The Young Topologists Meeting (YTM) is an annual conference for graduate students, recent PhDs, and other junior researchers in topology, both pure and applied. This year, it is jointly organized by Stockholm University and KTH Royal Institute of Technology. Previous editions of the conference have been organized by the University of Münster, EPFL, the University of Copenhagen, and Stockholm University/KTH.
This yearly meeting is an opportunity for young researchers in topology to share their work and make new connections. In addition to short talks given by the participants and a poster session, the program features three guest lecture series, by
Frédéric Chazal
(Inria Saclay),
Manuel Krannich
(Karlsruhe Institute of Technology), and
Maria Yakerson
(IMJ-PRG).
Frédéric Chazal - Persistent homology for machine learning: a measure perspective
Topological Data Analysis (TDA) is a modern and innovative approach in data science that has gained significant interest over the past decade and has found numerous practical applications. By leveraging concepts from algebraic topology, TDA aims to extract meaningful topological patterns from complex datasets — patterns that can be essential for understanding the underlying structure of the data.
At the heart of TDA lies persistent homology, a robust and mathematically grounded tool that tracks the appearance and disappearance of topological features across multiple scales. This multiscale viewpoint makes TDA particularly effective for analyzing noisy, high-dimensional, or unstructured data, where traditional techniques may fall short.
Topological information extracted through persistent homology is typically represented by persistence barcodes (sets of intervals) or persistence diagrams (sets of points in the plane). While visually intuitive, these representations are not readily compatible with standard machine learning pipelines. Bridging this gap — by designing relevant vector representations of persistence diagrams and studying their statistical properties — has become an active area of research, leading to numerous recent advances.
This course will begin with a basic and informal introduction to persistent homology and the classical TDA pipeline. It will then present a measure-theoretic perspective on persistence diagrams and demonstrate its mathematical and practical value in machine learning through selected theoretical results and concrete examples.
Manuel Krannich - TBA
Maria Yakerson - Motivic obstruction theory
In topology, obstruction theory is a powerful tool that allows one to tackle lifting and extension problems. In particular, obstruction theory helps to classify vector bundles in terms of algebraic invariants. More concretely, it often provides an answer to the question whether a vector bundle can be decomposed as a direct sum with a trivial subbundle.
Motivic homotopy theory is a modern research area that combines homotopy theory with algebraic geometry. The main motto is that we apply, when possible, methods from homotopy theory to gain new information about objects in algebraic geometry. In particular, there is a motivic version of obstruction theory, developed by F. Morel, A. Asok, J. Fasel et al., which allows us to approach splitting problems for algebraic vector bundles on smooth affine varieties. In this lecture series, we will see the main instruments of motivic obstruction theory which stem from topological ideas, and we will learn how these ideas give applications in algebra and algebraic geometry.
The conference will begin at 10:00 on Monday, June 23rd and end at 16:00 on Friday, June 27th. The detailed schedule will come later.
Registration is closed. We have contacted all participants; if you have not received anything from us, please check your spam folder or let us know :)
Registration to give a talk, to present a poster, or for funding closed on March 21st, 2025. Registration for simple attendance closed on April 25th, 2025. There is no registration or conference fee.
YTM 2025 will be taking place mostly on KTH campus, with one half-day at Albano (SU). Information on how to get to KTH:
link
.
The closest hotel to the conference is the Elite Hotel Arcadia. Some hostels around Stockholm are Generator Stockholm, City Hostel, and Zinkensdamm. These hostels are a ~30 minute public transportation trip away from the conference.
The organizing committee is: Benedetta Andina, Ronno Das, Christina Kapatsori, Oliver Lindström, Jan McGarry Furriol, Isaac Ren, Elmo Vuorenmaa, and Björn Wehlin.
