About
I am a Master’s student in mathematics at Stockholm University, working in spectral theory and quantum graphs, with a particular interest in the interaction between topology and operator theory.
My publications of any kind can be found here .
Interests
Quantum Graphs and Topology Change
As a Master’s student, I worked under the supervision of Pavel Kurasov. The result of this work is my master thesis “Berry’s Phase for Quantum Graphs”.
In my Master’s thesis, I studied topology change on a figure-eight metric graph via parameter-dependent vertex conditions. The goal was to understand how changes in connectivity affect spectral properties of the Laplacian.
In particular, we showed that a full cycle of topology change induces a nontrivial Berry phase \(\pi\) for real-valued eigenfunctions. This demonstrates a direct link between topology change and geometric phase in quantum graph models.
The model is based on the condition \[ i (S_{\theta} - I) \overrightarrow{\psi} = (S_{\theta} + I) \partial \overrightarrow{\psi}. \]
This induces topology change, illustrated below.
As a result, we obtain a Berry phase \[ \psi^{(2 \pi)} = e^{i \pi} \psi^{(0)}. \]
This suggests that topology change in quantum graphs has observable geometric effects and may be relevant for models of quantum systems with varying connectivity.
Coding Theory and Krawtchouk Polynomials
During my Bachelor’s studies, I worked under supervision of Nikita Gogin on Krawtchouk matrices which were used in several interesting applications.
Live Preview of Krawtchouk Matrices:
One of the applications was the derivation of new formulae for Bernstein and Chebyshev polynomials. Also we developed an algorithm for computing Bernstein polynomials.
Also, we studied connections of discrete functions, Krawtchouk polynomials, finite geometries, and primality.
I have two repositories on Github related to this mathematical object: MWViewer (which I used on PCA2023), krview (small program in Zig I made for fun).
In addition, I’m a contributor to the OEIS (Online Encyclopedia of Integer Sequences).
Most of my contributions are involved with the de Koninck problem which is an unsolved problem in number theory.
You can find my resume here .
Education
Stockholm University / KTH Royal Institute of Technology
Master’s degree in Mathematics
Petrozavodsk State University
Bachelor’s degree in Mathematics
Thesis
"Berry Phase for Quantum Graphs"
Pavel Kurasov
Contributions
- Studied topology change via parameter-dependent vertex conditions
- Derived explicit continuous eigenfunction families
- Showed topology change induces a nontrivial Berry phase π for real-valued eigenfunctions
- Established connection between topology change and operator domain structure
"Bernstein Polynomials and MacWilliams Transform"
Nikita Gogin, Vladimir Kuznetsov
Contributions
- Studied MacWilliams (Krawtchouk) transform and applications in approximation theory
- Found new formulae for Bernstein and Chebyshev polynomials
- Developed an algorithm for computing Bernstein polynomials
Publications
Preprints
Conference Publications
OEIS Contributions
Authored Sequences
- A355045 — Least multiple \(k\) of \(p_n\) such that the Dedekind \(\psi(k)\) is a power of \(\text{rad}(k)\).
- A355059 — The exponents \(m\) satisfying \(\psi(k) = \text{rad}(k)^m\) for the terms in A355045.
- A337775 — Least multiple \(k\) of \(p_n\) such that the Euler \(\phi(k)\) is a power of \(\text{rad}(k)\).
- A337776 — The exponents \(m\) satisfying \(\phi(k) = \text{rad}(k)^m\) for the terms in A337775.
Editorial Contributions
- A000108 (Catalan Numbers) — Proved an identity linking terms to a specific index of Krawtchouk polynomials: \(a(n) = \mathcal{K}^{(2n+1, n, 1)}\).