Workshops

• Advances in partial differential equations in physics and materials science, May 29-31, 2024.

Group working seminars

The Group working seminars are taking place online via the Zoom platform. For any further information please contact Georgia Karali. 

December 2023 – May 2024 (The seminars were taking place on Thursdays, 4 pm)

• Asymptotic analysis methods for deterministic and stochastic reaction-diffusion equations (Speaker: Georgia Karali)

At first, a brief review of asymptotic methodologies on deterministic and stochastic reaction-diffusion equation is given. Then, we discuss limiting behavior of stochastic partial differential equations driven by multiplicative noise and deterministic non-autonomous terms. We also examine as a special case, reactions-diffusion systems driven by colored noise. This lecture introduces the basic mathematical tools of asymptotic analysis for the next lectures.

• Sharp Interface problems (Speaker: Georgia Karali)

A sharp interface problem for the Cahn-Hilliard equation is studied. More precisely and by using asymptotic analysis, we investigate that the sharp interface limit for the multidimensional homogeneous generalized Cahn-Hilliard equation is the homogeneous Hele-Shaw problem.  In addition, we analyze an analogous problem for the stochastic Cahn-Hilliard equation.

• Study of deterministic and stochastic free boundary problems (Speaker: Kostas Tzirakis)

We specialize in the study of the two-phase Stefan free boundary problems.

• Study of radial solutions (Speaker: Kostas Tzirakis)

We study radial solutions for the deterministic and stochastic combined Cahn-Hilliard/Allen-Cahn equation.

• Malliavin derivative with applications to finance I (Speaker: Dimitris Farazakis)

We introduce the canonical probability space and we define the Malliavin operator in this space. We apply this operator on the stochastic Ito integral by using the Malliavin formula. Then, we study existence and uniqueness theorem of stochastic reflected partial differential equation with only one reflecting barrier in combination with the definition of a localization argument (a localization of a random variable).

• Malliavin derivative with applications to finance II (Speaker: Dimitris Farazakis)

We investigate Malliavin calculus on stochastic reflected partial differential equations driven by multiplicative space-time white noise with Dirichlet conditions. The existence of absolute continuity of a random variable is examined, and as a consequence it implies that a density exists. In addition, we consider some applications in mathematical finance.