Random Structures

Inspire the next generation of female scientists!💡
For the Int’l Day of Women and Girls in Science,
@univie.ac.at is offering an opportunity to meet mathematicians up close.

𝗗𝗲𝘁𝗮𝗶𝗹𝘀:
⏰ March 4, 2026
📍 Maths Faculty
🗣️ 🇩🇪 + 🇬🇧
🪙 Free

Register 👉 tinyurl.com/38m6z4s3

🔄 Know someone? Forward this!

Excited to see our young researchers featured 👏

Portrait of Nishu Kumari, postdoc researcher at the University of Vienna. She has black hair, wears glasses and a red patterned blouse, and sits under a tree against the backdrop of an entrance to a building. The image includes the Her Maths Story logo and her name and title.

“I feel that many women (…), might not know what (…) a career in maths actually means (…). I believe it is important to tell them that this is an option.” - Nishu Kumari

➡️https://hermathsstory.eu/nishu-kumari/

#HerMathsStory #Academia #Combinatorics #Europe #Postdoc @randomstructures.bsky.social

It's the 100th anniversary of Schrödinger's Equation!

Join international experts this week as they cover a century of quantum breakthroughs at ESI Vienna.

No registration required!

👉 Find the full program here: www.esi.ac.at/events/e596/

© 📸 ESI/Uni Wien

@esivienna.bsky.social @univie.ac.at

pic of nathanael with his book and the title a book a decade in the making

A decade of labour went into this book!

Nathanaël received the physical copy of his book Gaussian Free Field and Liouville Quantum Gravity published late last year.

He and co-author Ellen Powell were inspired ten years ago in Cambridge.

Order here 👉 www.cambridge.org/core/books/g...

a picture of Marcus and the title of the paper with the words congratulations

Big milestone for our team member Marcus!
His first paper just went up on arXiv this week on the 1/4-phenomenon of placement probabilities of tilings in the Aztec diamond.

Give him a round of applause 👏

👉 Read the paper here: arxiv.org/abs/2512.08377

dark blue background and in yellow the word publication and name of publication A Generalization of Conjugation of Integer Partitions and list of some of the co-authors: Seamus Albion Ilse Fischer Christian Krattenthaler et al

Spotlight on publication no. 2 of 2025:
A Generalization of Conjugation of Integer Partitions

Read the full paper here 👉 www.combinatorics.org/ojs/index.ph...

Thanks so much for featuring one of outstanding researchers and team members 👏

Check out Ilse's profile over on Her Maths Story!

We think it's really worth a read 👏

#womeninmaths #mathematics #austria #womeninstem

YouTube video by Universität Wien 🤓Logisches Denken: Mathematik spielend lernen🎲 | Universität Wien

Our team member Marcus worked with @univie.ac.at for their Future Skills series. We love the result!

Watch here:
www.youtube.com/watch?v=YaSB...

What future skills do you think we need?

#futureproof #maths #stem

Our very own Mihyun from TU Graz has an excellent feature on @hermathsstory.bsky.social Go check it out! 👏

Thanks so much for featuring Mihyun!

A text box that reads our publications and another text box, both bright yellow, with the name of the paper (see posting text) and author shane chern et a. with a graphic of a paper and a megaphone

Our first official publication of 2025: "A bijective look at gapfree partitions: between local and global" by Shane Chern et al.

Shane said of this milestone:
“A toast to George, my dearest PhD advisor!"

Check it out here 👉 link.springer.com/article/10.1...

a hand holding up a trophy on a dark blue background and the words congratulations academic ranking of world universities 2025 written on it

Our 3 unis have placed in the top 25% (ok, since we’re pedantic, the top 24%–28% 😉) of the Academic Ranking of World Universities 2025!

1️⃣ Uni of Vienna → Group 101–150
(+ 31st in maths!)
2️⃣ TU Wien → Group 201–300

3️⃣ TU Graz → Group 601–700

Congratulations to all unis!

Counting independent sets in percolated graphs via the Ising model Given a graph $G$, we form a random subgraph $G_p$ by including each edge of $G$ independently with probability $p$. We provide an asymptotic expansion of the expected number of independent sets in random subgraphs of regular bipartite graphs satisfying certain vertex-isoperimetric properties, extending the work of Kronenberg and Spinka on the percolated hypercube. Combining graph containers with the cluster expansion from statistical physics, we give an expansion of the partition function of the Ising model in certain range of the parameters. Among other applications, we obtain results for even tori of growing side-length. As a tool, we prove a refined container lemma for the Ising model, which mildly improves recent bounds of Jenssen, Malekshahian, and Park.

Read the full paper here: arxiv.org/abs/2504.08715

A dark blue background with title of the Preprint Counting Independent sets in percolated graphs via the Ising model and an illustration of the Ising model figure from the research

Our paper on percolated graphs is a compelling example of how combining ideas from combinatorics, probability, and statistical physics can lead to new insights.



Our approach is based on the initial insight that, in expectation, the problem behaves like the Ising Model.

Link in comments 👇

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Excited to announce Nathanael has been named a Fellow of the IMS for his contributions to probability theory and mathematical physics.

“I couldn't be prouder to have been named a Fellow. The IMS publishes the best journals in the field, making sure these are priced affordably and inclusively.”

A portrait of Andres

View from Facculty of Mathematics of Uni Vienna

Old building in Budapest

We hosted Andres Contreras Hip from Chicago for a 2-week research visit in Vienna! He joined us for maths collaboration, talks, and even visited the Budapest-Vienna Seminar.
Andres concluded: “Great math, food & music in a superb city.”
Swipe to see Vienna & Budapest through his eyes!

Nathanael and Prof Sun on campus at PKU

PKU campus in spring

Nathanael at the Institute of Mathematics in Beijing

A german quote "We must know, we will know" above the door to a lecture hall at PKU

Nathanael just returned from a research trip to China, where he met Prof Sun at PKU.

He said:
“I was hugely impressed by the scientific level, which is on a strikingly exponential upward trajectory. China is building a world-class scientific environment, and probability community in particular."

blue and yellow structure in the shape of a heart on blue background and the name Random Structures

We're a research cluster uniting experts from @univie.ac.at , @tuwien.at & @tugraz.bsky.social to explore the intersection of #probability and #combinatorics & tackle some of maths' most fascinating problems!

Generously funded by @fwf-at.bsky.social

#RandomStructures #Mathematics #MathResearch