## 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).

Topics I have recently worked on include graph Ramsey theory, arithmetic Ramsey theory, extremal problems for hypergraphs, random and pseudorandom graphs, 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.

In Fall semester 2023, I will be teaching Extremal Graph Theory (doctoral course), Discrete Mathematics and Game Theory. Please write to me if you have any questions on those.

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 there. I'd be very happy to exchange on any of those topics! 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

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

23 January 2024, Oxford Discrete Mathematics and Probability Seminar (online).

Discrete Mathematics Seminar at the University of Victoria (British Columbia, Canada), 14 March 2024.

# Ekstremalna teorija grafova

### (napredni kolegij, 2023.-2024.)

Teme kolegija će se prilagoditi polaznicima, ali gradivo će uglavnom biti podskup sljedećih triju kolegija.

David Conlon, Extremal Graph Theory,

Yufei Zhao, Probabilistic Method in Combinatorics,

Extremal Combinatorics na Carnegie Mellon Sveučilištu.

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

## Talks (2020 onwards)

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

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 at MNM student conference 2023, 19 August 2023. Topic: Randomised Algorithms.

I am an active member of the National Mathematics Competitions Committee.

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.

Submitted

N. Broutin, N. Kamčev and G. Lugosi, Increasing paths in random temporal graphs.

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

Accepted or published

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.