Pierre Patie
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Pierre Patie

I am broadly interested in the study and applications of linear operators and related objects. This encompasses the following topics:

  Isospectral classes of linear operators: (pseudo-) unitary conjugation, Markov interwining, interweaving, gateway (duality) and weak similarity orbit
    ↬ Spectral and perturbation theory of (non)-selfadjoint operators
    ↬ Convergence to equilibrium, hypocoercivity, hyper(ultra)contractivity, cut-off phenomena
    ↬ Scaling limit and universality
    ↬ Representation theory and operator algebra

   Potential theory of Markov processes
    ↬ Martin boundary and exit problems for (non)-Markovian processes with jumps
    ↬ Boundary crossing problems
    ↬ Optimal stopping problems

  Computational mathematics

  Special topics:   Self-similar Markov processes,   Exponential functional of Lévy processes,   Subdiffusive processes,   The moment problem,   Special functions,   Asymptotic analysis,   Financial and insurance mathematics and Neurology


Full list of Publications and my ORCID iD iconORCID Profile


Some recently published/accepted papers

List of co-authors: L. Alili, G. Ascione, F. Avram, C. Bartholmé, L. Chaumont, M. Chazal, A. Chee, P. Cheridito, M.C.H. Choi, M. Cissé, C. Constantinescu, G. D'Onofrio, P. Embrechts, R. Frey, X.Y. Han, B. Jarrow, R. Kaufmann, T. Konstantopoulos, A. Kyprianou, Y. Liu, R.L. Loeffen, L. Miclo, J.-C. Pardo, J.L. Pedersen, L. Sacerdote, R. Sarkar, M. Savov, T. Simon, A. Srapionyan, E. Tanré, T. Tian, B. Toaldo, A. Vaidyanathan, S. Vakeroudis, J. Wang, C . Winter, Y. Zhao

PhD Students

Here are the PhD students I have/had the chance to work with:

  • Filip Stojanovic (ORIE, Cornell), since 2023

  • Andrew Chee (ORIE, Cornell), 2023
    Algebraic, analytical and numerical perspectives on the universe of integrable systems
  • Rohan Sarkar (ORIE, Cornell), 2021
    Continuous and discrete self-similarity via classification schemes of Markov processes, and the van Dantzig problem
  • Jian Wang (ORIE, Cornell), 2020
    Continuous time skip-free Markov process and study of branching process with immigration
  • Aditya Vaidyanathan (CAM, Cornell), 2019
    Contributions to the Stieltjes moment problems and to the intertwining of Markov semigroups
  • Anna Srapyonian (CAM, Cornell), 2019
    Some spectral ideas applied to finance and to self-similar and long-range dependent processes
  • Michael C.H. Choi (ORIE, Cornell), 2017
    Analysis of non-reversible Markov chains
  • Yixuan Zhao (ORIE, Cornell), 2017
    Spectral expansions and excursion theory for non-self-adjoint Markov semigroups with applications in mathematical finance
  • Christopher Van Weverberg (ULB), co-supervised with G. Deelstra, 2015
    Contributions to the study of affine processes with applications in insurance
  • Carine Bartholmé (ULB), 2014
    Self-similarity and exponential functionals of Lévy processes