# Gregory W. Moore

## Directory information

 Position: Faculty Research group: Email address: Telephone: (732) 445-4375 Dept. Fax: (732) 445-4343 Office: Serin E362 Mailing address: Greg Moore NHETC Department of Physics and Astronomy Rutgers, The State University of New Jersey 136 Frelinghuysen Road Piscataway, NJ 08854-8019 USA

## Teaching

Advanced Topics in Mathematical Physics, Fall 2010. will be offered instead. Lectures can be viewed online here

## Research Activities

My work focuses on mathematical physics, with an emphasis on string theory, M-theory, and gauge theories more generally.
My work places particular emphasis on the underlying mathematical structures and applications to and from modern mathematics.
Specific research interests include:

1. 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.
2. Effective low energy supergravity theories in string compactification and the computation of nonperturbative stringy effects in effective supergravities.
3. D-branes on Calabi-Yau manifolds and BPS state counting. Relations to Borcherds products, automorphic forms, black-hole entropy, and wall-crossing.
4. Applications of the theory of automorphic forms to conformal field theory, string compactification, black hole entropy counting, and the AdS/CFT correspondence.
5. 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.
6. Conformal field theories. Rational conformal field theories, especially applications to the theory of anyons and nonabelions.
7. Topological field theories, and applications to invariants of manifolds.
8. String field theory.
9. String cosmology and time-dependence in string theory
10. Does the alleged landscape of N=1 effective four-dimensional string vacua'' really exist?

## Expository, Historical, and Philosophical

1. What is a brane?'' . Published in: Notices of the American Mathematical Society, Vol. 52, No. 2, pp.214-215.
2. 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 .
3. 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 .
4. Response to the 2014 Eisenbud Prize''. I wrote this since the AMS requested a response.
5. 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 .
6. 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 .

