**Work Experience**
- Deputy Director
Institute of Mathematics, Academia Sinica
2013/8 - Present
- 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 T. Arakawa, H. Yamada) "Parafermion vertex operator algebras and W-algebras",
*Trans. Amer. Math. Soc., *
371 (2019-03), no. 6, 4277-4301.
- (with Hiroki Shimakura) "Inertia groups and uniqueness of holomorphic vertex operator algebras",
*Transformation groups, *
(2019), .
- (with C. P. Jiang, H. Yamauchi) "Vertex operator algebras generated by Ising vectors of $\sigma$-type",
*Mathematische Zeitschrift, *
(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 (2019), no. 1, 31-54-.
- (with H. Shimakura) "On orbifold constructions associated with the Leech lattice vertex operator algebra",
*Mathematical Proceedings of the Cambridge Philosophical Society., *
(2019), .
- (with Xingjun Lin) "A Holomorphic vertex operator algebra of central charge 24 with weight one Lie algebra $F_{4,6}A_{2,2}$",
*J. Pure and Applied Algebra, *
(2019), .
- (with Hiroki Shimakura) "Reverse orbifold construction and uniqueness of holomorphic vertex operator algebras",
*Trans. Amer. Math. Soc., *
(2019), .
- (with T. Abe, H. Yamada) "On $\mathbb{Z}_p$-orbifold constructions of the Moonshine vertex operator algebra",
*Mathematische Zeitschrift, *
290 (2018-10), no. 1, 683- 697-.
- (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 (2018), 24-51-.
- (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 (2018), no. 1-2, 75-100-.
- (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., *
(2017), .
- (with Hiroshi Yamauchi) "The Conway-Miyamoto correspondences for the Fischer 3-transposition groups",
*preprint, *
(2017), .
- (with Hiroshi Yamauchi) "3-dimensional Griess algebras and Miyamoto involutions",
*Bull. Inst. Math. Acad. Sin. (N.S.), *
(2017), .
- (with H.Y. Chen) "Quantum dimensions and fusion rules of the VOA $V_{L_{C\times D}}^\tau$",
*Journal of Algebra, *
459 (2016-08), 309-349.
- (with H. Shimakura) "Orbifold construction of holomorphic vertex operator algebras associated to inner automorphisms",
*Communications in Mathematical Physics, *
342 (2016-03), no. 3, 803-841.
- (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 (2016), 1575-1585.
- (with C.S. Su) "Griess algebras generated by the Griess algebras of two 3A-algebras with a common axis",
*J. Math Soc. Japan, *
67 (2015-04), no. 2, 453-476.
- (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 (2015), no. 1, 111-137.
- (with H. Yamauchi) "On 3-transposition groups generated by $\sigma$-involutions associated to $c=4/5$ Virasoro vectors",
*J. Algebra, *
416 (2014), 84-121.
- (with H.Y. Chen) "An explicit Majorana representation of the group $3^2{:}2$ of $3C$-pure type",
*Pacific Journal of Mathematics, *
271 (2014), no. 1, 25-51.
- (with Hsian Yang Chen) "Weyl groups and vertex operator algebras generated by Ising vectors satisfying $(2B,3C)$ condition",
*Rev. Math. Phys., *
26 (2014), no. 6, 1450011-(24 pages).
- "A level-rank duality for parafermion vertex operator algebras of type A",
*Proc. Amer. Math. Soc., *
142 (2014), no. 12, 4133-4142.
- (with T. Arakawa, H. Yamada) "Zhu's algebras, $C_2$-algebras and $C_2$-cofiniteness of parafermion vertex operator algebras",
*Adv. Math., *
264 (2014), 261-295.
- (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 (2014), no. 1, 148-173.
- (with C.S. Su) "Griess algebras generated by 3 Ising vectors of central 2A-type",
*J. algebra, *
374 (2013), 141-166.
- (with R.L. Griess) "Moonshine paths for $3A$ and $6A$ nodes of the extended $E_8$-diagram",
*J. Algebra, *
379 (2013), 85-112.
- (with Masaaki Harada; Akihiro Munemasa) "Residue codes of extremal Type II $\mathbb{Z}_4$-codes and the moonshine vertex operator algebra",
*Math. Z., *
274 (2013), no. 1, 685-700.
- (with Robert L.~Griess Jr.) "A new existence proof of the Monster by VOA theory",
*Michigan Mathematical Journal, *
61 (2012), 555-573.
- (with R.L. Griess, Jr.) "Diagonal lattices and rootless $EE_8$ pairs",
*J. Pure and Applied Algebra, *
216 (2012), no. 1, 154-169.
- (with H. Shimakura) "Quadratic spaces and holomorphic framed vertex operator algebras of central charge 24",
*Proceedings of the London Mathematical Society, *
104 (2012), no. 3, 540-576. (doi: 10.1112/plms/pdr041)
- (with G. Hoehn, H. Yamauchi) "McKay's $E_6$ observation on the largest Fischer group",
*Comm. Math. Phys., *
310 (2012), 329-365.
- (with Gerald Hoehn; Hiroshi Yamauchi) "McKay's $E_7$ observations on the Baby Monster",
*Inter. Math. Res. Not., *
2012 (2012), 166-212.
- "On the constructions of holomorphic vertex operator algebras of central charge 24",
*Comm. Math. Phys., *
305 (2011), no. 1, 153-198.
