**Work Experience**
- Deputy Director
Institute of Mathematics, Academia Sinica
2013/8 - 2019/11
- Research Fellow
Academia Sinica, Taiwan
2009 - Present
- Professor
National Cheng Kung University
2004 - 2009
- Associate Professor
National Cheng Kung University
2001 - 2004
- Assistant Professor
National Cheng Kung University
2000 - 2001
- Research Associate
University of Tsukuba
1997 - 2000
- Lecturer
Ohio State University
1996 - 1997

** Awards **
- Outstanding Research Award, National Science Council, Taiwan, R.O.C.,
2009-2011
- Distinguished Professor, National Cheng Kung University,
2008

** Research Descriptions **

Dr. Lam's research interest is on the structural and representation theory of vertex operator algebras and their applications to the theory of sporadic simple groups. In particular, he is interested in a special vertex operator algebra called Moonshine vertex operator algebra whose full automorphism group is the Monster simple group.

** Selected Publications ↓ **
- (with Jethro van Ekeren, Sven Möller, Hiroki Shimakura) "Schellekens' list and the very strange formula"
,
*Advances in Mathematics*
, 380, 2021-03.
- (with Hsian-Yang Chen) "Fourvolutions and automorphism groups of orbifold lattice vertex operator algebras"
,
*Taiwanese J. Math.*
, 2021.
- (with Hiromichi Yamada) "Sigma involutions associated with parafermion vertex operator algebra $K(sl_2,k)$"
,
*Linear and Multilinear Algebra*
, 2021.
- (with Hiroki Shimakura) "Extra automorphisms of cyclic orbifolds of lattice vertex operator algebras"
,
*arXiv:2103.08085*
, 2021.
- (with Naoki Chigira, Masahiko Miyamoto) "Orbifold construction and Lorentzian construction of Leech lattice vertex operator algebra"
,
*arXiv:2104.03098*
, 2021.
- (with J. Connor Grady, James E. Tener, Hiroshi Yamauchi) "Classification of extremal vertex operator algebras with two simple modules"
,
*Journal of Mathematical Physics*
, 61 (5), 2020.
- (with Lin, Xingjun) "A holomorphic vertex operator algebra of central charge 24 with the weight one Lie algebra $F_{4,6}A_{2,2}$"
,
*J. Pure Appl. Algebra*
, 224 (3), 1241-1279, 2020.
- "Cyclic orbifolds of lattice vertex operator algebras having group-like fusions"
,
*Letters in Mathematical Physics*
, 110 (5), 1081-1112, 2020.
- (with Hiroki Shimakura) "Inertia groups and uniqueness of holomorphic vertex operator algebras"
,
*Transformation groups*
, 2020.
- (with H. Shimakura) "On orbifold constructions associated with the Leech lattice vertex operator algebra"
,
*Mathematical Proceedings of the Cambridge Philosophical Society.*
, 168 (2), 261-285, 2020.
- (with Hiroki Shimakura) "Reverse orbifold construction and uniqueness of holomorphic vertex operator algebras"
,
*Trans. Amer. Math. Soc.*
, 372 (10), 7001-7024, 2019-11.
- (with T. Arakawa, H. Yamada) "Parafermion vertex operator algebras and W-algebras"
,
*Trans. Amer. Math. Soc.*
, 371 (6), 4277-4301, 2019-03.
- (with D. Adamovic, V. Pedić, N. Yu) "On irreducibility of modules of Whittaker type for cyclic orbifold vertex algebras"
,
*J. Algebra*
, 539, 1-23, 2019.
- (with C. P. Jiang, H. Yamauchi) "Vertex operator algebras generated by Ising vectors of $\sigma$-type"
,
*Mathematische Zeitschrift*
, 293 (1-2), 425-442, 2019.
- (with C. P. Jiang) "Level-Rank Duality for Vertex Operator Algebras of types B and D"
,
*Bull. Inst. Math. Acad. Sin. (N.S.)*
, 14 (1), 31-54, 2019.
- (with Hiroshi Yamauchi) "3-dimensional Griess algebras and Miyamoto involutions"
,
*Bull. Inst. Math. Acad. Sin. (N.S.)*
, 14 (2), 119-147, 2019.
