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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?
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
- 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 Recent Talks
- 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
- 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.
- 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 .
- 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 and lecture notes available 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. You could watch the videos of the actual lectures here . However, I am reminded of Mark Twain's wonderful chapter conclusion: ``Let us draw the curtain of charity over the rest of the scene.''
- 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 .
· 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