PhD graduate.

Email: lt2739@columbia.edu (l.toniazzi@warwick.ac.uk)

CV: link.

PhD Supervisors: Prof V. Kolokoltsov and Dr R. Tribe.

Research interests: Fractional PDEs and stochastic jump processes. I have been focusing on time-fractional/nonlocal evolution equations, their wellposedness, regularity and stochastic representation for solutions.

Publications/preprints:

[1] Hernández-Hernández, Kolokoltsov, Toniazzi (2017). Generalised fractional evolution equations of Caputo type. Chaos, Solitons & Fractals, 102:184-196. arXiv:1706.00319.

[2] Toniazzi (2019). Stochastic solutions for space-time fractional evolution equations on a bounded domain. Journal of Mathematical Analysis and Applications, 469(2):594-622. arXiv:1805.02464.

[3] Du, Toniazzi, Zhou (2018). Stochastic solutions for time-nonlocal evolution equations. Submitted. arXiv:1810.08788.

Conference/seminar talks in 2018:

Sep. 2018 - Bielefeld University, Germany. 9th International Conference on Stochastic Analysis and Its Applications.

Sep. 2018 - Swansea University, UK. Probability and NonLocal PDEs Interplay and Cross-Impact.  Slides (gif-version)

Sep. 2018 - BCAM, Spain. 6th Fractional Calculus, Probability and Nonlocal Operators Conference.

Oct. 2018 - Politecnico di Milano, Italy. Analysis seminar.

Tutoring: Applications from undergraduates in search of project ideas are welcome. Possible topics: fractional calculus, differential equations, stochastic jump processes, random walks in random environments.