- (with T. Abe, H. Yamada) "On $\mathbb{Z}_p$-orbifold constructions of the Moonshine vertex operator algebra"
,
*Mathematische Zeitschrift*
, 290 (1), 683- 697-, 2018-10.
- (with T. Abe, H. Yamada) "Extensions of tensor products of $\mathbb{Z}_p$-orbifold models of the lattice vertex operator algebra $V_{\sqrt{2}A_{p-1}}$"
,
*J. Algebra*
, 510, 24-51-, 2018.
- (with Chongying Dong, Li Ren) "Modular framed vertex operator algebras"
, 2018.
- (with Hsian-Yang Chen, Hiroki Shimakura) "$\mathbb{Z}_3$-orbifold construction of the Moonshine vertex operator algebra and some maximal 3-local subgroups of the Monster"
,
*Mathematische Zeitschrift*
, 288 (1-2), 75-100-, 2018.
- (with Kazuya Kawasetsu, Xingjun Lin) "$\mathbb{Z}_2$-orbifold construction associated with $(−1)$-isometry and uniqueness of holomorphic vertex operator algebras of central charge 24"
,
*Proceedings of Amer. Math. Soc.*
, 146 (5), 1937-1950, 2018.
- (with Hiroshi Yamauchi) "The Conway-Miyamoto correspondences for the Fischer 3-transposition groups"
,
*preprint*
, 2017.
- (with H.Y. Chen) "Quantum dimensions and fusion rules of the VOA $V_{L_{C\times D}}^\tau$"
,
*Journal of Algebra*
, 459, 309-349, 2016-08.
- (with H. Shimakura) "Orbifold construction of holomorphic vertex operator algebras associated to inner automorphisms"
,
*Communications in Mathematical Physics*
, 342 (3), 803-841, 2016-03.
- (with H. Shimakura) "A holomorphic vertex operator algebras of central charge 24 whose weight one Lie algebra has type $A_{6,7}$"
,
*Letters in Mathematical Physics*
, 106, 1575-1585, 2016.
- (with C.S. Su) "Griess algebras generated by the Griess algebras of two 3A-algebras with a common axis"
,
*J. Math Soc. Japan*
, 67 (2), 453-476, 2015-04.
- (with R.L. Griess Jr.) "Groups of Lie Type, Vertex Algebras, and Modular Moonshine"
,
*International Mathematics Research Notices*
, 2015.
- (with H. Shimakura) "Classification of holomorphic framed vertex operator algebras of central charge 24"
,
*Amer. J. Math*
, 137 (1), 111-137, 2015.
- (with H. Yamauchi) "On 3-transposition groups generated by $\sigma$-involutions associated to $c=4/5$ Virasoro vectors"
,
*J. Algebra*
, 416, 84-121, 2014.
- (with H.Y. Chen) "An explicit Majorana representation of the group $3^2{:}2$ of $3C$-pure type"
,
*Pacific Journal of Mathematics*
, 271 (1), 25-51, 2014.
- (with Hsian Yang Chen) "Weyl groups and vertex operator algebras generated by Ising vectors satisfying $(2B,3C)$ condition"
,
*Rev. Math. Phys.*
, 26 (6), 1450011-(24 pages), 2014.
- "A level-rank duality for parafermion vertex operator algebras of type A"
,
*Proc. Amer. Math. Soc.*
, 142 (12), 4133-4142, 2014.
- (with T. Arakawa, H. Yamada) "Zhu's algebras, $C_2$-algebras and $C_2$-cofiniteness of parafermion vertex operator algebras"
,
*Adv. Math.*
, 264, 261-295, 2014.
- (with H.Y. Chen) "Coset Construction of $\mathbb{Z}/3$ orbifold vertex operator algebra $V_{\sqrt{2}A_2}^\tau$"
,
*J. Pure and Applied Algebra*
, 218 (1), 148-173, 2014.
- (with C.S. Su) "Griess algebras generated by 3 Ising vectors of central 2A-type"
,
*J. algebra*
, 374, 141-166, 2013.
- (with R.L. Griess) "Moonshine paths for $3A$ and $6A$ nodes of the extended $E_8$-diagram"
,
*J. Algebra*
, 379, 85-112, 2013.
- (with Masaaki Harada; Akihiro Munemasa) "Residue codes of extremal Type II $\mathbb{Z}_4$-codes and the moonshine vertex operator algebra"
,
*Math. Z.*
, 274 (1), 685-700, 2013.
