here .
- Surface defects in d=4, N=2 theories, BPS states, wall-crossing, and hyperkahler geometry, Simons Center Workshop on Branes and Bethe Ansatz, SCGP, March 25, 2011 Here are Lecture Notes . Video available here .
- Modular Tensor Categories from Six Dimensional Field Theories, Symposium For Michael Freedman's 60th Birthday, KITP, UCSB, April 16, 2011. Video available here .
- Surface defects and the BPS spectrum of 4d N=2 theories, IHES, Three Strings Generations, Paris, May 17, 2011. Powerpoint presentation here . A slightly different version presented at the Solvay Conference in Brussels is here .
- On Recent Applications of Six Dimensional (0,2) Theory to Physical Mathematics, Review Talk at Strings 2011, Uppsala, Sweden, June 29, 2011 Powerpoint presentation here . A pdf version is here . Video available here .
- Three Transverse Intersections Between Physical Mathematics and Condensed Matter Theory, at the Conference Strongly Interacting Electrons in Low Dimensions: New Orders, Symmetries, and Excitations, in honor of Duncan Haldane's 60th birthday. Princeton, September 14, 2011. Powerpoint presentation here and pdf here .
- A very long lecture on the physical relation of Donaldson to Seiberg-Witten invariants of four-manifolds. A 4.5 hour-long lecture, with 40pp. of texed handouts presented at the Simons Center for Geometry and Physics School on Supersymmetric Field Theories and Their Implications, March 8, 2012. Video available here and lecture notes are here .
- Spectral Networks and Their Applications, Caltech, March 30, at the conference ``N=4 Super Yang-Mills Theory, 35 years after.'' Powerpoint presentation here .
- Progress in D=4, N=2 Field Theory, Strings-Math 2012, Bonn, July 2012 Powerpoint presentation here .
- Lectures at St. Ottilien: Quantum Symmetries and K-Theory. Lecture notes here .
- Plenary talk at the ICMP in Aalborg, Denmark, August 8, 2012. Powerpoint version here and pdf here .
- Felix Klein Lectures: ``Applications of the six-dimensional (2,0) theory to physical mathematics.'' October 1 - 11, 2012 at the Hausdorff Insitute for Mathematics, Bonn. Lecture notes, which are still very much UNDER CONSTRUCTION, are available here . Constructive comments, criticisms and reference requests are welcome. The videos of the actual lectures are here .
- The talk I would have given at the Simons Center for Geometry and Physics on Oct. 31, if hurricane Sandy hadn't gotten in the way, is here . It is called ``BPS Degeneracies and Hyperkahler Geometry.''
- A report on work in progress with D. Gaiotto and E. Witten, given at the conference "Aspects of Topology" for G. Segal's 70th birthday is here . A pdf version is here .
- Here is the talk I gave at the SCGP workshop ``Topological Phases of Matter.'' A pdf version is here . Video of the talk is here .
- Here is the talk I gave at the Strings 2013 conference in Seoul, South Korea. A pdf version is here . Video of the talk is here .
- An update on the work in progress with D. Gaiotto and E. Witten, "Algebra of the Infrared,'' given at the SCGP conference "Quiver Varieties," Oct. 15, 2013 is here . A pdf version is here . This talk is directed more at mathematicians than physicists.
- A version of the previous talk, "Algebra of the Infrared: Massive d=2 N=(2,2) QFT'', or ``A short ride with a big machine,'' given at the KITP Workshop on Nonperturbative Methods in Field Theory, March 11, 2014 is here . A pdf version is here . This talk is directed more at physicists than mathematicians. (The actual talk at the KITP was an unmitigated disaster due to technical problems with the projector. The video is not recommended.)
- This version emphasizes the formal webology apparatus, "Web formalism and the IR limit of d=2 N=(2,2) QFT'', or ``A short ride with a big machine,'' scheduled to be given at String-Math2014, June 12, 2014: here . A pdf version is here . This talk is directed more at mathematicians than physicists.
- These are lectures delivered at the Erwin Schrodinger Institute in Vienna, August 18-21, 2014. They review the paper with D. Freed on ``Twisted Equivariant Matter.'' An extended set of notes with many proofs and examples is here . A truncated version of these notes, which omits many proofs and examples and is closer to the actual lectures can be found here .
