(in Polish) Cząstki na wysokości 6 1000-1S25CW6

ORGANIZATION:
Each semester begins with an organizational meeting where we introduce the topic of the current edition of the seminar. We also offer an introductory lecture on the subject and share materials that will be used. Presentation topics are then distributed among the participants, taking into account their current knowledge and interests. We are available to help with any questions that may arise during preparation.

SEMINAR:
The seminar takes the form of a multi-day trip. Presentations are given according to a prearranged schedule. One day is devoted to an excursion (e.g., a mountain hike or a kayaking trip), which is an integral part of the seminar. It serves both to reinforce the material and to build connections among participants. The seminar also provides an excellent opportunity for informal discussions about future academic paths - whether to pursue a PhD, what to choose for a Master's thesis, etc.

TOPIC:
We aim for each edition of the seminar to address contemporary research questions. This gives participants the opportunity to attend scientific conferences, workshops, or summer/winter schools and to understand the talks presented there. We also aim to build a sense of community among researchers working in analysis, so the topics are often connected to other areas of mathematics and physics.
In previous years, we have explored:
• Bayesian inverse problems for PDEs (statistics),
• Gradient flows in Wasserstein spaces (probability),
• Convex integration methods for the Euler equation (differential geometry, fluid mechanics).

This year’s seminar will focus on hyperbolic conservation laws, based on the excellent monograph by C. M. Dafermos, "Hyperbolic Conservation Laws in Continuum Physics". We will discuss fundamental concepts such as weak solutions, shock waves, Rankine–Hugoniot conditions, and entropy solutions. Particular attention will be paid to the existence and uniqueness of solutions, as well as the formation of discontinuities in hyperbolic systems. While the seminar is theoretical in nature, we will also consider physical examples from fluid mechanics and elasticity theory.

WHO PARTICIPATES:
In previous years, the seminar has included undergraduate and Master’s students, PhD students, faculty, and guests from outside the department. Participants have come not only from the field of PDEs, but also from statistics and probability theory.

If you have any questions or uncertainties, please don’t hesitate to contact the organizers.