Dr. Leonardo Tolomeo

Lecturer
School of Mathematics, University of Edinburgh 		Mailing address:
School of Mathematics
The University of Edinburgh,
James Clerk Maxwell Building, Room 5601
The King's Buildings, Peter Guthrie Tait Road
Edinburgh, EH9 3FD, United Kingdom
Office: Room 5601
E-mail: l.tolomeo ατ ed.ac.uk
Home Curriculum Vitae Publications Talks Teaching

Publications:

Published and accepted papers:

  1. (with A. Martini, F. Ricci) Convolution kernels versus spectral multipliers for sub-Laplacians on groups of polynomial growth (arXiv link), J. Funct. Anal. 277 (2019), no. 6, 1603–1638.
  2. (with A. Amenta) A dichotomy concerning uniform boundedness of Riesz transforms on Riemannian manifolds (arXiv link), Proc. Amer. Math. Soc. 147 (2019), no. 11, 4797–4803.
  3. Unique ergodicity for a class of stochastic hyperbolic equations with additive space-time white noise (arXiv link), Comm. Math. Phys. 377 (2020), 1311–1347.
  4. Global well-posedness of the two-dimensional stochastic nonlinear wave equation on an unbounded domain (arXiv link), Ann. Probab. 49 (2021), no. 3, 1402–1426.
  5. (with M. Gubinelli, H. Koch, T. Oh) Global dynamics for the two-dimensional stochastic nonlinear wave equations (arXiv link), Int. Math. Res. Not. IMRN 2022, no. 21, 16954–16999.
  6. (with V. Cavina, P.A. Erdman, P. Abiuso, V. Giovannetti) Maximum power heat engines and refrigerators in the fast-driving regime (arXiv link), Phys. Rev. A 104 (2021), no. 3, Paper No. 032226, 22 pp.
  7. (with T. Oh, P. Sosoe) Optimal integrability threshold for gibbs measures associated with focusing NLS on the torus, (arXiv link) Invent. Math. 227 (2022), no. 3, 1323–1429.
  8. (with T. Oh, M. Okamoto) Focusing Φ34-model with a Hartree-type nonlinearity (arXiv link), to appear in Mem. Amer. Math. Soc.
  9. (with J. Forlano) On the unique ergodicity for a class of 2 dimensional stochastic wave equations, arXiv:2102.09075, to appear in Trans. Amer. Math. Soc.
  10. (with T. Robert, K. Seong, Y. Wang) Focusing Gibbs measures with harmonic potential, arXiv:2212.11386, to appear in Ann. Inst. Henri Poincaré Probab. Stat.
  11. (with T. Oh, M. Okamoto) Stochastic quantization of the Φ33-model, arXiv:2108.0677, to appear in Mem. Eur. Math. Soc.
  12. (with T. Oh, K. Seong) A remark on Gibbs measures with log-correlated Gaussian fields, arXiv:2012.06729, to appear in Forum Math. Sigma.

Preprints:

  1. (with J. Forlano) Quasi-invariance of Gaussian measures of negative regularity for fractional nonlinear Schrödinger equations, arXiv:2205.11453.
  2. (with M. Romito) Yet another notion of irregularity through small ball estimates, arXiv:2207.02716.
  3. (with T. Oh, Y. Wang, G. Zheng) Hyperbolic P(Φ)2-model on the plane, arXiv:2211.03735.
  4. (with H. Weber) Phase transition for invariant measures of the focusing Schrödinger equation, arXiv:2306.07697.
  5. Ergodicity for the hyperbolic P(Φ)2-model, arXiv:2310.02190.
  6. (with V. D. Dinh, N. Rougerie, Y. Wang) Statistical mechanics of the radial focusing nonlinear Schrödinger equation in general traps, arXiv:2312.06232.

In preparation:

  1. (with J. Coe) Sharp quasi-invariance threshold for the cubic Szegö equation.
  2. (with A. Hocquet, M. Romito) About Some Notions of irregularity of paths.