University seminar "Horizons of Science Disciplines", January 16, 2025
The Center for Advanced Studies at Warsaw University of Technology invites you to the university-wide scientific seminar Horizons of Scientific Disciplines .
The seminar aims to showcase the achievements of teams representing specific scientific disciplines at Warsaw University of Technology. The planned meeting, focusing on mathematical issues, will feature two topics: " Between Easy and Hard ," presented by Dr. Paweł Rzążewski , DSc, Eng ., and " Two Problems in Physics Solved Exactly ," presented by Dr. Tomasz Cieślak from the Faculty of Mathematics and Information Science at Warsaw University of Technology. The moderator will be Prof. Grzegorz Świątek from the same faculty.
The online meeting will take place on the TEAMS platform
NP-hardness theory, developed in the 1970s, states that there are problems that are unlikely to be solved efficiently (i.e., in polynomial time with respect to the input size). Many examples of such problems can be found in the world of graph theory. A graph consists of a set of vertices, with some pairs of vertices connected by edges. Graphs are a convenient tool for mathematically modeling many real-world problems, such as those involving social networks.
Canonical (NP-)hard graph problems include the Largest Independent Set and Coloring. The fact that these problems (likely) cannot be solved quickly is only the beginning of the story. It often turns out that if input graphs have a certain structure, this structure can be exploited algorithmically. Such results provide a bridge between purely mathematical questions about graph structure and theoretical computer science.
Two physics problems solved rigorously - abstract
We will present rigorous solutions to two problems from the physical sciences. The first concerns vortices shedding from the wing of a taking-off airplane. Understanding this phenomenon is crucial, as such vortices threaten airport safety. We will show that Ludwik Prandtl's description indicates a weak solution to Euler's equation (the equation of an inviscid fluid). These rigorous solutions will improve the asymptotic estimates previously used in engineering literature. Next, we will discuss the linear instability of the objects described. In the final part of the lecture, we will describe (in a rigorous mathematical manner) all possible asymptotic states of a heated string. We will also present results on the conservation of the total energy of such a string during its evolution.
The online meeting will take place on January 16, 2025 at 4:15 p.m. on the TEAMS platform .
Registration for the event is required at the link below .
If you have any additional questions, please contact us at hdn.csz[at]pw.edu.pl
We invite all interested parties to participate in the seminar.