- (with Robert L.~Griess Jr.) "A new existence proof of the Monster by VOA theory"
,
*Michigan Mathematical Journal*
, 61, 555-573, 2012.
- (with R.L. Griess, Jr.) "Diagonal lattices and rootless $EE_8$ pairs"
,
*J. Pure and Applied Algebra*
, 216 (1), 154-169, 2012.
- (with H. Shimakura) "Quadratic spaces and holomorphic framed vertex operator algebras of central charge 24"
,
*Proceedings of the London Mathematical Society*
, 104 (3), 540-576, 2012. (doi: 10.1112/plms/pdr041)
- (with G. Hoehn, H. Yamauchi) "McKay's $E_6$ observation on the largest Fischer group"
,
*Comm. Math. Phys.*
, 310, 329-365, 2012.
- (with Gerald Hoehn; Hiroshi Yamauchi) "McKay's $E_7$ observations on the Baby Monster"
,
*Inter. Math. Res. Not.*
, 2012, 166-212, 2012.
- "On the constructions of holomorphic vertex operator algebras of central charge 24"
,
*Comm. Math. Phys.*
, 305 (1), 153-198, 2011.
- (with Robert L. Griess Jr.) "A moonshine path for $5A$ and associated lattices of ranks 8 and 16"
,
*J. Algebra*
, 331, 338-361, 2011.
- (with R. L. Griess) "A moonshine path from $E_8$ to the Monster"
,
*J. Pure and Applied Algebra*
, 215, 927-948, 2011.
- (with R.L. Griess Jr.) "Dihedral groups and Sums of $EE_8$-lattices"
,
*Pure and applied mathematics quarterly*
, 7 (3), 621-743, 2011.
- (with C. Dong, Q. Wang and H. Yamada) "The structure of parafermion vertex operator algebras"
,
*J. Algebra*
, 323 (2), 371-381, 2010.
- (with C. Dong,and H. Yamada) "W-algebras related to parafermion algebras"
,
*J. Algebra*
, 332, 2236-2043, 2009.
- (with H. Shimakura) "Frame Stabilizers for Framed Vertex Operator Algebras Associated to Lattices Having 4-Frames"
,
*Int. Math. Res. Notices*
, 2009, 4547-4577, 2009.
- (with S. Sakuma) "On a class of vertex operator algebras having a faithful $S_{n+1}$-action"
,
*Taiwanese J. Math*
, 12 (9), 2465-2488, 2008.
- (with R.L. Griess Jr.) "Rootless pairs of EE8-lattices"
,
*Electronic Research Announcements in Mathematical Sciences*
, 15, 52-61, 2008.
- (with C. Dong,and H. Yamada) "W-algebras in lattice vertex operator algebras, in Lie Theory and Its Applications in Physics VII, ed. by H.-D. Doebner and V. K. Dobrev, Proc. of the VII International Workshop"
,
*Varna, Bulgaria*
, 2007 (35), 25-35, 2008.
- (with H. Yamauchi) "On the structure of framed vertex operator algebras and their pointwise frame stabilizers"
,
*Commun. Math. Phys.*
, 277 (1), 237-285, 2008.
- (with H. Shimakura) "Ising vectors in the vertex operator algebra $V_{\Lambda}^+$ associated with the Leech lattice Λ"
,
*Intern. Math. Res.*
, 2007, 2007.
- (with H. Yamauchi) "A characterization of the moonshine vertex operator algebra by means of Virasoro frames"
,
*Intern. Math. Res. Notices*
, 2007, 2007.
- (with T. S. Chen) "Extension of the tensor product of unitary Virasoro vertex operator algebras"
,
*Communications in Algebras*
, 35 (8), 2487-2505, 2007.
- (with C. Dong, R. L. Griess) "Uniqueness results of Frenkel–Lepowsky -Meurman's moonshine vertex operator algebra"
,
*American Journal of Mathematics*
, 129 (2), 583-609, 2007.
- (with S. Sakuma and H. Yamauchi) "Ising vectors and automorphism groups of commutant subalgebras related to root systems"
,
*Mathematische Zeitschrift*
, 255 (3), 597-626, 2007.
