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.
Utorak, 10.12. u 13:15h, predavaonica 105 i online:
Patrik Vasung (Sveučilište u Zagrebu), Hindmanov teorem
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.
Utorak, 10.12. u 14:15h, predavaonica 105 i online:
Helena Marciuš (Sveučilište u Zagrebu), 0-1 zakon za slučajne grafove
U ovom seminaru promatramo slučajne grafove G(n, n-α) 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.
Utorak, 19.11. u 13:15h, predavaonica 105 i online:
Teo Šestak (Sveučilište u Zagrebu), Dokaz Szemerédijeve leme pomoću ultrafiltra
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.
Utorak, 17.12. u 16:15h, u sklopu Seminara za vjerojatnots
Domagoj Bradač (ETH Zurich), Unique subgraphs are rare
Utorak, 26. 11., predavaonica A002, u 13:00:
Petar Nizić Nikolac (ETH Zurich), The Rise and Fall of the Bunkbed Conjecture
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.
Utorak, 26. 11., predavaonica A002, u sklopu Seminara za teoriju vjerojatnosti
u 13:00: Petar Nizić Nikolac (ETH Zurich), "Bunkbed conjecture"
u 14:00: Tadej Petar Tukara (Sveučilište u Zagrebu), "Metoda flag algebri"
Utorak, 10. 12. u 13:15h, predavaonica 105 i online
Patrik Vasung (Sveučilište u Zagrebu), "Hindmanov teorem"
Abstracts tbc
Kolika je šansa da svih 600 vozača bacanjem kockice dobije 1?
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 😊
Ukoliko imamo 12 mostova, kako bismo osigurali jednoliku raspodjelu automobila?
Moramo naći način da jedan vozač „izvuče“ slučajan broj između 1 i 12. To se može primjerice uz pomoć 12 karata, ili 12 loto kuglica, ili uz pomoć računala (pokušajte upisati u google "random number from 1 to 12"). Ako svih 600 vozača odabere nasumični most na taj način, dobit ćemo otprilike jednoliku raspodjelu.
Usput, jedno rješenje koje se nameće je da vozač baci dvije kockice i odabere njihov zbroj. No, taj način nije „jednolik“ jer, primjerice, nijedan vozač ne može dobiti 1.
Kolika je plava površina ispod krivulje u videu?
Krivulja je simetrična, pa je plava površina ispod krivulje jednaka bijeloj površini iznad krivulje. Ta površina iznosi 50cm^2.
Postoji li skup od devet karata bez tablić trojki?
Postoji, primjerice 8, 9, 10,...16.
Upcoming talks & activities
SLMath program Probability and statistics of discrete structures, January - May 2025
Graph Theory workshop at the Bellairs Research Institute, March 2025
Probability and Combinatorics workshop at the Bellairs Research Institute, 28 Mar - 4 Apr 2025
Finite Geometry and Ramsey Theory workshop at Banff International Research Station, 7 - 12 September 2025
Combinatorics, Probability and Computing workshop at Oberwolfach, 14-19 September 2025.
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)
Workshop on Synergies of combinatorics and theoretical computer science, Lausanne, 19-23 August 2024.
NS FOCS workshop, Novi Sad, 22-26 July 2024.
Extremal Graphs and Hypergraphs worskhop, Mittag-Leffler Institute, 8-12 July 2024
British Combinatorial Conference, London, 4-5 July 2024.
8th Croatian Mathematical Congress, Osijek, 2-3 July 2024 (invited)
BIMSA seminar in Discrete Mathematics, 14 May 2024, Canonical colourings in random graphs, online.
Oxford Discrete Mathematics and Probability Seminar, 23 January 2024, online.
Discrete Mathematics Seminar at the University of Victoria (British Columbia, Canada), 14 March 2024, online.
45th Australasian Combinatorics Conference, 11 December 2023 (invited as winner of the CMSA Prize), Common and Sidorenko linear patterns.
1st Brazilian School of Combinatorics (1ª Escola Brasileira de Combinatória), 11-15 September 2023, Turan-type problems for hypergraphs.
