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Account of the winter school on singularities and low-dimensional topology

Authors Alex Kubasch
Publication date 02/15/2023
The lecturers and TAs (photo by Gergely Szilágyi)

Recently, I participated in the Winter school in singularities and low-dimensional topology at the Alfréd Rényi Institute of Mathematics. This was the opening event of the Erdős Center semester Singularities and low-dimensional topology. The workshop was intended to form a link between low-dimensional topology and singularity theory in the minds of more than a hundred young researchers and PhD-students such as myself.

Keeping in mind the different mathematical backgrounds of the participants, the programme kicked off with a 2-day pre-school to get everyone on the same page. The lectures of Vera Vértesi, Marco Marengon, András Stipsicz and András Némethi confidently sailed us through an ocean of basic definitions of both fields, from Morse to Milnor, through Kirby and Alexander.

The meat of the workshop was a 5-day school with 4 courses consisting of 4 lectures each. Kyle Hayden put his knot-theoretic 4D-glasses on the audience in order to be able to actually „see” the intersection form, genus-minimizing surfaces, and exotic 4-dimensional Euclidean spaces. The lecture-series of Michael Wong went full circle (unknot) beginning with grid homology, then guiding us through the definition of Heegaard Floer homology and finally ending up back at knot Floer homology. The astonishing relationship between the deformation theory of plane curve singularities and the HOMFLY polynomials of their links unfolded seamlessly during the classes of Duco van Straten. Finally, András Némethi laid out an easy-to-follow recipe for homemade cohomology theories, as well as introducing the analytic lattice cohomology of curves and the topological version for surfaces.

In spite of having been exposed previously to most of the concepts discussed at the workshop, I still learned something new in all of the courses, not least because of the willingness of the lecturers to discuss any questions and ideas of the audience. After the talks there was an optional TA session at the end of every day and the event was concluded by a cascade of lightning talks presented by the participants on Friday afternoon.

Group photo of the Winter school in singularities and low-dimensional topology (photo by Gergely Szilágyi)

The one thing however that deformed this event into a singular experience was the opportunity to meet a multiplicity of other young mathematicians from all over the world. Hence some optional social activities were also part of the programme: we toured the Buda castle and the seventh district, went bouldering and ice skating, saw art exhibitions, relaxed in the thermal baths and explored the ruin bars of Budapest.

In a nutshell: the divisors were exceptional, the knots strongly (quasi-)positive, the lectures enlightening and the people charming, so I for one am excited for the next instalments of the Singularities and low-dimensional topology semester.

Some anonymous comments we received

Lectures were well designed, accessible mostly, organizers were so friendly. I feel motivated and encouraged a lot to learn the material in detail.

It was a very friendly environment where it felt like everyone (including the lecturers) wanted to learn and work together. The breaks and organised activities really helped to make the school feel like an event, rather than just a set of people going to lectures.

It was the best experience ever! I liked the fact that there are many experts around me to whom I can ask my questions.

It was really an awesome school! The course topics were picked in a great way, the lecturers were good with differences mainly in pace and organization. The atmosphere of the school was thrilling with a lot of interaction both mathematically and socially!

I really liked the teaching assistant time. It was quite helpful and all of the assistants were really good and kind!

Thank you a lot for organising such a wonderful winter school. Everything was so well organised and the experience was very pleasing! This was the first time I've participated in such an event and I am so happy that my first experience was at the Renyi Institute!

It was amazing, thanks for the incredible week!



Alex Kubasch (ELTE & Rényi Institute)