- These are lectures delivered at the Journees de Physiques Mathematiques Lyon on ``BPS States, Hitchin Systems, and Quivers,'' Sept. 3-5, 2014. They review the paper with D. Gaiotto and E. Witten ``Algebra of the Infrared: String Field Theory Structures in Massive N=(2,2) Field Theory in Two Dimensions.'' The first of the lecture series is here . A powerpoint version is here .
- Talk delivered at the IAS, Oct. 13, 2014. ``Algebraic structure of the IR limit of massive d=2 N=(2,2) QFT.'' A pdf version is here . A powerpoint version is here .
- Talk delivered at the SCGP, Nov. 17, 2014. ``Web formalism and the IR limit of massive 2D N=(2,2) QFT -or - A short ride with a big machine.'' A pdf version is here . A powerpoint version is here .
- Three talks delivered at the Conference on Homological Mirror Symmetry, Jan. 26-30, 2015. Lecture notes are here .
- A pair of talks on LG models and the web formalism, given at Harvard and Brandeis, March 5 and 6, 2015. The talk at Harvard is aimed mostly at physicists and is here . The talk at the FRG conference at Brandeis is aimed mostly at mathematicians and is here .
- A talk ``Measuring the elliptic genus,'' given at the workshop ``(Mock) Modularity, Moonshine, and String Theory,'' at the Perimeter Institute, April 17, 2015 can be viewed here .
- Two pedagogical lectures, ``Quantum Mechanics And The 10-Fold Way,'' at the PiTP School, ``New Insights Into Quantum Matter,'' Institute for Advanced Study, July 27 and 28, 2015. The lectures can be viewed viewed here . There are typed lecture notes . In addition there are handwritten notes closer to the actual lectures. See the Munich lectures below for these. (The lectures are better and more complete in the Munich school.)
- ``Measuring The Elliptic Genus,'' given at ``AndyFest: A Celebration of the Science of Andrew Strominger,'' Harvard University, July 31, 2015. The powerpoint is here and a pdf version is here .
- ``Physics Predictions For L2 Kernels Of Dirac-Like Operators On Monopole Moduli Spaces,'' given at the workshop on metric and analytic aspects of moduli spaces, Isaac Newton Institute, Cambridge, UK, August 13, 2015. Video of the seminar is available here .
- Three pedagogical lectures, ``Quantum Mechanics And 10-Fold Ways,'' at the school on topological phases of matter, Arnold Sommerfeld Center for Theoretical physics, Munich, September , 2015. The lectures can be viewed viewed here . The handwritten notes for these are Lecture 1 , Lecture 2 , and Lecture 3 .
- ``Monopolia,'' delivered at the Seventh New England String Theory Meeting, Brown University, November 6, 2015. The powerpoint is here and a pdf version is here . A longer (and improved) version, delivered at the CUNY workshop, Dec. 4 is here and a pdf version is here .
- An updated version of the Aalborg review from 2012, ``d=4, N=2 Field Theory and Physical Mathematics,'' given to the AMS chapter of graduate students at Rutgers, Dec. 17, 2015 is here .
- A talk about monopoles and BPS states that I WOULD have given at the conference ``Geometry and Physics: Mirror symmetry, Hodge theory, and related topics,'' held at the University of Miami, January 25-30, 2016, in honor of Ron Donagi's 60th birthday, had it not been for the absolutely astonishing and total incompetence of United Airlines, can be found here .
- A talk given in honor of Dave Morrison's 60th birthday, delivered at Caltech, Feb. 25, 2016 at the DaveDay conference is here and a pdf version is here .
- An updated version of ``Monopolia,'' delivered at the Nambu Memorial Symposium, Sunday March 13, 2016 is here and a pdf version is here .
- A colloquium-level talk reviewing four-dimensional N=2 field theories and some aspects of BPS states, at Johns Hopkins, Monday, April 11, 2016, is here . This is a pdf version . A better version, given at Yale, Monday, February 23, 2017 is here . This is a pdf version . A version for CERN, scheduled for July 12, 2017 is here .
- A talk updating my DaveDay talk, delivered June 23 at the Retrospective CY workshop at Herstmonceaux Castle is here . This is a pdf version . And here is a further updated version given at the SCGP workshop on Automorphic Forms and String Theory, August 31, 2016. Finally this is a version given at Yale, and the pdf is here .
- My StringMath2016 talk, delivered in Paris, June 27 is here . This is a pdf version . Here is the Aspen version .
- Talk for Dirac Medal ceremony, delivered in Trieste, August 8, is here and this is a pdf version .