- (with H. Yamada and H. Yamauchi) "Vertex operator algebra, extended E8 diagram and McKay’s observation on the Monster simple group"
,
*Transactions of American Mathematical Society*
, 359 (9), 4107-4123, 2007.
- (with M. Miyamoto) "Niemeier Lattices, Coxeter elements and McKay's E8 observation on the Monster simple group"
,
*Intern. Math. Res. Notices*
, 2006.
- (with H. Yamada, and H. Yamauchi) "McKay's observation and vertex operator algebras generated by two conformal vectors of central charge 1/2"
,
*Intern. Math. Res. Paper*
(3), 117-181, 2005.
- (with Yamada H) "Tricritical 3-state Potts model and vertex operator algebras constructed from ternary codes"
,
*Communications in Algebra*
, 32 (11), 4197-4219, 2004.
- (with C. Dong, K. Tanabe, H. Yamada, and K. Yokoyama) "$\mathbb{Z}_3$ symmetry and $W_3$ algebra in lattice vertex operator algebras"
,
*Pacific Journal of Mathematics*
, 215 (5), 245-296, 2004.
- (with H. Yamada) "Decomposition of the lattice vertex operator algebra $V_{\sqrt{2}A_{\ell}}$"
,
*Journal of Algebra*
, 272 (2), 614-624, 2004.
- (with M. Kitazume, and H. Yamada) "3-state Potts model, Moonshine vertex operator algebra and 3A-elements of the Monster group"
,
*International Mathematics Research Notices*
, 23, 1269-1303, 2003.
- (with N. Lam, and H. Yamauchi) "Extension of unitary Virasoro vertex operator algebra by a simple module"
,
*International Mathematics Research Notices*
, 11, 577-611, 2003.
- (with H. Yamada) "$\mathbb{Z}_3$-twisted representations of lattice vertex operator algebras"
,
*Communications in Algebra*
, 31 (6), 3001-3020, 2003.
- (with M. Kitazume, and H. Yamada) "Moonshine vertex operator algebra as L(1/2,0) × L(7/10,0) × L(4/5,0) × L(1,0) -modules"
,
*Journal of Pure and Applied Algebra*
, 173 (1), 15-48, 2002.
- (with M. Kitazume, and H. Yamada) "A class of vertex operator algebras constructed from $\mathbb{Z}_8$-codes"
,
*Journal of Algebra*
, 338-359, 2001.
- "Induced modules for orbifold vertex operator algebras"
,
*Journal of Mathematical Society of Japan*
, 53 (3), 541-557, 2001.
- "Fusion rules for Hamming code vertex operator algebra"
,
*Communications in Algebra*
, 29 (5), 2125-2145, 2001.
- (with C. Dong,and H. Yamada) "Decomposition of the vertex operator algebra $V_{\sqrt{2}D_n}$"
,
*Communications in Contemporary Mathematics*
, 3 (1), 137-151, 2001.
- "Representations of ternary code vertex operator algebras"
,
*Communications in Algebra*
, 29 (3), 951-971, 2001.
- "Some twisted modules for framed vertex operator algebras"
,
*Journal of Algebra*
, 231, 331-341, 2000.
- (with K.Kitazume, and H. Yamada) "Decomposition of the Moonshine vertex operator algebra as Virasoro modules"
,
*Journal of Algebra*
, 226, 893-919, 2000.
- (with H. Yamada) "$\mathbb{Z}_2\times \mathbb{Z}_2$ codes and vertex operator algebras"
,
*Journal of Algebra*
, 224, 268-291, 2000.
- (with C. Dong,and H. Yamada) "Decomposition of the vertex operator algebra $V_{\sqrt{2}A_3}$"
,
*Journal of Algebra*
, 222, 500-510, 1999.
- "Code vertex operator algebras under coordinates change"
,
*Communications in Algebra*
, 27 (9), 4587-4605, 1999.
- "Twisted repesentations of code vertex operator algebras"
,
*Journal of Algebra*
, 217 (7), 275-299, 1999.
- "On VOA associated with special Jordan algebras"
,
*Communications in Algebra*
, 27 (4), 1665-1681, 1999.
- "Construction of vertex operator algebras form commutative associative algebras"
,
*Communications in Algebra*
, 24 (14), 4439-4460, 1996.
- (with K. Harada) "'Inverses' of Virasoro operators"
,
*Communications in Algebra*
, 23 (12), 4405-4413, 1995.