Andrew R. Linshaw

Professor Department of Mathematics University of Denver 2390 S. York St. Denver, CO 80208 USA

Office: Knudson Hall 214 Phone: (303) 871-2802 Fax: (303) 871-3173 email: andrew.linshaw@du.edu

• RESEARCH INTERESTS: Representation theory, invariant theory, vertex algebras and infinite-dimensional Lie algebras

• FUNDING: I am currently supported by National Science Foundation Grant DMS-2401382 and Simons Foundation Grant MPS-TSM-00007694. Previously, I was supported by National Science Foundation Grant DMS-2001484 from 2020-2024, Simons Foundation Grant 635650 from 2019-2020, and Simons Foundation Grant 318755 from 2014-2019.

• PUBLICATIONS AND PREPRINTS:
  
  
  • The cohomology algebra of the semi-infinite Weil complex, Commun. Math. Phys. 267 (2006), 13-23. Arxiv.
    
  • Howe pairs in the theory of vertex algebras (with B. Lian), J. Algebra 317 (2007), 111-152. Arxiv.
    
  • Chiral equivariant cohomology I (with B. Lian), Adv. Math. 209 (2007), 99-161. Arxiv.
    
  • Chiral equivariant cohomology II (with B. Lian and B. Song), Trans. Am. Math. Soc. 360 (2008), 4739-4776. Arxiv.
    
  • Invariant chiral differential operators and the W_3 algebra, J. Pure Appl. Algebra 213 (2009), 632-648. Arxiv.
    
  • Introduction to invariant chiral differential operators, Contemp. Math. 497 (2009), 157-168. (Geoffrey Mason's 60th birthday conference).
    
  • A Hilbert theorem for vertex algebras, Transform. Groups, 15, No. 2 (2010), 427-448. Arxiv.
    
  • Chiral equivariant cohomology III (with B. Lian and B. Song), Amer. J. Math. 132, No. 6 (2010), 1549-1590. Arxiv.
    
  • Chiral equivariant cohomology of a point: a first look, Commun. Math. Phys. 306 (2011), 381-417. Arxiv.
    
  • Invariant subalgebras of ghost systems, AIP Conf. Proc. 1243 (2010), 179-190. (Lie Theory and its Applications in Physics: VIII International Workshop).
    
  • Invariant theory and the W_{1+ ∞} algebra with negative integral central charge, J. Eur. Math. Soc. 13, No. 6 (2011), 1737-1768. Arxiv.
    
  • Chiral equivariant cohomology of spheres (with B. Lian and B. Song), Contemp. Math. 557 (2011), 41-75. (Gregg Zuckerman's 60th birthday conference).
    
  • Fermionic coset, critical level W^(2)_4 algebra, and higher spins (with T. Creutzig and P. Gao), J. High Energy Phys. 2012, No. 4, 031. Arxiv.
    
  • Invariant theory and the Heisenberg vertex algebra, Int. Math. Res. Not. 17 (2012), 4014-4050. Arxiv.
    
  • Invariant subalgebras of affine vertex algebras, Adv. Math. 234 (2013), 61-84. Arxiv.
    
  • A commutant realization of Odake's algebra (with T. Creutzig), Transform. Groups, 18, No. 3 (2013), 615-637. Arxiv.
    
  • A commutant realization of W^(2)_n at critical level (with T. Creutzig and P. Gao), Int. Math. Res. Not. 3 (2014), 577-609. Arxiv.
    
  • Arc spaces and the vertex algebra commutant problem (with G. Schwarz and B. Song), Adv. Math. 277 (2015), 338-364. Arxiv.
    
  • The super W_{1+ ∞} algebra with integral central charge (with T. Creutzig), Trans. Am. Math. Soc. 367, No. 8 (2015), 5521-5551. Arxiv.
    
  • Twisted chiral de Rham complex, generalized geometry, and T-duality (with V. Mathai), Commun. Math. Phys. 339, No. 2 (2015), 663-697. Arxiv.
    
  • Jet schemes and invariant theory (with G. Schwarz and B. Song), Ann. Inst. Fourier, 65, No. 6 (2015), 2571-2599. Arxiv.
    
  • The structure of the Kac-Wang-Yan algebra, Commun. Math. Phys. 345, No. 2 (2016) 545-585. Arxiv.
    
  • Orbifolds of symplectic fermion algebras (with T. Creutzig), Trans. Am. Math. Soc. 369, No. 1 (2017), 467-494. Arxiv.
    
  • The Z_2 orbifold of the W_3 algebra (with M. Al-Ali), Commun. Math. Phys. 353, No. 3 (2017) 1129-1150. Arxiv.
    
  • Orbifolds and cosets of minimal W-algebras (with T. Arakawa, T. Creutzig, and K. Kawasetsu), Commun. Math. Phys. 355, No. 1 (2017), 339-372. Arxiv.
    
  • Cosets of Bershadsky-Polyakov algebras and rational W-algebras of type A (with T. Arakawa and T. Creutzig), Selecta Math. New Series, 23, No. 4 (2017), 2369-2395. Arxiv.
    
