Daniel T. Soukup

• October 2019: After a very busy summer, I am excited for a new chapter and to start working on completely new problems as a data scientist. This will be my new webpage but this academic site will remain here as well of course.


• June/July 2019: Time flies! We have wrapped up the Combinatorial Set Theory course already. The final set of notes and all the problem sets are available here. Otherwise, organising the YSTW and ESTC conferences took over our lives here but in the end, it all went great. You can find all the slides, photos, abstracts here on the websites. Also, new lecture video from my plenary talk at the Fields Institute from this May.


• March/April 2019: Courses started at the University and I was busy giving my first graduate level course in Combinatorial Set Theory. Course materials (notes and problem sets) are continuously updated here. I had a great research visit to Hamburg thanks to Benedikt Löwe. We worked with Imre Leader and Christian Reiher on partition relations; I gave a talk at the Discrete Math Seminar on minimal walks; and had some great chats with Joshua Erde, Attila Joó and Max Pitz. Thanks everyone for the hospitality! Finally, the details of our conferences are coming together, it looks like we'll have a great meeting.


• February 2019: Two great research visits kicked off February: I gave a talk on D-spaces and our new joint work with Paul Szeptycki in Budapest ( abstract), and a talk on strong edge-colourings of graphs with uncountable chromatic number at Bar-Ilan University while visiting Assaf Rinot ( abstract). Speaking of D-spaces, our paper with Paul is now submitted to Topology and its Applications (the prerint is on arxiv). Finally, we opened registration for the European Set Theory Conference and Advanced Class on the website.


• January 2019: Happy New Year! Wrapping up a longer project from last year, I submitted a two-part paper titled 'Ladder system uniformization on trees' to the Archive for Mathematical Logic and Fundamenta Mathematicaepre (preprint on arxiv). Otherwise, January was busy with preparing for my topics course on combinatorial set theory.


• December 2018: I gave a two-part lecture on ladder system uniformization on trees: the first talk focused mostly on the classical theory, the second part summarized my recent work. You can watch both Part I and Part II and find more details in the preprint on arxiv. More and more information will appear about the European Set Theory Conference and Advanced Class at our website.


• November 2018: Another successful high school talk is in the books. My favourite comment from one student: "Maybe I should consider becoming a mathematician instead of opening a brewery after graduation..." Later this month, I will be visiting Imre Leader and Benedikt Löwe in Cambridge to talk about recent advances on Hindman-type results for the real line. See my abstract for the Combinatorics Seminar here. Also, more details are being finalized about the European Set Theory Conference and the Advanced Class in Set Theory (aka the next installment of the Young Set Theory Conference) for 2019. The preliminary website is up.


• October 2018: I have been organizing some talks at high schools in Budapest and the first one is happening next week. I'll be talking about asymetric cryptography and a nice implementation using graphs. Also, our paper with P. Ellis on cycle reversions was accepted at the European Journal of Combinatorics and the sum-set paper with P. Komjáth, I. Leader, P. A. Russell, S. Shelah and Z. Vidnyánszky will appear in the Proceedings of AMS.


• September 2018: We started a Youtube channel for the KGRC where we already posted lectures from our recent conference. We plan to record seminar talks in the future as well. I also have some new notes on Galvin's conjecture based on a recent paper by D. Raghavan and S. Todorcevic.


• August 2018: We finalized and submitted the second part of our 'independent transversals' paper with Andres Aranda, Claude Laflamme and Robert Woodrow (see Publications). The Set Theory Today meeting starts in 10 days with 100 people from around the globe. We are ready to both stream the talks live and record them so look out for further announcements.


• July 2018: New lecture video available. Scroll down for my semi-plenary talk at the 2017 Spring Topology and Dynamical Systems Conference on topological spaces with small dense sets. Or click here.


• July 2018: I gave a talk at the Settop conference on ladder system uniformization on trees and uncountable minimal linear orders. Slide are here.


• June 2018: I visited the University of Hamburg to talk at the research seminar of the Discrete Math group on dichromatic number problems, and to give an invited lecture at the Undecidability Studierendenkolleg. You can find my slides here on monochromatic sumsets in large direct sums.


• May 2018: I gave a talk on Davies-trees at the Séminaire Général de Logique (Paris 7). You can find the slides here.


• April 2018: We are organizing an exciting meeting at the KGRC with a long list of great speakers. Click here for more information.


• December 2017: I was very happy to receive the Grünwald Géza Prize from the Bolyai Society at the Rényi Institute. The prize is awarded since 1951 to Hungarian mathematicians under 30 for outstanding achievements in pure mathematics research.


• September 2017: Somehow, I appear in a Spiegel article on the Heidelberg Laureate Forum.

In plain words, I am interested in understanding large, seemingly random and chaotic abstract mathematical objects by looking at the collection of well-behaving substructures with certain properties. How large can these nice substructures be? How do local and global properties of these structures interact and affect each other?

Imagine a giant network that we know is dense by some measure (my work revolves around the chromatic number as a global measure). It is known that locally, this density is not necessarily detectable. However, are there always large highly connected clusters? In my PhD thesis, I answered an old question of Erdős and Hajnal by showing that there could be graphs with uncountable chromatic number but with no infinitely connected, uncountable subgraphs.

My work is motivated by still open classical problems, as well as recent research by Komjáth, Thomasse, Thomassen, Shelah and Todorcevic among others. Hopefully you'll find the most important academic informations about me on this website. Feel free to contact me in case you got interested in any of the things I work with.

I am also passionate about teaching, active learning methods and I recently dabbled in high-school outreach and criptography.