研究員 | 傅約翰

聯絡資訊
- jduncan$\color{red}{@}$gate.sinica.edu.tw
- +886 2 2368-5999 ext. 738
- +886 2 2368-9771
- Moonshine
- vertex algebra
- finite simple groups
- automorphic forms
- arithmetic of algebraic varieties
- conformal field theory
- quantum gravity
- Ph.D. in Mathematics Yale University (2001 - 2006)
- M. S. University of Auckland, Wellington, New Zealand (1999 - 2001)
相關連結
經歷
- Associate Professor Emory University 2018/9 - 2021
- Assistant Professor Emory University 2015/7 - 2018/8
- Project Associate Professor Tokyo University, Japan 2015/5 - 2015/8
- Assistant Professor (tenure track) Case Western Reserve University 2010/10 - 2015/6
- Junior Research Fellow King’s College, Cambridge, U.K 2009/10 - 2010/9
- Benjamin Peirce Lecturer on Mathematics Harvard University 2006/7 - 2009/6
研究簡介
The focus of my work is moonshine, and involves aspects of number theory, algebra, geometry and mathematical physics.
部分著作目錄
- (with Miranda C. N. Cheng and Michael H. Mertens) "Class Numbers, Cyclic Simple Groups and Arithmetic"
, Journal of the London Mathematical Society
, 2022. (Accepted)
- (with Jeffrey A. Harvey and Brandon C. Rayhaun) "Two New Avatars of Moonshine for the Thompson Group"
, arXiv
, 2022. (preprint)
- (with Jeffrey A. Harvey and Brandon C. Rayhaun) "Modular Products and Modules for Finite Groups"
, Algebras and Representation Theory
, 2022. (Accepted)
- (with Jeffrey A. Harvey and Brandon C. Rayhaun) "An Overview of Penumbral Moonshine"
, arXiv
, 2021. (preprint)
- (with Vassilis Anagiannis, Miranda C. N. Cheng, and Roberto Volpato) "Vertex operator superalgebra/sigma model correspondences: The four-torus case"
, Progress of Theoretical and Experimental Physics
, 2021 (8), 2021.
- (with Miranda C. N. Cheng) "Optimal Mock Jacobi Theta Functions"
, Advances in Mathematics
, 372, 2020.
- "A Short Introduction to the Algebra, Geometry, Number Theory and Physics of Moonshine" , Partition Functions and Automorphic Forms , 2020.
- (with David A. McGady) "Modular Forms on the Double Half-Plane"
, International Journal of Number Theory
, 16 (09), 1989-2003, 2020.
- "From the Monster to Thompson to O’Nan"
, Proceedings of the Conference on Vertex Operator Algebras, Number Theory and Related Topics, Contemporary Mathematics
, 753, 2020.
- (with Miranda C. N. Cheng) "Meromorphic Jacobi Forms of Half-Integral Index and Umbral Moonshine Modules"
, Communications in Mathematical Physics
, 370 (3), 759-780, 2019.
- (with Andrew O’Desky) "Super vertex algebras, meromorphic Jacobi forms and umbral moonshine"
, J. Algebra
, 515, 389-407, 2018.
- (with Miranda C. N. Cheng, Sarah M. Harrison, Jeffrey A. Harvey, Shamit Kachru and Brandon C. Rayhaun) "Attractive Strings and Five-Branes, Skew-Holomorphic Jacobi Forms and Moonshine"
, J. High Energy Physics
, 130, 2018.
- (with Miranda C. N. Cheng and Jeffrey A. Harvey) "Weight One Jacobi Forms and Umbral Moonshine" , J. Phys. A: Math. Theor , 51, 2018.
- (with Thomas Creutzig and Wolfgang Riedler) "Self-Dual Vertex Operator Superalgebras and Superconformal Field Theory"
, J. Phys. A: Math. Theor
, 51, 2018.
- (with Michael H. Mertens and Ken Ono) "O’Nan Moonshine and Arithmetic"
, American Journal of Mathematics
, 2017.
- (with Michael H. Mertens and Ken Ono) "Pariah moonshine"
, Nature Communications
, 8 (1), 2017.
