Mentoring Experience
Quasiconformal trees (Spring 2024, ongoing), Graduate reading course by Vyron Vellis
Participating in a reading course offered to a UTK graduate student, Fotis Ioannidis. Jointly guiding the student and working on a research project on quasiconformal trees and embeddability theorems, which is part of the student's PhD thesis.
Participating in a reading course offered to a UTK graduate student, Fotis Ioannidis. Jointly guiding the student and working on a research project on quasiconformal trees and embeddability theorems, which is part of the student's PhD thesis.
Experiments on the random walk hypothesis (Fall 2024, ongoing), Knox Math Lab project
Mentoring a group of 2 undergraduate students to perform experiments on the "random walk hypothesis", a financial theory that has motivated several lines of research within different areas of finance and mathematics. It states that stock market price movements follow similar principles to those of a random walk. This project aims to experimentally compare certain stock graphs with those of random walks, by employing probabilistic and data analytic tools.
Mentoring a group of 2 undergraduate students to perform experiments on the "random walk hypothesis", a financial theory that has motivated several lines of research within different areas of finance and mathematics. It states that stock market price movements follow similar principles to those of a random walk. This project aims to experimentally compare certain stock graphs with those of random walks, by employing probabilistic and data analytic tools.
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.