- My talk at NatiFest at the Institute for Advanced Study, Princeton, September 15, 2016, is here and this is a pdf version . (To view the powerpoint you need to use the slide show and the custom show ``NatiReverseOrder1’’ - it is the only way to get PowerPoint to number the slides in decreasing order. Of course, what matters to most members of the audience is how many slides remain in a talk, not how many have already been covered.)
- Powerpoint for my talk at the PCTS conference, ``New Developments in Conformal Field Theory Above Two Dimensions (CFT),'' called simply ``Three Remarks on N=2 d=4 Field Theory,'' is here and this is a pdf version . Link to the conference is here . A version scheduled to be given on July 3, 2017 at the workshop ``String Theory and Quantum Gravity,'' in Ascona, Switzerland, is here and this is a pdf version .
- Powerpoint for my comments at the PCTS panel discussion combining the previous conference with ``The Quantum Hall Effect: Past, Present & Future (QHE),'' is here and this is a pdf version . Link to the conference is here .
- Lecture notes on ``The Physical Approach To Donaldson And Seiberg-Witten Invariants,'' - STILL UNDER CONSTRUCTION - for lectures delivered at the SCGP March 22,23,24, 2017 are here . Comments are welcome. Lectures can be viewed on the SCGP video portal here . A fourth lecture concluding the series was delivered at the SCGP, April 26, 2017 and the powerpoint is here . The talk is available on the SCGP Video portal. A pdf version is here . Here are handwritten lecture notes for Lecture 1 , Lecture 2 , and Lecture 3 .
- Here are handwritten notes of my talk at the Aspen workshop ``New Moonshines and Quantum Gravity,'' entitled Uber T-Dualische Transformationen: Giving Orbifold Groups A Lyft .
- A talk on the u-plane integral and partition functions of twisted supersymmetric field theories given at the Euro-Strings Conference at Kings College London, April 2018 is here in pdf and here in powerpoint
- A talk on the cancellation of global anomalies in six-dimensional supergravity theories, given on May 16, 2018 at MIT is here in pdf and here in powerpoint
- My StringMath-2018 talk, ``Partition Functions Of Twisted Supersymmetric Gauge Theories On Four-Manifolds via u-Plane Integrals,'' delivered on June 20, 2018 in Sendai is here in powerpoint and here in pdf
- My Strings-2018 talk, ``Global Anomalies In Six-Dimensional Supergravity,'' delivered on June 29, 2018 in Okinawa is here in powerpoint and here in pdf
- Here are three lectures on class S field theories delivered at the Hamburg School On Higgs Bundles, September 10,11,13, 2018. The lecture notes for Lecture 1 have several sources for background material. They are all readily available except for my ITP lectures on D-branes. For light reading you can look at my article in the Notices of the AMS. In fact, Lecture 1 took all the time, (in part due to a lot of good questions from the students). But, for the record, here are my notes for the intended Lecture 2 and Lecture 3 .
- Slightly updated colloquium "Four-dimensional N=2 supersymmetric field theories and Physical Mathematics,'' delivered at Stanford, Nov. 27, 2018 is here in powerpoint and here in pdf
- Seminar at Stanford "Finding The Golay Code In A K3 Sigma-Model'' delivered at Stanford, Dec. 3, 2018 is .....
- "K3 Surfaces, Matheiu Moonshine, and (Quantum) Error Correcting Codes'' delivered Tuesday, Jan. 15, Austin TX, at Dan Freed's 60th birthday conference, ``Between Topology And Quantum Field Theory,'' is here in powerpoint and here in pdf
- ``Categorified Wall Crossing And Twisted Masses,'' Simons Center for Geometry and Physics workshop on holomorphic differentials, Feb. 6, 2019. Video of talk available at SCGP video portal.
- ``Categorified Wall Crossing And Twisted Masses - v2,'' Simons Center for Geometry and Physics workshop on Challenges at the Interface of Hitchin Systems and String Theory, March 21, 2019. A video of the talk is available on the SCGP video portal. Lecture notes are here in pdf
- "Moonshine Phenomena, Supersymmetry, and (Quantum) Error Correcting Codes'' delivered Friday, April 12, Yale, at Nick Read's 60th birthday conference, ``Field theory in condensed matter: a symposium in honor of Nick Read,'' is here in powerpoint and here in pdf
- I gave a talk for the general public on May 29, 2019 at this event. The talk is here. and also online. A slightly revised version for the Park City Mathematics Institute, scheduled to be delivered on July 9, 2019 is here in power point and here in pdf .