- (with Miranda C. N. Cheng, Sarah Harrison and Shamit Kachru) "Equivariant K3 Invariants"
, Communications in Number Theory and Physics
, 11 (1), 2017.
- (with Jeffrey A. Harvey) "The Umbral Moonshine Module for the Unique Unimodular Niemeier Root System"
, Algebra and Number Theory
, 11 (3), 505-535, 2017.
- (with Ken Ono) "The Jack Daniels Problem"
, Journal of Number Theory
, 161, 230-239, 2016-04.
- (with Sander MackCrane) "Derived Equivalences of K3 Surfaces and Twined Elliptic Genera"
, Research in the Mathematical Sciences
, 3:1, 2016.
- (with Michael Griffin and Ken Ono) "Proof of the Umbral Moonshine Conjecture"
, Research in the Mathematical Sciences
, 2:16, 2015.
- (with Michael Griffin and Ken Ono) "Moonshine"
, Research in the Mathematical Sciences
, 2:11, 2015.
- (with Kathrin Bringmann and Larry Rolen) "Maass-Jacobi Poincar´e Series and Mathieu Moonshine"
, Advances in Mathematics
, 281, 248-278, 2015.
- (with Sander Mack-Crane) "The Moonshine Module for Conway’s Group"
, Forum of Mathematics, Sigma
, 3, 2015.
- (with Miranda C. N. Cheng, Xi Dong, Sarah Harrison, Shamit Kachru and Timm Wrase) "Mock Modular Mathieu Moonshine Modules"
, Research in the Mathematical Sciences
, 2:13, 2015.
- (with Miranda C. N. Cheng and Jeffrey A. Harvey) "Umbral Moonshine and the Niemeier Lattices"
, Research in the Mathematical Sciences
, 1:3, 2014.
- "Umbral Moonshine and Linear Codes" , RIMS Kôkyûroku (1872), 2014.
- (with Miranda C. N. Cheng) "On the Discrete Groups of Mathieu Moonshine"
, Perspectives in Representation Theory, Contemporary Mathematics
, 610, 2014.
- (with Pavel Etingof, Ivan Ip, Mikhail Khovanov, Matvei Libine, Anthony Licata, Alistair Savage and Michael Schlosser) "On the work of Igor Frenkel" , Perspectives in Representation Theory, Contemporary Mathematics , 610, 2014.
- (with Miranda C. N. Cheng) "Rademacher Sums and Rademacher Series"
, Conformal Field Theory, Automorphic Forms and Related Topics, Contributions in Mathematical and Computational Sciences
, 8, 143-182, 2014.
- (with Miranda C. N. Cheng and Jeffrey A. Harvey) "Umbral Moonshine"
, Communications in Number Theory and Physics
, 8 (2), 101-242, 2014.
- (with Miranda C. N. Cheng, Xi Dong, Jeffrey A. Harvey, Shamit Kachru and Timm Wrase) "Mathieu Moonshine and N = 2 String Compactifications"
, Journal of High Energy Physics
, 09, 2013.
- (with Miranda C. N. Cheng) "The Largest Mathieu Group and (Mock) Automorphic Forms"
, String-Math 2011, Proceedings of Symposia in Pure Mathematics
, 85, 2012.
- (with Miranda C. N. Cheng) "On Rademacher Sums, the Largest Mathieu Group, and the Holographic Modularity of Moonshine"
, Communications in Number Theory and Physics
, 6 (3), 697-758, 2012.
- (with Christopher J. Cummins) "An E8 correspondence for multiplicative eta-products" , Canadian Mathematical Bulletin , 55, 67-72, 2012.
- (with Igor B. Frenkel) "Rademacher sums, moonshine and gravity"
, Communications in Number Theory and Physics
, 5 (4), 849-976, 2011.
- "Vertex operators and sporadic groups"
, Moonshine - The First Quarter Century and Beyond
, 2010.
- "Extensions of the Virasoro algebra" , Lie Theory and its Applications in Physics VII , 431-438, 2008.
- "Arithmetic groups and the affine E8 Dynkin diagram"
, CRM Proceedings and Lecture Notes
, 47, 2008.
- "Super-moonshine for Conway’s largest sporadic group"
, Duke Math. J.
, 139 (2), 255-315, 2007.
所長及副所長