Basic Notions Seminar:
The Centre is running a hybrid seminar on basic notions, which is mainly aimed at PhD students, advanced Masters students, and early PostDocs. Anyone else who is interested is also welcome to join and also to give talks if they'd like, however preference will be given to the mentioned target group.
The main idea of the Basic Notions seminar is to bring together scientists from different backgrounds to give introductory talks on the basic concepts they use on a daily basis. In this way we improve our foundation for interdisciplinary work.
The seminar takes place on Mondays, 10:15 am via Zoom and in IMPAN's room 106.
The meeting ID is 954 3153 7513.
Please contact Julian Brüggemann to get the passcode.
If you would like to give a talk as part of our Basic Notions Seminar please contact Julian Brüggemann.
Upcoming Talks
- The talk on December 16 is canceled due to a change of plans of the speaker.
- Christmas Break: The seminar will take a break over the Christmas and New Year holidays. It will resume on Monday 13/01/2025.
Past Talks
- 09/12/2024, 11:15-12:00,
Julian Brüggemann: Spaces of discrete Morse functions, merge trees, and barcodes
Abstract: This is a practice talk for the talk I am going to present at the AMS Special Session on the Open Neighborhood of Applied Topology at the Joint Maths Meeting of the AMS 2025.
Discrete Morse theory is a versatile tool from combinatorial algebraic topology. In a nutshell, discrete Morse theory uses certain well-behaved functions, the so-called discrete Morse functions, from the face poset of any regular CW complex to the real numbers. In addition to providing sublevel-filtrations, discrete Morse functions provide numerous tools to investigate topological properties and to find theoretic guarantees for various algorithms. Merge trees are combinatorial descriptors for the development of path components within different levels of filtered spaces. They have been introduced in the context of visualization, where they are used to approximate and compute contour trees.
In this talk, we consider the space of discrete Morse functions, investigate some basic properties, and see how this space is connected to spaces of merge trees and barcodes. Previous knowledge on discrete Morse theory will not be required for this talk, but some familiarity with posets (i.e. partially ordered sets) will be very helpful. - 02/12/2024, 10:15,
Marta Marszewska: Using ECP for the Analysis of Dynamic Systems
Abstract: The seminar will explore the use of Euler Characteristic Profiles (ECP) as a tool for analyzing vector fields in dynamic systems. In addition to ECP, alternative approaches such as optimal transport metrics and histogram analysis will be introduced, offering new perspectives for understanding the structure and behavior of vector fields. - 25/11/2024, 10:15,
Jakub Malinowski: Symmetries and crystallography
Abstract: This talk is an introduction to the topic of space/crystallographic groups. During the talk, I will present the definition of space groups and classic Bieberbach theorems. As motivation, I will talk briefly about the use of symmetry in crystallography. - 18/11/2024, 10:15,
Mateusz Masłowski: Efficient Techniques for Simulating One-Dimensional Electromagnetic Waves in Vacuum
Abstract: In this talk, we'll delve into the numerical modeling of one-dimensional electromagnetic waves in a vacuum. I'll introduce the basic concepts of Maxwell's equations in a simplified, one-dimensional form and discuss the finite-difference time-domain (FDTD) method for solving these equations. We'll explore the role of the Green's function in this context, providing a framework for efficiently computing the evolution of electromagnetic fields. As motivation, I'll touch on the importance of electromagnetic wave modeling in applications like wireless communication and data transmission. - 04/11/2024, 10:15
John Rick Manzanares: Exploring Centrality in Networks
Abstract: In our interconnected world, the study of networks provides valuable insights into the dynamics of complex systems. This talk will explore some measures of centrality that identify influential elements within networks, examining how we can quantify importance across different network structures. Additionally, we will briefly discuss an interplay between network science and topological data analysis, highlighting how these areas complement each other in understanding network behavior. - 28/10/2024, 10:15
Julian Brüggemann: Discrete Morse Theory and TDA
Abstract: In this talk, we will introduce/recall some basic notions from comtinatorial topology, e.g. cell/ simplicial complexes, face posets, and discrete Morse functions. Moreover, we will discuss possible applications in TDA.