- (with Robert L. Griess Jr.) "A moonshine path for $5A$ and associated lattices of ranks 8 and 16",
*J. Algebra, *
331 (2011), 338-361.
- (with R. L. Griess) "A moonshine path from $E_8$ to the Monster",
*J. Pure and Applied Algebra, *
215 (2011), 927-948.
- (with R.L. Griess Jr.) "Dihedral groups and Sums of $EE_8$-lattices",
*Pure and applied mathematics quarterly, *
7 (2011), no. 3, 621-743.
- (with C. Dong, Q. Wang and H. Yamada) "The structure of parafermion vertex operator algebras",
*J. Algebra, *
323 (2010), no. 2, 371-381.
- (with C. Dong,and H. Yamada) "W-algebras related to parafermion algebras",
*J. Algebra, *
332 (2009), 2236-2043.
- (with H. Shimakura) "Frame Stabilizers for Framed Vertex Operator Algebras Associated to Lattices Having 4-Frames",
*Int. Math. Res. Notices, *
2009 (2009), 4547-4577.
- (with S. Sakuma) "On a class of vertex operator algebras having a faithful $S_{n+1}$-action",
*Taiwanese J. Math, *
12 (2008), no. 9, 2465-2488.
- (with R.L. Griess Jr.) "Rootless pairs of EE8-lattices",
*Electronic Research Announcements in Mathematical Sciences, *
15 (2008), 52-61.
- (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 (2008), no. 35, 25-35.
- (with H. Yamauchi) "On the structure of framed vertex operator algebras and their pointwise frame stabilizers",
*Commun. Math. Phys., *
277 (2008), no. 1, 237-285.
- (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 (2007), no. 8, 2487-2505.
- (with C. Dong, R. L. Griess) "Uniqueness results of Frenkel–Lepowsky -Meurman's moonshine vertex operator algebra",
*American Journal of Mathematics, *
129 (2007), no. 2, 583-609.
- (with S. Sakuma and H. Yamauchi) "Ising vectors and automorphism groups of commutant subalgebras related to root systems",
*Mathematische Zeitschrift, *
255 (2007), no. 3, 597-626.
- (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 (2007), no. 9, 4107-4123.
- (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, *
(2005), no. 3, 117-181.
- (with Yamada H) "Tricritical 3-state Potts model and vertex operator algebras constructed from ternary codes",
*Communications in Algebra, *
32 (2004), no. 11, 4197-4219.
- (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 (2004), no. 5, 245-296.
- (with H. Yamada) "Decomposition of the lattice vertex operator algebra $V_{\sqrt{2}A_{\ell}}$",
*Journal of Algebra, *
272 (2004), no. 2, 614-624.
- (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 (2003), 1269-1303.
- (with N. Lam, and H. Yamauchi) "Extension of unitary Virasoro vertex operator algebra by a simple module",
*International Mathematics Research Notices, *
11 (2003), 577-611.
- (with H. Yamada) "$\mathbb{Z}_3$-twisted representations of lattice vertex operator algebras",
*Communications in Algebra, *
31 (2003), no. 6, 3001-3020.
- (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 (2002), no. 1, 15-48.
- (with M. Kitazume, and H. Yamada) "A class of vertex operator algebras constructed from $\mathbb{Z}_8$-codes",
*Journal of Algebra, *
(2001), 338-359.
- "Induced modules for orbifold vertex operator algebras",
*Journal of Mathematical Society of Japan, *
53 (2001), no. 3, 541-557.
- "Fusion rules for Hamming code vertex operator algebra",
*Communications in Algebra, *
29 (2001), no. 5, 2125-2145.
- (with C. Dong,and H. Yamada) "Decomposition of the vertex operator algebra $V_{\sqrt{2}D_n}$",
*Communications in Contemporary Mathematics, *
3 (2001), no. 1, 137-151.
- "Representations of ternary code vertex operator algebras",
*Communications in Algebra, *
29 (2001), no. 3, 951-971.
- "Some twisted modules for framed vertex operator algebras",
*Journal of Algebra, *
231 (2000), 331-341.
- (with K.Kitazume, and H. Yamada) "Decomposition of the Moonshine vertex operator algebra as Virasoro modules",
*Journal of Algebra, *
226 (2000), 893-919.
- (with H. Yamada) "$\mathbb{Z}_2\times \mathbb{Z}_2$ codes and vertex operator algebras",
*Journal of Algebra, *
224 (2000), 268-291.
- (with C. Dong,and H. Yamada) "Decomposition of the vertex operator algebra $V_{\sqrt{2}A_3}$",
*Journal of Algebra, *
222 (1999), 500-510.
- "Code vertex operator algebras under coordinates change",
*Communications in Algebra, *
27 (1999), no. 9, 4587-4605.
- "Twisted repesentations of code vertex operator algebras",
*Journal of Algebra, *
217 (1999), no. 7, 275-299.
- "On VOA associated with special Jordan algebras",
*Communications in Algebra, *
27 (1999), no. 4, 1665-1681.
- "Construction of vertex operator algebras form commutative associative algebras",
*Communications in Algebra, *
24 (1996), no. 14, 4439-4460.
- (with K. Harada) "'Inverses' of Virasoro operators",
*Communications in Algebra, *
23 (1995), no. 12, 4405-4413.