  • T-duality of singular spacetime compactifications in an H-flux (with V. Mathai), J. Geom. Phys. 129 (2018) 269-278. Arxiv.
    
  • Cosets of the W^k(sl_4, f_{subreg})-algebra (with T. Creutzig), Contemp. Math. 711 (2018), 105-117. Arxiv.
    
  • Cosets of affine vertex algebras inside larger structures (with T. Creutzig), J. Algebra 517 (2019) 396-438. Arxiv.
    
  • Schur-Weyl duality for Heisenberg cosets (with T. Creutzig, S. Kanade, and D. Ridout), Transform. Groups, 24, No. 2 (2019), 301-354. Arxiv.
    
  • W-algebras as coset vertex algebras (with T. Arakawa and T. Creutzig), Invent. Math. 218, no. 1 (2019), 145-195. Arxiv.
    
  • Universal two-parameter even spin W_{∞}-algebra (with S. Kanade), Adv. Math. 355 (2019), 106774, 58pp. Arxiv.
    
  • Singular support of a vertex algebra and the arc space of its associated scheme (with T. Arakawa), Representations and Nilpotent Orbits of Lie Algebraic Systems, In Honour of the 75th Birthday of Tony Joseph, Progr. Math. 330 (2019), 1-17. Arxiv.
    
  • Simple current extensions beyond semi-simplicity (with T. Creutzig and S. Kanade), Commun. Contemp. Math. 22, no. 1 (2020), 1950001, 49 pp. Arxiv.
    
  • S-duality for the large N=4 superconformal algebra (with T. Creutzig and D. Gaiotto), Commun. Math. Phys. 374, no. 3 (2020), 1787-1808. Arxiv.
    
  • Universal two-parameter W_{∞}-algebra and vertex algebras of type W(2,3,...,N), Compos. Math. 157, no. 1 (2021), 12-82. Arxiv.
    
  • T-duality and the exotic chiral de Rham complex (with V. Mathai), Commun. Math. Phys. 385, no. 2 (2021), 1133-1161. Arxiv.
    
  • N=4 superconformal algebras and diagonal cosets (with T. Creutzig and B. Feigin), Int. Math. Res. Not. no. 3 (2022), 2180-2223. Arxiv.
    
  • Invariant subalgebras of the small N=4 superconformal algebra (with T. Creutzig and W. Riedler), Transform. Groups 27, no. 3 (2022), 797-832. Arxiv.
    
  • Generalized parafermions of orthogonal type (with T. Creutzig and V. Kovalchuk), J. Algebra 593 (2022), 178-192. Arxiv.
    
  • Trialities of W-algebras (with T. Creutzig), Cambridge J. Math. vol. 10, no. 1 (2022), 69-194. Arxiv.
    
  • Trialities of orthosymplectic W-algebras (with T. Creutzig), Adv. Math. 409 (2022), 108678, 79pp. Arxiv.
    
  • The global sections of chiral de Rham complexes on compact Ricci-flat Kahler manifolds II (with B. Song), Comm. Math. Phys. 399 (2023), 189-202. Arxiv.
    
  • Orbifolds of Gaiotto-Rapcak Y-algebras (with M. Al-Ali), J. Algebra 625 (2023), 1-27. Arxiv.
    
  • Cosets of free field algebras via arc spaces (with B. Song), Int. Math. Res. Not. vol. 2024, no. 1 (2024), 47-114. Arxiv.
    
  • Standard monomials and invariant theory for arc spaces I: general linear group (with B. Song), Commun. Contemp. Math. vol. 26, no. 4 (2024) 2350013, 38pp. Arxiv.
    
  • Standard monomials and invariant theory for arc spaces II: symplectic group (with B. Song), J. Algebraic Geometry 33 (2024), 601-628. Arxiv.
    
  • Classical freeness of orthosymplectic affine vertex superalgebras (with T. Creutzig and B. Song), Proc. Am. Math. Soc. vol 152, no. 10 (2024), 4087-4094. Arxiv.
    
  • Standard monomials and invariant theory for arc spaces III: special linear group (with B. Song), J. Algebra 664, Part B (2025), 289-327. Arxiv.
    
  • Ordinary modules for vertex algebras of osp(1|2n) (with T. Creutzig and N. Genra), published online in J. Reine Angew. Math. Arxiv.
    
  • Vertex algebras and commutative algebras (with B. Lian), published online in Harvard CMSA, The Literature and History of Mathematical Science. Arxiv.
    
  • Ito's conjecture and the coset realization of W^k(sl(3|2)) (with N. Genra), to appear in RIMS Kokyuroku Bessatsu. Arxiv.
    
  • One example of a chiral Lie group (with F. Malikov), to appear in RIMS Kokyuroku Bessatsu. Arxiv.
    
  • Duality via convolution of W-algebras (with T. Creutzig, S. Nakatsuka, and R. Sato), Arxiv.
    
  • On the structure of W-algebras in type A (with T. Creutzig, J. Fasquel, and S. Nakatsuka), Arxiv.
    
  • Building blocks for W-algebras of classical types (with T. Creutzig and V. Kovalchuk), Arxiv.
    
  
  

• MY ARTWORK