Foundations of Computational Mathematics, 12-21 June, Common systems are rare.
2023 London Colloquia in Combinatorics, 11 May 2023, Canonical colourings in random graphs..
Princeton Discrete Math(s :)) Seminar, 23 March 2023, The Turan density of 3-uniform tight cycles.
IAS CSDM Seminar, 3 April 2023.
HMD research colloquium in Zagreb, 23 November 2022, Turan-type problems for hypergraphs. All are welcome, in particular, English speakers!
ICS seminar in Prague, 8 September 2022, Canonical colourings in random graphs.
DMV annual meeting, Berlin, 12 - 16 September, Canonical colourings in random graphs.
Random Structures & Algorithms Conference, Gniezno, 1 - 5 August 2022
University of Uppsala (Probability and Combinatorics Seminar), 20 June 2022, Sparse Ramsey graphs
FU Berlin (Berlin Research seminar in Combinatorics), 1 June 2022, The Turán density of 3-uniform tight cycles
TU Graz (Graz Combinatorics seminar), 4 March 2022, Counting Regular Hypegraphs.
Copenhagen-Jerusalem Combinatorics Seminar, 25 November 2022, Common systems are rare.
London School of Economics, 22 October 2021, Sparse Ramsey graphs.
Cambridge University, 21 October 2021, Common systems are rare.
University College London, 11 October 2021, Common and Sidorenko systems of equations
University of Zagreb (Stochastic methods in analytic and applied problems seminar), 5 October 2021, Banalni sustavi su rijetki
CMSA seminar, 29 September 2021
Eurocomb 2021, 8 September 2021
Emory University, 30 April 2021, Monochromatic lines with few intervals
(invited). 2020 Australasian Graduate Symposium in Combinatorics, 18 December 2020, Robust sparse graphs. See video.
Women’s Combinatorics Colloquium, 5 November 2020, The size Ramsey number of graphs with bounded treewidth
University of Illinois Urbana-Champaign, 13 October, Asymptotic enumeration of regular hypergraphs
(invited). Arithmetic Ramsey theory in Manchester, 10-13 September 2018, Intervals in the Hales-Jewett theorem. See video.
Service and outreach activities
Conferences I have co-organised
At ECM 2024 in Seville, 15-19 July 2024, I am co-organising (with Richard Lang) a mini-symposium on Extremal and Probabilistic Combinatorics, taking place on Tue and Wed afternoon.
Constructive and Probabilistic Methods in Combinatorics 2023, with Anamari Nakić, 4-8 September 2023 in Zagreb, Croatia.
Second Adriatic Workshop in Graphs and Probability (June 2023), with Vida Dujmović.
CMSA seminar series and the CMSA day in 2020.
Popularisation talk for mathematics teachers (Županijsko stručno vijeće nastavnika matematike u gimnazijama Grada Zagreba, 26 June 2024. Slides).
Popularisation talk at MNM student conference 2023, 19 August 2023. Topic: Randomised Algorithms.
I am an active member of the National Mathematics Competitions Committee, mostly participating in problem selection and grading. In 2024, I was a deputy leader for the Croatian EGMO team.
Faculty of Science Open Day. You can watch our videos (in Croatian) here.
5 March 2022: Znanost u prolazu, 11 ujutro na Cvjetnom trgu. Dođite upoznati 15-ak hrvatskih znanstvenica!
In February and March 2022, I co-organised a leadership workshop for Penkala, facilitated by Sanjin Marion.
Co-organised Mutimir, 28.-29. 12. 2021. - a retreat for young researchers from any field.
30 November 2021: science@home with Penkala. Ivana Valentić (mathematics) and Martina Glavan (medicine) will present their research (in Croatian) to a non-specialist audience.
24-25 September 2021: Science Picnic with Young Talented Mathematicians (MNM)
coordinator at Middle European Mathematical Olympiad 2021
organising a round-table for Penkala on the 'purpose of life' in academia. Here is an illustration of our discussion.
(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.