- I gave a series of pedagogical lectures on Chern-Simons theory during the week of June 3, 2019. A preliminary version of the lecture notes can be found here. These notes are still a mess and much work remains to be done. Any constructive criticism is welcome.
- I gave an overview of the papers of Gaiotto, Moore, and Neitzke at the IAS group meeting, Sept. 18, 2019. The talk is video-archived on the IAS website. My lecture notes are here.
- I gave a talk on work with Ahsan Khan on including twisted masses in the categorified wall-crossing story here. This was given November 28, 2019 at the workshop at DESY and in December at UT Austin, both unrecorded. The title was ``Branes And Interfaces For 2D Landau-Ginzburg Models With Twisted Masses.''
- I gave an invited address at the Joint Mathematics Meeting (JMM) in Denver, on Jan. 18, 2020. A powerpoint version (with two corrections) can be found here. A pdf version is here. A video of the talk is here.
- I gave a talk in the series, Western Hemisphere Colloquium on Geometry and Physics, on July 20, 2020. The title is, ``Breaking News, About N=2* SYM on Four-Manifolds, Without Spin.'' A powerpoint version can be found here. A pdf version is here.
- I gave a Zoominar at Caltech, August 14, 2020, ``Moonshine Phenomena, Supersymmetry, and Quantum Codes.'' A powerpoint version can be found here. A pdf version is here.
- I gave a talk at the KITP conference on modularity, Dec. 3, 2020, ``N=2* Supersymmetric Yang Mills Theory, Four-Manifold Invariants, And Mock Modularity.'' A powerpoint version can be found here. A pdf version is here.
- A hastily prepared summary of some background for Fei Yan's talk at a Simons Collaboration on special holonomy can be found here.
- Another talk on N=2* SYM and four-manifold invariants, with interesting comments by IAS faculty, on March 15, 2021 is here.
- Another talk on my work on N=2* and 4-fold invariants can be found a talk at the Newton Institute workshop ``New connections in number theory and physics'' here in powerpoint and here in pdf
- ``2d Categorical Wall-Crossing With Twisted Masses And An Application To Knot Invariants.'' One version was delivered June 2, 9am (in Japan) at the IPMU conference Number Theory, Strings, and Quantum Physics. A video of the talk is here . A better version was given September 22, 2021 at Yan Soibelman's M-seminar. The powerpoint is here in powerpoint and here in pdf . The video is available here , and there are a number of interesting comments by Yan after the talk. A shorter version, aimed at a broader audience is here in powerpoint and here in pdf . It was given at the conference ``Seminal Interactions between Mathematics and Physics'' at the Academia Nazionale dei Lincei ``in'' Rome, September 29, 2021. Videos of the talks at the conference can be found here .
- I gave a short presentation with Nikita Nekrasov in a discussion session at the Simons Collaboration on Global Categorical Symmetry kickoff meeting. Slides are here in powerpoint.
- I gave a talk on Summing Over Bordisms In TQFT at the Harvard CMSA, March 16, 2022. Slides are here in powerpoint. and here in pdf. and youtube video of the talk is here.
- A talk on the mathematics of square dancing is here in powerpoint. Delivered on May 11, 2022 at MikeFest, the 60th birthday conference at the IHES, Paris, for Mike Douglas. The talks are available here.
- A talk for Jeff Harvey's 65th birthday at JeffFest at the University of Chicago is here in powerpoint. Delivered on May 14, 2022. This talk, and all the other talks at JeffFest can be accessed here.
- A talk for Sasha Goncharov's 60th birthday at Yale, but delivered by zoom, Delivered May 23, 2022. The powerpoint slides are here.
- A talk for Igor Frenkel's 70th birthday conference at the SCGP, but delivered by zoom. Delivered June 3, 2022. The powerpoint slides are here. The pdf of the slides is here.
- ``Quantum Field Theory and Invariants Of Smooth Manifolds,'' delivered by zoom at the British Math Colloquium, June 6, 2022. Powerpoint slides of a preliminary version are here in powerpoint and here in pdf. This talk is similar to my JMM talk in January 2020, but has been slightly improved and the last twenty-five minutes updated to reflect new developments. A video of the talk can be found here
- ``Three Pedestrian Overpasses Between Number Theory And Physics,'' delivered, via zoom, at the Workshop, ``Crossing the bridge: New connections in number theory and physics,'' at the Isaac Newton Institute, Cambridge, on August 25, 2022, with conference website . Here are the slides in powerpoint and in pdf .
