Research interests

Geometric representation theory of Lie algebras, vertex algebras, D-modules, geometric Langlands program, stochastic differential equations

Work experience

• 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                                            

Education

• 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

Publications

• 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.