Postdoctoral researcher, Aalto University, Espoo, Finland.
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Research Interests
I am mainly interested in Algebraic Geometry and its relationships with Representation theory of Lie algebras. Especially I studied techniques of Schubert Calculus via Hasse-Schmidt Derivations on Exterior algebras, with applications to vertex operators. I am currently working on algebraic aspects of PDEs with constant coefficients and on the notion of Integrals on the Fermionic Fock space (in collaboration with A. Contiero, L. Gatto, R. Vidal Martins).
Polynomial Ring Representations of Endomorphisms of Exterior Powers (with A. Contiero, L. Gatto, R. Vidal Martins),
Collectanea Math. 2021, doi.org/10.1007/s13348-020-00310-5, .pdf available at the Journal site (Open Access);O. Behzad, A. Nasrollah Nejad, Universal factorization algebras of polynomials represent Lie algebras of endomorphisms,
J. Algebra and Its Applications, 2021, doi: 10.1142/S0219498822500724; Available at (ArXiv:2006.07893.pdf), Journal version available upon request writing here;O. Behzad, L. Gatto, Bosonic and Fermionic Representations of Endomorphism of Exterior Algebras, Fundamenta Math. (2021), DOI:10.4064/fm9-12-2020, Available at ArXiv:009.00479.pdf;
On the vertex operator representation of Lie algebras of matrices. J. Algebra 597 (2022),47--74, doi.org/10.1016/j.jalgebra.2022.01.009, Available at ArXiv:2108.12895.pdf
D. A.Carrilo, D.Behzad, K. Kytola, Aalto University: Fock space of local fields of the discrete gaussian free fields. ( In progress )
SLIDES OF MY TALKS
1) (February 6, 2021) Slideshow of my Ph.D. Defense. Hasse-Schmidt Derivations and vertex Operators on Exterior Algebras
2) (April 15, 2021) Slideshow of my talk at IPM) Representing Lie algebras of vector space endomorphisms via Schubert Derivations
3) (August 3, 2021) Slideshow of my MARM talk at University of Namibia at Windhoek, Multiplying exterior powers by matrices
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