Young Topologists Meeting 2025

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 - Embedding calculus and applications to diffeomorphism groups

Embedding calculus is a homotopy-theoretic tool to study the topology of spaces of embeddings between manifolds by remembering the restrictions of embeddings to collections of finitely many points in the source manifold. Traditionally, this tool has been used to study spaces of embeddings between manifolds of codimension at least 3, but recent years also have seen a number of striking applications of embedding calculus to the study of spaces of diffeomorphisms and homeomorphisms. 

In this lecture series, I will give a general introduction to embedding calculus and explain some of its recent applications. 

I will not assume any prior exposure to embedding calculus, but some basic familiarity with high-dimensional manifold theory and the language of infinity-categories will be helpful. There are many good introductions to these subjects; Kosinski's book "Differential Manifolds" and Land's book "Introduction to Infinity-Categories“ are among them.

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. Consult the digital booklet (pdf 190 kB)  for the full schedule and all abstracts.

Contributed talk slots consist of two parallel talks. "Fika" is the Swedish term for coffee breaks accompanied by pastries :) 

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.

Map for YTM 2025 (pdf 2.4 MB)

Guide to Stockholm (pdf 51 kB)

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.

You can contact us at ytm2025@math.su.se .