## Some Talks

1. 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
2. Lectures at the Les Houches Meeting on Number Theory, Geometry, and
Physics. Les Houches, March 9-21, 2003.
3. Localized tachyon flows and Hirzebruch-Jung spaces, at the conference
Avant Strings,'' Institut des Hautes Etudes Scientifiques, Paris, June 15, 2004.
4. On the quantization of Page charges, at the conference
Avant Strings,'' Institut des Hautes  Etudes Scientifiques, Paris, June 23, 2004
5. Anomalies, Gauss Laws, and Page charges, at the conference
Strings 2004,'' Paris, July 1, 2004.
6. Testing some Black Hole/Topological String conjectures,  Institute
for Advanced Study, April 11, 2005
7. Lie Algebras, BPS States, and String Duality, Summer workshop on
Groups and Algebras in M-theory
, Rutgers Math Department, May 31, 2005
8. Black holes and Arithmetic, Talk delivered at the Mathematicshe Arbeitstagung,
Max Planck Institute, Bonn, Germany, 11 June 2005.
9. Remarks on the Hamiltonian Formulation of Some
Generalized Abelian Gauge Theories, Talk delivered at the workshop,
Geometric Topology and Connections with
Quantum Field Theory,
Oberwolfach, Germany, June 13, 2005.
10. Noncommutativity of Electric and Magnetic Fluxes, Amsterdam Workshop on
String Theory,
June 22, 2005,
11. Electric and Magnetic Flux Do Not Commute, Aspen Workshop in Superstring
Cosmology
, Aspen, Co, August 9, 2005
12. Mathematics Aspects of Fluxes,, KITP Workshop on Mathematics of String Theory,
Cosmology
, Santa Barbara, October 11, 2005
13. An uncertainty principle for fluxes, with applications to self-dual fields, , CUNY, June 28, 2006 (26th International Colloquium on Group Theoretical Methods in Physics)
14. Split Polar Attractors , Harvard, September 29, 2006
15. Wall-crossing and an entropy enigma , Strings 2007, Madrid, June 28,2007. For question period see this link.
16. 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
17. Wall-crossing formulae for BPS states and some applications , Clay Mathematics Institute workshop on K3's and modular forms,
Cambridge, Mass, March 20, 2008
18. 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 .
19. Mathematical Foundations of Orientifolds , UCSB, July 18, 2008
20. Four-dimensional wall-crossing from three-dimensional field theory , KITP Miniprogram on Langlands Duality, July 31, 2008.
21. Wall-crossing formulae for BPS states and some applications , Zurich Prestrings, Zurich, August 11, 2008
22. Four-dimensional wall-crossing from three-dimensional field theory , Zurich Prestrings, Zurich, August 12, 2008
23. Mathematical Foundations of Orientifolds , Zurich Prestrings, Zurich, August 11, 2008
24. Update on Wall-Crossing , Strings 2008, CERN, August 22, 2008. Video of the talk available here.
25. 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
26. Extremal N=2, 2D CFT and Constraints of Modularity Institute for Advanced Study, Nov. 5, 2008
27. Overview of the theory of Self-dual fields AMS Meeting, Washington DC, Jan. 8, 2009. A pdf version is available here
28. Four-dimensional wall-crossing from three-dimensional field theory Simons Center Workshop, StonyBrook, Jan. 13, 2009
29. 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
30. BPS States, Hitchin Systems, and the WKB Approximation Workshop on Mirror Symmetry, Hausdorff Center for Mathematics, Bonn, June 3, 2009
31. 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.
32. The RR charge of an orientifold, Michigan Conference on Topology and Physics, Ann Arbor, Feb. 7, 2010 and Oberwolfach workshop, June 8,2010
33. 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
34. Line Operators in N=2 Gauge Theories, Simons Center Workshop on Quantum Teichmuller Theory, SUNY, Stonybrook, March 30, 2010. The paper is available here
35. 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 .
36. 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 .
37. 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 .
38. Modular Tensor Categories from Six Dimensional Field Theories, Symposium For Michael Freedman's 60th Birthday, KITP, UCSB, April 16, 2011. Video available here .
39. 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 .
40. 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 .
41. 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 .
42. 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 .
43. Spectral Networks and Their Applications, Caltech, March 30, at the conference N=4 Super Yang-Mills Theory, 35 years after.'' Powerpoint presentation here .
44. Progress in D=4, N=2 Field Theory, Strings-Math 2012, Bonn, July 2012 Powerpoint presentation here .
45. Lectures at St. Ottilien: Quantum Symmetries and K-Theory. Lecture notes here .
46. Plenary talk at the ICMP in Aalborg, Denmark, August 8, 2012. Powerpoint version here and pdf here .
47. 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.''
48. 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.''
49. 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 .
50. 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 .
51. 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 .
52. 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.
53. 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.)
54. 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.
55. 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 .
56. 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 .
57. 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 .
58. 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 .
59. Three talks delivered at the Conference on Homological Mirror Symmetry, Jan. 26-30, 2015. Lecture notes are here .
60. 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 .
61. 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 .
62. 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.)
63. 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 .
64. 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 .
65. 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 .
66. 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 .
67. 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 .
68. 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 .
69. 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 .
70. An updated version of Monopolia,'' delivered at the Nambu Memorial Symposium, Sunday March 13, 2016 is here and a pdf version is here .
71. A colloquium-level talk reviewing four-dimensional N=2 field theories and some aspects of BPS states, scheduled to be delivered at Johns Hopkins, Monday, April 11, 2016, is here . This is a pdf version .
72. 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.
73. My StringMath2016 talk, delivered in Paris, June 27 is here . This is a pdf version . Here is the Aspen version .
74. Talk for Dirac Medal ceremony, delivered in Trieste, August 8, is here and this is a pdf version .
75. 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.)

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 tex file Dbranes_Ktheory_Final.tex, and the  figures as    ClayFigsFinal_EPS.zip   or  as  ClayFigsFinal_GIF.zip