Below I report 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.

Project 1: Approximate Bayesian Computation (ABC) for point processes in neuroscience. Keywords: simulation-based inference; hitting times; deep learning strategies.
Project 2: Inference for models of neural activity (with R. Everitt Link opens in a new windowand A. JohansenLink opens in a new window). Keywords: ABC; SMC, particle MCMC; SDEs.
Project 3: Interface for stochastic differential equations (SDEs) based on advanced numerical schemes. Keywords: simulation-based inference; SDEs; numerical methods for SDEs.
Project 4:Probabilistic time-parallel numerical schemes for high-dimensional differential equations (with T. SullivanLink opens in a new window). Keywords: parallel in time schemes; ODEs/SDEs; emulators; probabilistic numerics; uncertainty quantification. More information is available hereLink opens in a new window.

PhD Students:

• 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 differential equations.
• Aria AhariLink opens in a new window (current, 2021- 2024) with Larbi AliliLink opens in a new window. Aria is working on hitting times for diffusion and Lèvy processes to time-varying thresholds.
• Kamran PentlandLink opens in a new window (current, 2020-2023): Mathematics of Real-World Systems CDT student, University of Warwick. Kamran is working on the development of time-parallel numerical integration algorithms using probabilistic methods, with the goal of speeding up the simulation of nuclear magnetic fusion, in collaboration with our external partners Dr. Debasmita Samaddar and Dr. Lynton Appel at UKAEALink opens in a new window.
• 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

Master students:

• 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).

Bachelor 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.