Geometric representation theory of Lie algebras, vertex algebras, D-modules, geometric Langlands program, stochastic differential equations
RSJ Securities, Prague
Mathematical Analysts, July 2018 – present
Institute de Matemática e Estatística, Universidade de Sao Paulo
Posdoctoral position, May 2017 – June 2018
Mathematical Institute of Charles University
Senior Assistent Professor, January 2017 – April 2017
Institute of Mathematics of the Academy of Science of the Czech Republic
Posdoctoral position, December 2009 – January 2011
Charles University in Prague, 2005 – 2009
Phd degree in Geometry and Topology, Global Analysis and General Structures
Phd thesis: Moduli spaces of Lie algebroid connections
Charles University in Prague, 2000 – 2005
Master's degree in Theoretical Physics
Diploma thesis: Parially massless fields in AdS/CFT correspondence
T. Arakawa, V. Futorny, L. Křižka, Generalized Grothendieck's simultaneous resolution and associated varieties of simple affine vertex algebras, arXiv:2404.02365
V. Futorny, O. Hernández Morales, L. Křižka, Admissible representations of simple affine vertex algebras, J. Algebra 628 (2023) 22-70.
V. Futorny, L. Křižka, Positive energy representations of affine vertex algebras, Comm. Math. Phys. 383 (2021), 841–891.
V. Futorny, L. Křižka, Twisting functors and Gelfand–Tsetlin modules over semisimple Lie algebras, Commun. Contemp. Math (2022), https://doi.org/10.1142/S0219199722500316.
V. Futorny, L. Křižka, J. Zhang, Generalized Verma modules over Uq(sln(C)), Algebr. Represent. Theory 23 (2020), 811–832.
V. Futorny, L. Křižka, Geometric construction of Gelfand–Tsetlin modules over simple Lie algebras, J. Pure Appl. Algebra 223 (2019), no. 11, 4901–4924.
V. Futorny, L. Křižka, J. Zhang, Quantum Howe duality and invariant polynomials, J. Algebra 530 (2019), 326–367.
V. Futorny, L. Křižka, P. Somberg, Geometric realizations of affine Kac–Moody algebras, J. Algebra 528 (2019), 177–216.
L. Křižka, P. Somberg, Conformal Galilei algebras, symmetric polynomials and singular vectors, Lett. Math. Phys. 108 (2018), no. 1, 1–44.
L. Křižka, P. Somberg, Differential invariants on symplectic spinors in contact projective geometry, J. Math Phys. 58 (2017), no. 9, 091701, 22p.
L. Křižka, P. Somberg, Algebraic analysis of scalar generalized Verma modules of Heisenberg parabolic type I: An-series, Transform. Groups 22 (2017), no. 2, 403–451.
L. Křižka, P. Somberg, Equivariant differential operators on spinors in conformal geometry, Complex Var. Elliptic Equ. 62 (2017), no. 5, 583–599.
M. Holíková, L. Křižka, P. Somberg, Projective structure, SL(3,R) and the symplectic Dirac operator, Arch. Math. 52 no. 5, (2016), 313–324.
L. Křižka, P. Somberg, On the composition structure of the twisted Verma modules for sl(3,C), Arch. Math. 51 no. 5, (2015), 315–329.
L. Křižka, Moduli spaces of flat Lie algebroid connections, arXiv:1012.3180v1.
L. Křižka, Moduli spaces of Lie algebroid connections, Arch. Math. 44 no. 5, (2008), 403–418.