Algebra, Geometry and Mathematical Physics

The research has four main directions:

Algebra
structure theory and cohomology of Lie and other nonassociative algebras, their applications in mathematical physics

Matrix theory
special and structured matrices and their applications

Analysis
spectral theory, quaternionic and Clifford analysis, fractional calculus

Mathematical physics
Schrödinger operators, Lieb-Thirring-type inequalities, quantum waveguides and quantum graphs, geometric theory of nonholonomic systems, their symmetries and  conservation laws

Research group

Selected publications:

R. Abreu Blaya, J. Bory Reyes, M.A. Pérez-de la Rosa, B. Schneider,
Poincaré-Bertrand and Hilbert formulas for the Cauchy-Cimmino singular integrals,
Advances in Applied Clifford Algebras 24 (2017), no.4, 2933-2960

R. Abreu Blaya, J. Bory Reyes, M.A. Pérez-de la Rosa, B. Schneider,
Integral formulas of the Hilbert, Poincaré-Bertrand, Schwarz and Poisson type for the $\beta$-analytic function theory,
Journal of Mathematical Analysis and Applications 492 (2020), no.2, 1-17

D. Barseghyan, P. Exner,
Spectral geometry in a rotating frame: properties of the ground state.
Journal of Mathematical Analysis and Applications 489 (2020), no.1, 124-130

D. Barseghyan, P. Exner,
A magnetic version of the Smilansky model,
Journal of Physics A: Mathematical and Theoretical 50 (2017), no.48, 485203

D. Barseghyan, B. Schneider,
Eigenvalue bound for Schroedinger operators with unbounded magnetic field,
Reports on Mathematical Physics 85 (2020), no.2, 239-251

P. Exner, O. Turek, M. Tater,
A family of quantum graph vertex couplings interpolating between different symmetries,
Journal of Physics A: Mathematical and Theoretical 51 (2018), no.28, 285301

S. Gerhold, Z. Tomovski,
Asymptotic expansion of Mathieu power series and trigonometric Mathieu series,
Journal of Mathematical Analysis and Applications 479 (2019), no.2, 1882-1892

A. Grishkov, P. Zusmanovich,
Deformations of current Lie algebras. I. Small algebras in characteristic 2,
Journal of Algebra 473 (2017), 513-544

T. Sandev and Z. Tomovski,
Fractional Equations and Models. Theory and Applications,
Springer, 2019

T. Sandev, Z. Tomovski, J.L.A. Dubbeldam, A. Chechkin,
Generalized diffusion-wave equation with memory kernel,
J. Phys. A, Math. Theor. 52 (2019), no.1, 015201

M. Swaczyna, P. Volný,
Uniform projectile motion: dynamics, symmetries and conservation laws,
Reports on Mathematical Physics 73 (2014), no.2, 177-199.

M. Swaczyna, P. Volný,
Uniform motions in central fields,
Journal of Geometric Mechanics 9 (2017), no.1, pp. 91-130

O. Turek,
Gaps in the spectrum of a cuboidal periodic lattice graph, Reports on Mathematical Physics 83 (2019), no.1, 107-127

O. Turek, D. Goyeneche,
A generalization of circulant Hadamard and conference matrices, Linear Algebra and its Applications 569 (2019), 241-265

P. Zusmanovich, On the last question of Stefan Banach,
Expositiones Mathematicae 34 (2016), no.4, 454-466

P. Zusmanovich, On Lie p-algebras of cohomological dimension one,
Indagationes Mathematicae 30 (2019), no.2, 288-299

Grants:

17-01706S - GACR, Matematicko-fyzikální modely nových materiálu
(Mathematical-Physics Models of Novel Materials)
(PI: Exner, participants Barseghyan and Turek)

Grant 01211/2016/RRC of the Regional Authority of the Moravian-Silesian Region

Grant MSK 44/3316 of the Regional Authority of the Moravian-Silesian Region

Grant 0924/2016/SaS by the Statutory City of Ostrava

Grant 18/00726-5 by FAPESP (Research agency of the state of Sao Paulo, Brazil) supporting 2-month visit by Zusmanovich

Grant 13/12050-2 by FAPESP supporting 1-year visit by Zusmanovich

Updated: 14. 09. 2022