- 9:30 H. Hatzikirou (TU Braunschweig & Helmholtz centre for infection research):
*The role of cell-decision making on tumor development*
Tumors can be regarded as multicellular complex system of interacting cellular decision-makers.
Decisions of interacting cells allow for the emergence of higher order organizational structures,
such as tumors. At the same time, the new emergent structures exert selective forces on the cell
phenotype decision dynamics. Here I investigate the impact on tumor development of a particular
type of cancer cell decision-making the so-called migration/proliferation phenotypic plasticity
(or *Go-or-Grow*) found in brain tumors. This mechanism implies a mutually exclusive switching
between migratory and proliferative phenotypes. In this talk, I will discuss the identification
of an emerging Allee effect, as a consequence of *Go-or-Grow* dependency on local tumor
cell density, in terms of brain tumor initiation, persistency and potential therapeutic
implications.

- 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*
Currently, most of the basic mechanisms governing tumor-immune system interactions,
in combination with modulations of tumor-associated vasculature, are far from being
completely understood.
In this talk I will present a mathematical model of vascularized
tumor growth, where the main novelty is the modelling of the interplay between
functional tumor vasculature and effector recruitment dynamics. Parameters were
calibrated on the basis of different in vivo Rag1^{-/-} and wild-type (WT)
BALB/c murine tumor growth experiments.
The model analysis supports that vasculature normalization
can be a plausible and effective strategy to treat cancer when combined with appropriate
immuno-stimulation. We find that improved levels of functional vasculature, potentially
mediated by vascular normalization or stress alleviation strategies, can provide beneficial
outcomes in terms of tumor burden reduction and control. Normalization of tumor blood
vessels opens a therapeutic window of opportunity to augment the anti-tumor immune
responses, as well as to reduce the intratumoral immunosuppression and hypoxia due to
vascular abnormalities. The potential success of normalizing tumor vasculature closely
depends on the effector cell recruitment dynamics and tumor sizes. Furthermore, an
arbitrary increase of initial effector cell concentration does not necessarily imply tumor
control, and we evidence the existence of an optimal effector concentration range for
tumor shrinkage. Based on these findings, we suggest a theory-driven therapeutic
proposal that optimally combines immune- and vaso-modulatory interventions. Finally, I
will also show an example of how the proposed mathematical model is used to
investigate the therapeutic potential of bacterial infections against solid tumors.

- 11:45 L. Bianchi (TU Berlin):
*Amplitude equations for stochastic Swift-Hohenberg equation*
We consider a mathematical model for the Rayleigh-Benard convection, the
stochastic Swift-Hohenberg equation

∂_{t}u
= - (1 + ∂_{x}^{2})^{2}u
+ ε^{2}νu - u^{3}
+ ε^{3⁄2}ξ(t,x).

Near its change of stability, a solution of this equation can be described in a
multiscale setting as the product of a slowly varying amplitude equation and
a faster periodic wave.

In this talk, after a very brief introduction to the problem in its deterministic
setting, I'll present some recent developments on this rigorous approximation
in the unbounded space domain setting.

- 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
**R**^{d} with a space-irregular
flux:

∂_{t}v + b·∇[v^{2}] + ∇v∘∂_{t}W = 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*
We will first give a brief overview of some recent
developments in KPZ and coupled KPZ equations.
Then, we will give a heuristic argument for Glauber-Kawasaki
dynamics leading to a nonlinear SPDE under a certain scaling limit.
This part is motivated by a suggestive talk of Franco Flandoli.

- 15:45
*Coffee break*

- 16:15 C. Geldhauser (Università di Pisa):
*Optimizing the fractional order in a nonlocal SPDE*
We study an optimization problem with SPDE constraints, which has
the peculiarity that the control parameter *s* is the
*s*^{th} power of the diffusion operator in the state
equation. Well-posedness of the state equation and differentiability
properties w.r.t. the fractional parameter *s*. We show that
under certain conditions on the noise, optimality conditions for the
control problem can be established. This is joint work with Enrico
Valdinoci.