Nina Kamčev

University of Zagreb

nina.kamcev at math.hr

Hello! I am an associate professor at the University of Zagreb, working in extremal and probabilistic combinatorics. I completed my PhD at ETH Zurich in 2018 under the supervision of Benny Sudakov. Between 2018 and 2023 I was a research fellow at Monash University and at the University of Zagreb (supported by the EU's Widening Fellowship).

My research interests lie in the area of extremal and probabilistic combinatorics, and they include graph Ramsey theory (for graphs and arithmetic structures), random graphs and processes, pseudorandomness, extremal problems for graphs and hypergraphs, asymptotic enumeration. I love hearing about new problems and  applying techniques from e.g. algebra and probability, so feel free to contact me on nina.kamcev at math.hr.

Quanta have recently published a beautiful video on some maths breakthroughs in 2023, two of which are in Discrete Mathematics.

In December 2023, I was awarded the CMSA prize for early-career researchers in Australasia, for joint work with Anita Liebenau and Natasha Morrison.

Here are some resources for master's thesis writing, talk preparation etc.

In 2024/25, I will be teaching Probabilistic Combinatorics (doctoral course, all are welcome), Discrete Mathematics and Game Theory. In 2023/24, I have taught Extremal Graph Theory. Please write to me if you have any questions on those. Most Extremal Graph Theory lecture videos (in Croatian) are online.

Among my `softer' academic interests are mentoring and leadership in research, sustainability, including women and minority groups, returning to Croatia, education vs. training, why and how fundamental science is worth pursuing. I would particularly like to participate in improving the quality of teaching and research in Zagreb, and opening new opportunities for students, but I am not claiming to have any authority on these topics. I'd be very happy to exchange on any of those questions! When nothing else remains, there is music and dancing :)


*This website is in construction and probably always will be. Suggestions are very welcome!Photo credit: Liana Yepremyan

Seminari vezani uz ekstremalnu i vjerojatnosnu kombinatoriku, 2024.

Hindmanov teorem kaže da za svako 2-bojenje prirodnih brojeva postoji beskonačan skup čiji je

skup svih konačnih suma elemenata jednobojan. U ovom seminaru predstaviti ćemo dokaz Hindmanovog teorema pomoću topološkog prostora ultrafiltara i razmotriti neke generalizacije tog teorema.


U ovom seminaru promatramo slučajne grafove G(n, n) gdje je α iracionalan broj.  Koristeći Ehrenfeucht-Fraisseove igre, dokazat ćemo da niz slučajnih grafova G(n, n−α) zadovoljava 0-1 zakon,  to jest da svako svojstvo grafa prvog reda vrijedi gotovo uvijek ili gotovo nikad.

Szemerédijeva lema o regularnosti je temeljni rezultat u kombinatorici s brojnim primjenama u ekstremalnoj kombinatorici, teoriji brojeva, računarstvu i drugim područjima.

U ovom seminaru ćemo dokazati tu lemu pomoću teorije modela i ultrafiltera koristeći svojstva konačno aditivnih mjera.

In this talk, we will explore the Bunkbed Conjecture, posed by Kasteleyn in the 1980s. Given a finite graph G, the bunkbed graph of G is the product graph G×{0,1}, consisting of two copies of G, and in addition, for each vertex in G we connect its two clones. The conjecture states that for any vertex (u, 0) in the bunkbed graph, the probability that it is connected to (v,0) is at least the probability that it is connected to (v, 1), under standard Bernoulli-p bond percolation. In the last decade, this conjecture has been answered positively for certain classes of graphs and limiting regimes of p, and negatively for a generalisation to hypergraphs, before being refuted in a recent paper by Gladkov, Pak, and Zimin. 

The seminar is a part of the Probability Theory seminar at PMF-MO.

Abstracts tbc

Šansa (ili formalno vjerojatnost) je 600-struki umnožak 1/6 * 1/6 * ... * 1/6. Znači, da bi svi vozači dobili 1, morali bismo (u očekivanju) eksperiment ponoviti 10^450 puta. Ispis tog broja je 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 😊


Upcoming talks & activities

Ekstremalna teorija grafova

(napredni kolegij, 2023.-2024.)

Link na skriptu i video predavanja

Kolegij uključuje probleme Turanovog tipa, kvazislučajne grafove, Szemeredijevu lemu o regularnosti, ulaganja grafova u plohe, osnove vjerojatnosne metode, algebarskih metoda i strukturalne teorije grafova.


For other teaching and supervising information, see the Teaching tab.

Talks (2020 onwards)

Service and outreach activities

Publications

[see ArXiv for up to date PDFs]

(Slightly out of date)

Submitted

S. Antoniuk, N. Kamčev and C. Reiher, Clique factors in randomly perturbed graphs: the transition points.

V. Agdur, N. Kamčev and F. Skerman, Universal lower bound on community structure of sparse graphs.

Accepted or published

N. Kamčev and M. Schacht, Canonical Ramsey colourings in random graphs, to appear in Journal of the London Mathematical Society.

N. Broutin, N. Kamčev and G. Lugosi, Increasing paths in random temporal graphs, to appear in Annals of applied Probability.

N. Kamčev, S. Letzter and A. Pokrovskiy, The Turán density of tight cycles in three-uniform hypergraphs, International Mathematics Research Notices.

N. Kamčev, A. Liebenau and N. Morrison, Towards a characterisation of Sidorenko systems, The Quarterly Journal of Mathematics

N. Kamčev, A. Müyesser, Unavoidable patterns in locally balanced colourings, Combinatorics, Proability & Computing.

N. Kamčev, A. Liebenau and N. Morrison, On uncommon systems of equations, Israel Journal of Mathematics.

S. Antoniuk, N. Kamčev and A. Ruciński, Properly colored Hamilton cycles in Dirac-type hypergraphs, The Electronic Journal of Combinatorics.

N. Kamčev and C. Spiegel, Another note on intervals in the Hales-Jewett theorem, The Electronic Journal of Combinatorics. Talk video.

N. Kamčev, A. Liebenau and N. Wormald, Asymptotic enumeration of hypergraphs by degree sequence, Advances in Combinatorics. Talk video.

N. Kamčev, A. Liebenau, D. Wood and L. Yepremyan, The size Ramsey number of graphs with bounded treewidth, SIAM Journal of Discrete Mathematics. Tutorial slides and video.

N. Kamčev, M. Krivelevich, N. Morrison and B. Sudakov, The Kőnig graph process, Random Structures & Algorithms.

D. Conlon and N. Kamčev, Intervals in the Hales-Jewett theorem, to appear in European Journal of Combinatorics.

T. Kalinowski, N. Kamčev and B. Sudakov, Zero forcing number of graphs, SIAM Journal of Discrete Mathematics 33-1 (2018), 95–115.

N. Kamčev, T. Łuczak and B. Sudakov, Anagram-free colourings of graphs, Combinatorics,  Probability and Computing (2017), 1–20.

N. Kamčev, B. Sudakov and J. Volec, Bounded colorings of multipartite graphs and hypergraphs, European Journal of Combinatorics 66 (2017), 235–249.

N. Kamčev, M. Krivelevich and B. Sudakov, Some remarks on rainbow connectivity, Journal of Graph Theory 83(4) (2015), 372–383.

N. Kamčev, Generalised knight’s tours, The Electronic Journal of Combinatorics 21 (1) (2014), #P1.31.