• 9:30 H. Hatzikirou (TU Braunschweig & Helmholtz centre for infection research): The role of cell-decision making on tumor development
  • 10:30 Coffee break
  • 11:00 J. C. Alfonso Lopez (TU Braunschweig & Helmholtz centre for infection research): Therapeutic potential of the interplay between immune system dynamic and tumor-associated vasculature
  • 11:45 L. Bianchi (TU Berlin): Amplitude equations for stochastic Swift-Hohenberg equation
  • 12:30 Lunch break
  • 14:00 M. Maurelli (TU Berlin & WIAS): Regularization by noise for scalar conservation laws
  • We say that a regularization by noise phenomenon occurs for a possibly ill-posed differential equation if this equation becomes well-posed (in a pathwise sense) under addition of noise. Most of the results in this direction are limited to SDEs and associated linear SPDEs.

    In this talk, we show a regularization by noise result for a nonlinear SPDE, namely a stochastic scalar conservation law on Rd with a space-irregular flux:

    tv + b·∇[v2] + ∇v∘∂tW = 0,

    where b = b(x) is a given deterministic, possibly irregular vector field, W is a d-dimensional Brownian motion ( denotes Stratonovich integration) and v = v(t, x, ω) is the scalar solution. More precisely we prove that, under suitable Sobolev assumptions on b and integrability assumptions on its divergence, the equation admits a unique entropy solution. The result is false without noise.

    The proof of uniqueness is based on a careful combination of arguments used in the linear case: first we show the renormalization property for the kinetic formulation of the equation, then we use second order PDE estimates and a duality argument to conclude.

    If time permits, we will discuss also some open questions.

  • 14:45 T. Funaki (University of Tokyo): KPZ, nonlinear fluctuations in Glauber-Kawasaki dynamics
  • 15:45 Coffee break
  • 16:15 C. Geldhauser (Università di Pisa): Optimizing the fractional order in a nonlocal SPDE


  • J. C. Alfonso Lopez (TU Braunschweig & Helmholtz centre for infection research)
  • Luigi Bianchi (TU Berlin)
  • Giuseppe Da Prato (Scuola Normale Superiore, Pisa)
  • Valeria De Mattei (Università di Pisa)
  • Gianluca Finocchio (Università di Pisa)
  • Franco Flandoli (Università di Pisa)
  • T. Funaki (University of Tokyo)
  • Carina Geldhauser (Università di Pisa)
  • Rita Giuliano (Università di Pisa)
  • Paolo Grazieschi (Università di Pisa)
  • Francesco Grotto (Università di Pisa)
  • H. Hatzikirou (TU Braunschweig & Helmholtz centre for infection research)
  • Marta Leocata (Università di Pisa)
  • Mario Maurelli (TU Berlin & WIAS)
  • Maurizio Pratelli (Università di Pisa)
  • Cristiano Ricci (Università di Firenze)
  • Marco Romito (Università di Pisa)
  • Dario Trevisan (Università di Pisa)

To register, please send a mail to Marco Romito.

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Aula Magna

Dipartimento di Matematica

Università di Pisa

Largo Bruno Pontecorvo 5

56127 Pisa



Supported by Università di Pisa (Fondi di ateneo) and the project PRA2016/41: Fenomeni singolari in problemi deterministici e stocastici ed applicazioni.