- ``Square Dancing And Its Relation To Mathematics,'' delivered on October 27, 2022, with Karin Rabe, at the Kansas State University Art and Mathematics Seminar Series. This is a summary . A video recording of the talk is available .
- ``Some Questions Of Possible Interest To This Collaboration,'' is a talk delivered at the Simons Foundation in New York on Friday, November 18, 2022 for the Simons Collaboration on Global Categorical Symmetry. The slides are here and a pdf version is here . The talk can be viewed online .
- ``Summing Over Bordisms In TQFT,'' was delivered in the Cardiff University series on geometry, mathematical physics, topology,... on Tuesday, November 22, 2022. These are the slides and this is the pdf version . A video recording of the talk is available at ???
- ``Supersymmetric QFT And Invariants Of Smooth Four-Manifolds,'' delivered to Yongbin Ruan's group at Zheijiang University, Tuesday, Jan. 3, 2023 (Beijing) via zoom. These are the slides and this is the pdf.
- ``Finite Symmetries Of Field Theory From TQFT,'' Oxford University Symmetry Seminar, Tuesday, May 23, 2023 via zoom. These are the slides and This is the pdf.
- On June 12,14,15,16, 2023 I gave four lectures at the TASI School ``Aspects Of Symmetry.'' Handwritten lecture notes are available for Lecture one on topological field theory and Lecture ``three'' on Generalized Abelian Gauge Theory (really this was lecture 2), and Lecture ``four'' on Differential cohomology (really this was lectures 3 and 4). In addition there are notes for material I didn't get to: on extended topological field theory and defects.
- Karin Rabe and I gave an updated version of our talk ``Square Dancing And Its Relation To Mathematics'' at TASI 2023, on June 13, 2023. The TASI lectures can be viewed on Youtube. This is the video of our talk on square dancing. ERRATUM: On slide 35, around 27:30 into the talk I state that the set of dancer states is a Z/4Z bundle over the set of FASR's. Actually, the situation is a bit more complicated. For generic FASR's there are 8 possible dancer states, not 4. There are two group operations on a dancer state that preserves the FASR. One is the group of 90 degree rotations around the flagpole center (as discussed in the talk). But there is also a group of cyclic permutations of boys and girls around the formation which forms a second action of Z/4Z. Two 90 degree rotations is equivalent to two cyclic permutations so that the bundle actually has structure group G=(Z/4Z x Z/4Z)/D where D is isomorphic to Z/2Z and is generated by (2,2). G is noncanonically isomorphic to Z/2Z x Z/4Z. The situation is actually even more complicated because on some special FASR's (such as a Squared Set) (1,-1) acts trivially, so we really have a G bundle over an orbifold.
- ``Finite Symmetries Of Field Theory From TQFT,'' Scheduled for the conference "Strings In Seoul," Sept. 15, 10am via zoom. These are the slides and This is the pdf. This is an improved version of the Oxford Seminar talk above. The talk can be viewed here.
- ``On The Physical Mathematics Dialogue,'' A talk delivered October 27, 2023 at the conference ``Mathematics in Science: Perspectives and Prospects,'' at the Harvard CMSA. This is a preliminary version of the slides , and here is a version in pdf, and this is a video of that talk.
- ``Update On Susy Field Theory And Invariants Of Smooth Four-Manifolds,'' delivered on February 2, 2024 at the Institute For Advanced Study. This is a preliminary version of the slides , and here is a version in pdf, and this is a video of that talk.
- ``Update On Susy Field Theory And Invariants Of Smooth Four-Manifolds,'' delivered on June 14, 2024 at StringMath 2024, ICTP Here is the powerpoint , this is a pdf version and this is a video of that talk.
- ``From Rational Conformal Field Theory To Modular Tensor Categories To Nonabelions,'' delivered on September 26, 2024 in the online Plectics Laboratories series Perspectives in Theoretical Physics on the history of physics. Here is the powerpoint , this is a pdf version . A recording will eventually be available on youtube.
· Clay Mathematical Institute Lectures
If you are looking for ``D-branes and K-theory in 2D topological field theory,’’ hep-th/0609042 you can get a pdf file here Dbranes_Ktheory_Final.pdf,
Or a postscript file here (warning 23MB!) Dbranes_Ktheory_Final.ps, or you can get the
Revised May 20, 2007