Research Projects:

• National Science Centre (Poland) grant 2019/33/B/ST1/02494 (2020-2023) [Principal Investigator]
  Geometric quantities related to nonlocal equations
• National Science Centre (Poland) grant 2017/27/B/ST1/01339 (2018-2021) [Investigator]
  Regularity and asymptotics for multidimensional Markovian evolutions
• National Science Centre (Poland) grant 2016/23/B/ST1/01665 (2017-2021) [Principal Investigator]
  Heat kernels: construction and estimates
• National Science Centre (Poland) grant 2015/17/B/ST1/01043 (2016-2019) [Investigator]
  Levy and Markov processes on Euclidean and hyperbolic spaces
• National Science Centre (Poland) grant Harmonia 2014/14/M/ST1/00600 (2015-2018) [Investigator]
  Analysis of nonlocal operators
• Ministry of Science and Higher Education (Poland) grant N N201 373136 (2009-2012) [Investigator]
  Potential theory of a class of Levy processes and their Feynman-Kac semigroups
• Ministry of Science and Higher Education (Poland) grant N N201 4112 33 (2007-2008) [Investigator]
  Potential theory of relativistic processes
• Polish State Committee for Scientific Research grant 1 P03A 020 28 (2005-2008) [Investigator]
  Harmonic measures and properties of semigroups of stable processes

Preprints:

39. W. Cygan, T. Grzywny and J. Lenczewska, Asymptotics and geometric flows for a class of nonlocal curvatures.
    arxiv: https://arxiv.org/abs/2308.16660
38. T. Grzywny and M. Kwaśnicki, Liouville's theorems for Lévy operators.
    arxiv: https://arxiv.org/abs/2301.08540
37. T. Grzywny, T. Jakubowski and G. Żurek, Estimates of gradient of L-harmonic functions for nonlocal operators with order α>1.
    arxiv: https://arxiv.org/abs/2208.00747
36. T. Grzywny and B. Trojan, Subordinated Markov processes: sharp estimates for heat kernels and the Green functions.
    arxiv: https://arxiv.org/abs/2110.01201
35. T. Grzywny, First exit times from a bounded interval for Lévy processes
    arxiv: http://arxiv.org/abs/1911.05022

Papers:

34. W. Cygan and T. Grzywny, Asymptotics of non-local perimeters.
    Annali di Matematica Pura ed Applicata 202(6) (2023), 2629-2651
    DOI: 10.1007/s10231-023-01332-z
    arxiv: https://arxiv.org/abs/2203.12343
33. G. Armstrong, K. Bogdan, T. Grzywny, Ł. Leżaj, and L. Wang, Yaglom limit for unimodal Lévy processes.
    Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 59(3) (2023), 1688-1721
    DOI: 10.1214/22-AIHP1301
    arxiv: http://arxiv.org/abs/2110.00873
32. K. Bogdan, T. Grzywny, K. Pietruska-Pałuba and A. Rutkowski, Nonlinear nonlocal Douglas identity
    Calculus of Variations and Partial Differential Equations 62(5) (2023), article 151
    DOI: 10.1007/s00526-023-02458-x
    arxiv: https://arxiv.org/abs/2006.01932
31. T. Grzywny and J. Lenczewska, Asymptotic expansion of the nonlocal heat content.
    Studia Mathematica 270(3) (2023), 339-359
    DOI: 10.4064/sm220831-26-1
    arxiv: https://arxiv.org/abs/2202.11662
30. T. Grzywny, Ł. Leżaj and B. Trojan, Transition densities of subordinators of positive order
    Journal of the Institute of Mathematics of Jussieu 22(3) (2023), 1119 - 1179
    DOI: 10.1017/S1474748021000360
    arxiv: https://arxiv.org/abs/1812.06793
29. T. Grzywny, K. Kaleta and P. Sztonyk, Heat kernels of non-local Schrödinger operators with Kato potentials.
    Journal of Differential Equations 340 (2022), 273-308
    DOI: 10.1016/j.jde.2022.08.038
    arxiv: https://arxiv.org/abs/2204.04239
28. T. Grzywny and K. Szczypkowski, Estimates of heat kernels of non-symmetric Lévy processes
    Forum Mathematicum 33(5) (2021), 1207-1236
    DOI: 10.1515/forum-2020-0364
    arxiv: https://arxiv.org/abs/1710.07793
27. T. Grzywny, Ł. Leżaj and M. Miśta, Hitting probabilities for Lévy processes on the real line
    ALEA, Lat. Am. J. Probab. Math. Stat. 18 (2021), 727-760
    DOI: 10.30757/ALEA.v18-27
    open access
26. T. Grzywny, M. Kassmann and Ł. Leżaj, Remarks on the nonlocal Dirichlet problem
    Potential Analysis 54(1) (2021), 119-151
    DOI: 10.1007/s11118-019-09820-9
    open access
25. T. Grzywny and K. Szczypkowski, Lévy processes: concentration function and heat kernel estimates
    Bernoulli 26(4) (2020), 3191-3223
    DOI: 10.3150/20-BEJ1220
    arxiv: https://arxiv.org/abs/1907.00778
24. K. Bogdan, T. Grzywny, K. Pietruska-Pałuba and A. Rutkowski, Extension theorem for nonlocal operators
    Journal de Mathematiques Pures et Appliquees 137 (2020), 33-69
    DOI: 10.1016/j.matpur.2019.09.005
    arxiv: https://arxiv.org/abs/1710.05880
23. T. Grzywny, T. Jakubowski and G. Żurek, Green function for gradient perturbation of unimodal Lévy processes in the real line
    Bulletin of the Malaysian Mathematical Sciences Society 43(2) (2020), 1223-1251
    DOI: 10.1007/s40840-019-00738-4
    arxiv: https://arxiv.org/abs/1802.01450
22. T. Grzywny, K.-Y. Kim and P. Kim, Estimates of Dirichlet heat kernel for symmetric Markov processes,
    Stoch. Pr. Appl. 130(1) (2020), 431-470
    DOI: 10.1016/j.spa.2019.03.017
    arxiv: http://arxiv.org/abs/1512.02717
21. T. Grzywny, M. Ryznar and B. Trojan, Asymptotic behaviour and estimates of slowly varying convolution semigroups,
    Int Math Res Notices 2019(23) (2019), 7193-7258
    DOI: 10.1093/imrn/rnx324
    arxiv: http://arxiv.org/abs/1606.04178
20. T. Grzywny and K. Szczypkowski, Heat kernels of non-symmetric Lévy-type operators
    J. Differential Equations, 267 (10) (2019), 6004 - 6064
    DOI: 10.1016/j.jde.2019.06.013
    arxiv: https://arxiv.org/abs/1804.01313
19. T. Grzywny, H. Park and R. Song, Spectral heat content for Lévy processes
    Mathematische Nachrichten, 292 (4) (2019), 805-825
    DOI: 10.1002/mana.201800035
    arxiv: https://arxiv.org/abs/1705.09463
18. K. Bogdan, T. Grzywny, T. Jakubowski and D. Pilarczyk, Fractional Laplacian with Hardy potential
    Communications in PDE, 44 (1) (2019), 20-50
    DOI: 10.1080/03605302.2018.1539102
    arxiv: https://arxiv.org/abs/1710.08378
17. W. Cygan and T. Grzywny, A note on the generalized heat content for Lévy processes
    Bulletin of the Korean Mathematical Society 55 (5) (2018), 1463-1481
    DOI: 10.4134/BKMS.b170835
    open access
16. T. Grzywny, M. Kwaśnicki, Potential kernels, probabilities of hitting a ball, harmonic functions and the boundary Harnack inequality for unimodal Lévy processes,
    Stoch. Pr. Appl. 128(1) (2018), 1-38
    DOI: 10.1016/j.spa.2017.04.004
    arxiv: https://arxiv.org/abs/1611.10304
15. T. Grzywny and K. Szczypkowski, Kato classes for Lévy processes,
    Potential Anal. 47(3) (2017), 245-276
    DOI: 10.1007/s11118-017-9614-1
    open access
14. W. Cygan, T. Grzywny and B. Trojan, Asymptotic behavior of densities of unimodal convolution semigroups,
    Trans. Amer. Math. Soc. 369(8) (2017), 5623-5644
    DOI: 10.1090/tran/6830
    arxiv: https://arxiv.org/abs/1504.08358
13. T. Grzywny, T. Jakubowski and G. Żurek, Green function for gradient perturbation of unimodal Lévy processes,
    Prob. Math. Stat. 37(1) (2017), 119-143
    DOI: 10.19195/0208-4147.37.1.5
    arxiv: https://arxiv.org/abs/1505.07700
12. T. Grzywny and M. Ryznar, Hitting times of points and intervals for symmetric Lévy processes,
    Potential Anal. 46(4) (2017), 739-777
    DOI: 10.1007/s11118-016-9600-z
    open access
11. W. Cygan and T. Grzywny, Heat content for convolution semigroups,
    J. Math. Anal. Appl. 446(2) (2017), 1393-1414
    DOI: 10.1016/j.jmaa.2016.09.051
    arxiv: https://arxiv.org/abs/1606.09168
10. K. Bogdan, T. Grzywny, M. Ryznar, Barriers, exit time and survival probability for unimodal Lévy processes,
    Prob. Th. Related Fields 162 (2015), 155-198
9. K. Bogdan, T. Grzywny, M. Ryznar, Dirichlet heat kernel for unimodal Lévy processes,
   Stoch. Pr. Appl. 124 (2014), 3612-3650
8. K. Bogdan, T. Grzywny, M. Ryznar, Density and tails of unimodal convolution semigroups,
   Journal of Functional Analysis 266(6) (2014), 3543-3571
7. T. Grzywny, On Harnack Inequality and Hölder Regularity for Isotropic Unimodal Lévy Processes,
   Potential Anal. 41 (2014), 1-29
6. T. Grzywny and M. Ryznar, Potential theory of one-dimensional geometric stable processes,
   Colloq. Math. 129(1) (2012), 7-40
5. K. Bogdan, T. Grzywny, M. Ryznar, Heat kernel estimates for the fractional Laplacian with Dirichlet conditions,
   Annals of Probability 38(5) (2010), 1901-1923
4. K. Bogdan and T. Grzywny, Heat kernel of fractional Laplacian in cones,
   Colloq. Math. 118 (2010), 365-377
3. T. Grzywny and M. Ryznar, Two-sided optimal bounds for Green functions of half-spaces for relativistic α-stable process,
   Potential Anal. 28 (2008), 201-239
2. T. Grzywny, Intrinsic ultracontractivity for Lévy processes,
   Prob. Math. Stat. 28 (2008), 91-106
1. T. Grzywny and M. Ryznar, Estimates of Green functions for some perturbations of fractional Laplacian,
   Illinois J. Math. 51 (2007), 1409-1438