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Personal website of Jonas McCandless

I am a mathematician with a PhD in algebraic topology from the University of Münster under the supervision of Thomas Nikolaus, and postdoctoral research experience at the Max Planck Institute for Mathematics in Bonn. Currently, I teach mathematics at the high school level, where I also help train students for the Georg Mohr competition, a qualifier for the mathematical olympiad.

Beyond the classroom, I am interested in stochastic processes, (partial) differential equations, and how machine learning can help us understand and forecast complex dynamical systems. Recent examples are my Neural SDE Forecaster project, where I apply these methods to continuous-time financial data, and my 1D Heat Equation Solver project, where I use C++ to solve this PDE using finite difference methods.

I am eager to apply my background in research mathematics, teaching, and machine learning to industry problems, particularly in data science, mathematical modelling, and quantitative finance.

Projects

Forecasting stock prices with neural stochastic differential equations.

A modular PyTorch framework for forecasting stock prices using neural stochastic differential equations (Neural SDEs). Specifically, this project uses neural networks to learn the drift and diffusion parameters in the Black–Scholes stochastic differential equation, which models the continuous-time dynamics of a stock price. The Euler–Maruyama method is implemented for numerical simulation, and the project provides a full pipeline from data retrieval via Yahoo Finance to forecasting and visualization with the trained neural SDE.

Solving the 1D heat equation using finite difference methods in C++.

A modular C++ framework for solving the 1D heat equation using finite difference methods: Forward Euler, Backward Euler, and Crank–Nicolson. Features an extensible object-oriented architecture with boundary and initial condition abstractions, an O(n) tridiagonal solver implemented via the Thomas algorithm, and validation against exact solutions. Includes a Python utility for visualizing the simulation results.

Papers

A chromatic vanishing result for TR with Liam Keenan. Proc. Amer. Math. Soc. 152 (2024)
Polygonic spectra and TR with coefficients with Achim Krause and Thomas Nikolaus.
On curves in K-theory and TR. J. Eur. Math. Soc. 26 (2023). There is a great blog post on this work written by Ben Antieau.

Teaching

Bonn 2024: Course on algebraic K-theory with Kaif Hilman.

Expository writings

Lecture notes on Algebraic K-theory with Kaif Hilman.
Recovering crystalline cohomology from periodic topological cyclic homology. Notes for my master thesis defense in Copenhagen, June 2019.
On the cyclotomic t-structure and filtrations on topological Hochschild homology. My master thesis written under the supervision of Lars Hesselholt. (May 2019)
Snaith's theorem and elliptic cohomology after Lurie. Notes for a talk given at the arbeitsgemeinschaft on elliptic cohomology in Oberwolfach, April 2019.
Duality and ambidexterity in K(n)-local spectra. A project written under the supervision of Tobias Barthel. (June 2018)
Topological Hochschild homology of E-infinity rings. Notes for a talk given at the arbeitsgemeinschaft on TC in Oberwolfach, April 2018.
Symmetric spectra with a view toward higher algebra. My bachelor thesis written under the supervision of Lars Hesselholt and Gijs Heuts. (June 2017)

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