This is a list of some possible PhD topics and some related keywords. Do not hesitate to contact me if you are interested in any of them.

- Approximate Bayesian Computation (ABC) for point processes in neuroscience. Keywords: simulation-based inference; hitting times; deep learning strategies.
- Inference for stochastic differential equations (SDEs) based on advanced numerical schemes. Keywords: simulation-based inference; SDEs; numerical methods for SDEs.
- Rough path theory with jumps. Keywords: controlled differential equations, iterated integrals, space-time Brownian motion.
- Probabilistic and Neural-Network based parallel-in-time solvers for complex models. Keywords: parallel in time schemes; ODEs/SDEs; emulators; probabilistic numerics; uncertainty quantification.
- Synergies between stochastic numerics and MCMC . Keywords: structure-preserving schemes; (generalised) underdamped Langevin Dynamics.

Current PhD Students:

• Tudor Onose (current, 2024-2027, Life Science) with Munehiro AsallyLink opens in a new window.
• Max Butler (current, 2024-2027, MathSys II CDT) with Anastasia (Tessy) PapavasiliouLink opens in a new window.
• Shu HuangLink opens in a new window (current, 2023-2026) with Adam Johansen Link opens in a new windowand Richard EverittLink opens in a new window. Shu is working on inference for SDEs combining MCMC, SMC approaches with reliable numerical schemes.
• Bowen Fang Link opens in a new window(current, 2023-2026) with Dario Spanó.Link opens in a new window Bowen is working on splitting numerical scheme for SDEs, with applications in neuroscience and population genetics.
• Guglielmo GattiglioLink opens in a new window (current, 2022-2025) with Lyudmila GrigoryevaLink opens in a new window. Guglielmo is working on probabilistic time-parallel numerical schemes for (partial/ordinary/stochastic) differential equations using GP and machine learning techniques.

Doctoral Alumni:

• Aria AhariLink opens in a new window (2021-2024) with Larbi AliliLink opens in a new window. Aria worked on hitting times for diffusion and Lèvy processes to time-varying thresholds. Title of the PhD thesis: Boundary crossing problems for one-dimensional Markov processes to moving boundaries
• Kamran PentlandLink opens in a new window (2020-2023) with Tim SullivanLink opens in a new window: Mathematics of Real-World Systems CDT student, University of Warwick.Kamran's work focused on the development of time-parallel numerical schemes for ODEs/PDEs using probabilistic methods, with the goal of speeding up the simulation of nuclear magnetic fusion, in collaboration with our external partners Debasmita Samaddar, James Buchanan and Lynton Appel at UKAEALink opens in a new window.
  Title: Towards probabilistic time-parallell algorithms for solving initial value problems.
• Irene TubikanecLink opens in a new window (2017-2021), Institute for Stochastics, JKU Linz (co-supervision with Professor Evelyn BuckwarLink opens in a new window).
  Title: Structure preserving numerical and statistical methods for stochastic differential equations with a focus on neuronal models.Link opens in a new window

MSc and IM students:

• Siyuan Ye (2024), MSc in Statistics, Warwick. Thesis: Time-Splitting Schemes Applied to Underdamped Langevin Equation.
• Ruhan Shah (2023-2024), MMORSE, Warwick. Thesis: AI-informed decision making based on Decision Field Theory
• Garry Cotton (2023), MSc in Statistics, Warwick. Thesis: AI-informed decision making based on decision field theory.
• Chuanjie Wu (2022), MSc in Statistics, Warwick. Thesis: Splitting numerical methods for stochastic models.
• Ramon Natallo-Kaluarachchi (2022), MMath student, Warwick. Thesis: Splitting integrators for spiking neuronal models.
• Johannes Eder (2020), Master student in Mathematics, JKU Linz, Austria.
  Thesis: Influence on the numerical methods (Taylor vs splitting) on multiplicative noise processes.
• Nora Koblinger (2020), Master student in Mathematics, JKU Linz, Austria.
  Thesis: Diffusion approximations of jump processes. An application to neuroscience.
• Lukas Schiefermueller (2019), Master student in Mathematics, JKU Linz, Austria.

  Thesis: Robust algorithms for pitch detection and parameter estimation.

• Martina Vesan (2018), Master student in Stochastics and Data Science, University of Turin, Italy.
  Thesis: Inference from discrete sampling and first passage times for diffusion processes via Approximate Bayesian Computation.

• Fabian Diermayr (2018), Master student in Mathematics, JKU Linz, Austria.
  Thesis: Record breaking events in diffusion processes.

• Bernhard Kepplinger (2017), Master student in Mathematics, JKU Linz, Austria.
  Thesis: The First Passage Time Problem: Analytical, Numerical and Statistical Methods (with R and Mathematica).

BSc students:

• Philipp Wagner (2019), Bachelor student in Mathematics, JKU Linz, Austria.
  Thesis: Investigation of multi-timescale adaptive threshold models via simulations.
• Patryk Grabski (2018), Bachelor student in Mathematics, JKU Linz, Austria. Thesis (in German): Poisson-Prozess.