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Quasiconformal trees (Spring 2024, ongoing), Graduate thesis with Vyron Vellis
Participating in a reading course offered to a UTK graduate student, Fotis Ioannidis. Jointly guiding the student with V. Vellis and working on a research project on quasiconformal trees and embeddability theorems, which is part of the student's PhD thesis.
Self-similarity of time series (Spring 2025), Undergraduate thesis
Supervised the undergraduate thesis of Alex Zhang on experiments regarding the self-similarity of certain time series in Python, using numerical and data-analytic tools.
Mathematically Modeling Investment Methods (Spring 2025), Knox Math Lab project
Mentored 1 graduate and 3 undergraduate students to build a mathematical model to theoretically and experimentally compare the returns of investment methods. Provided the students with a project plan, which involves defining functions and relations to model an investment choice, examples of methods, collecting stock market data, and performing experiments following the model to improve its structure, using Python and data-analytic tools.
Mentored 1 graduate and 3 undergraduate students to build a mathematical model to theoretically and experimentally compare the returns of investment methods. Provided the students with a project plan, which involves defining functions and relations to model an investment choice, examples of methods, collecting stock market data, and performing experiments following the model to improve its structure, using Python and data-analytic tools.
Experiments on the random walk hypothesis (Fall 2024), Knox Math Lab project
Mentored 1 graduate and 2 undergraduate students to perform experiments on the "random walk hypothesis". Provided the students with a project plan, which involves collecting inflation data, stock market data, adjusting graphs of famous stocks and indexes to inflation, and comparing the modified stock graphs to random walks using Python and data-analytic tools. Supervised the progress of the group jointly with the graduate student.
Mentored 1 graduate and 2 undergraduate students to perform experiments on the "random walk hypothesis". Provided the students with a project plan, which involves collecting inflation data, stock market data, adjusting graphs of famous stocks and indexes to inflation, and comparing the modified stock graphs to random walks using Python and data-analytic tools. Supervised the progress of the group jointly with the graduate student.
Randomness in Number Theory (Spring 2022)
Mentored a group of 5 undergraduate students. Guided them in building the required Number Theory background (on continued fractions) and Mathematica skills, co-ordinated their group work and supervised statistical and visual experiments on the c.f.e. of π using Python and Mathematica. The outcomes strengthen the conjecture that the c.f.e. digits of π follow the Gauss–Kuzmin distribution and were presented at MAA Mathfest, Philadelphia, August 2022 and UIUC IGL poster session, Spring 2022.
Mentored a group of 5 undergraduate students. Guided them in building the required Number Theory background (on continued fractions) and Mathematica skills, co-ordinated their group work and supervised statistical and visual experiments on the c.f.e. of π using Python and Mathematica. The outcomes strengthen the conjecture that the c.f.e. digits of π follow the Gauss–Kuzmin distribution and were presented at MAA Mathfest, Philadelphia, August 2022 and UIUC IGL poster session, Spring 2022.
Interactive visualizations with Mathematica - Fractal curves (Fall 2021)
Mentored a group of 2 undergraduate students. Guided them in building the required background on fractal Fourier series and Mathematica skills, co-ordinated their group work and supervised visual experiments on the fractal curves parametrized by said series using Mathematica. The plots produced indicate interesting dimension-theoretic properties of such curves and were presented at the UIUC IGL poster session, Fall 2021.
Mentored a group of 2 undergraduate students. Guided them in building the required background on fractal Fourier series and Mathematica skills, co-ordinated their group work and supervised visual experiments on the fractal curves parametrized by said series using Mathematica. The plots produced indicate interesting dimension-theoretic properties of such curves and were presented at the UIUC IGL poster session, Fall 2021.
Bedford-McMullen carpets (Fall 2021)
Independent research project
Independent research project
Mentored a group of 2 undergraduate students. Guided them in building the required background on planar fractals and dimensions, co-ordinated their group work and supervised coding of visual plots of Bedford-McMullen carpets using Mathematica. Said plots were combined in a single interactive demonstration (published in Nov 2021), where different types of dimensions (lower, Hausdorff, Minkowski, Assouad) of the depicted carpet also appear as outputs.
Mentored a group of 2 undergraduate students. Guided them in building the required background on planar fractals and dimensions, co-ordinated their group work and supervised coding of visual plots of Bedford-McMullen carpets using Mathematica. Said plots were combined in a single interactive demonstration (published in Nov 2021), where different types of dimensions (lower, Hausdorff, Minkowski, Assouad) of the depicted carpet also appear as outputs.
Interactive visualizations with Mathematica - Julia sets (Spring 2021)
Mentored a group of 5 undergraduate students. Guided them in building the required background on Complex Dynamics (mostly on Julia sets of polynomials) and Mathematica skills, co-ordinated their group work and supervised visual experiments on the Julia sets of cubic polynomials using Mathematica. The plots produced showcase how the Julia set of a cubic polynomial changes when its coefficients are changed and were presented at the UIUC IGL poster session, Spring 2021.
Mentored a group of 5 undergraduate students. Guided them in building the required background on Complex Dynamics (mostly on Julia sets of polynomials) and Mathematica skills, co-ordinated their group work and supervised visual experiments on the Julia sets of cubic polynomials using Mathematica. The plots produced showcase how the Julia set of a cubic polynomial changes when its coefficients are changed and were presented at the UIUC IGL poster session, Spring 2021.
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