Matija Bucic

PhD Student in Mathematics
Advisor: Benny Sudakov

Department of Mathematics
ETH Zürich

Contact Info:

E-mail address:

matija.bucic

math.ethz.ch

Office address:	Department of Mathematics, ETH, HG J 65
	Rämistrasse 101, 8092 Zürich, Switzerland
	Phone: +41 44 632 8509.

Fields of Interest: Ramsey Theory, Directed Graph Theory, Algebraic and Probabilistic Methods in Combinatorics,
Extremal Set Theory, Theoretical Computer Science, Random Structures

Curriculum Vitae: CV
Since 2016 I am a PhD student at ETH Zürich.
Before coming to ETH, my undergraduate and masters studies were at the University of Cambridge.

Research Papers

Submitted:

Unavoidable hypergraphs

The intersection spectrum of 3-chromatic intersecting hypergraphs

Large independent sets from local considerations

Erdős-Szekeres theorem for multidimensional arrays

To appear:

Clique minors in graphs with forbidden subgraphs and other restrictions

Large cliques and independent sets all over the place

Covering random graphs by monochromatic trees and Helly-type results for hypergraphs

Universal and unavoidable graphs

Tournament quasirandomness from local counting

Perfect matchings and derangements on graphs

Published:

List Ramsey numbers

Halfway to Rota's basis conjecture

Nearly-linear monotone paths in edge-ordered graphs

2-factors with k cycles in Hamiltonian graphs

Monochromatic trees in random tournaments

Multicolour bipartite Ramsey number of paths

Graph-Based Controller Synthesis for Safety-Constrained, Resilient Systems

Partition problems in high dimensional boxes

Three colour bipartite Ramsey number of cycles and paths

Minimum saturated families of sets

Directed Ramsey number for trees

Monochromatic paths in random tournaments

An Improved Bound for Disjoint Directed Cycles

Invited Talks

May 2020 - Stanford Online Combinatorics Seminar Large cliques and independent sets all over the place, (slides)
May 2020 - Extremal and Probabilistic Combinatorics Webinar, Tournament quasirandomness from local counting (video recording of the talk)
March 2020 - Joint FU Berlin–Tel Aviv University Workshop on Ramsey Theory, Israel Erdős-Szekeres theorem for multidimensional arrays (slides, long version)
January 2020 - Combinatorics Workshop in Oberwolfach Institute, Germany, Erdős-Szekeres theorem for multidimensional arrays (slides)
September 2019 - Workshop on Probabilistic and Extremal Combinatorics in Banff, Canada, Nearly-linear monotone paths in edge-ordered graphs (video recording of the talk)
August 2019 - British Combinatorial Conference 2019 in Birmingham, Covering graphs by monochromatic trees and Helly-type results for hypergraphs (slides)
June 2018 - SIAM Conference on Discrete Mathematics 2018 in Denver, USA, Bipartite Ramsey number of paths and cycles (slides)

Contributed Talks

July 2019 - Random Structures and Algorithms 2019 in Zürich, Switzerland. Covering graphs by monochromatic trees and Helly-type results for hypergraphs (slides)
August 2017 - Eurocomb 2017 in Vienna, Austria. Directed Ramsey number for trees (slides)
August 2017- Random Structures and Algorithms 2017 in Gniezno, Poland. (slides)

Seminar Talks

November 2019 - Combinatorics seminar at Tel Aviv University, The intersection spectrum of 3-chromatic intersecting hypergraphs (slides, long version)
November 2019 - Combinatorics seminar at University of Warwick, Erdős-Szekeres theorem for multidimensional arrays (slides, long version)
November 2019 - Mittagsseminar at ETH Zürich, Erdős-Szekeres theorem for multidimensional arrays (slides, short version)
May 2019 - Mittagsseminar at ETH Zürich, Covering random graphs by monochromatic trees and Helly-type results for hypergraphs (slides)
October 2018 - Mittagsseminar at ETH Zürich, Nearly-linear monotone paths in edge-ordered graphs (slides)
May 2018 - Combinatorics Seminar at University of Cambridge, Minimum saturated families of sets (board talk).
April 2018 - Graduate Seminar in Probability at ETH Zürich, From correlation inequalities to extremal set theory and back (board talk)
February 2018 - Mittagsseminar at ETH Zürich, Minimum saturated families of sets (slides)
March 2017 - Mittagsseminar at ETH Zürich,
March 2016 - Part III Seminar at University of Cambridge, Splitting Directed Graphs (board talk)

Teaching Info

Spring 2021 - course organiser Graph Theory
Autumn 2020 - course organiser Probabilistic Methods in Combinatorics
Spring 2020 - teaching assistant, course organiser Graph Theory
Autumn 2019 - teaching assistant, course organiser Algebraic Methods in Combinatorics
Spring 2019 - teaching assistant, course organiser Graph Theory
Spring 2018 - teaching assistant Graph Theory

Supervising Info

I had a pleasure of (co)supervising Vedran Mihal, for his Master Thesis:
Generalised Ramsey Theories
I had a pleasure of (co)supervising Michelle Sweering, for her Master Thesis:
Covering Problems in Hypergraphs
I had a pleasure of (co)supervising Erik Jahn, for his Bachelor Thesis, resulting in the following publication:
2-factors with k cycles in Hamiltonian graphs, published in JCTB.
I had a pleasure of (co)supervising Michelle Sweering, for her Semester project:
Combinatorial Perspective on the Log-rank Conjecture
I had a great pleasure of (co)supervising Sven Heberle, for his Master Thesis resulting, in the following publication:
Monochromatic trees in random tournaments, published in CPC.

Miscellaneous

I have refereed papers for many major combinatorial and general mathematics journals including:
1. Annals of Mathematics,
2. Combinatorica,
3. Journal of Combinatorial Theory Series B,
4. Journal of Combinatorial Theory Series A,
5. SIAM Journal on Discrete Mathematics,
6. European Journal of Combinatorics,
7. Journal of Graph Theory,
8. Electronic Journal of Combinatorics,
9. Discrete Mathematics and
10. Utilitas Mathematica.
I organised a Minisymposium titled: "Extremal Problems Involving Colouring" which was accepted at SIAM DM 2020, but the conference was subsequently canceled due to COVID-19. Conference website.
I participated in the organisation of the Random Structures and Algorithms 2019 conference in Zurich Conference website.
I participated in an excellent workshop on Graph and Hypergraph Colouring in Berlin 2018. Workshop website.
I had a great pleasure of leading the Croatian team to the IMO 2018. IMO website.
My Part III essay, under supervision of Perla Sousi: Ramanujan Graphs
Summer research project 2015 report, under supervision of Imre Leader: Splitting Directed Graphs
A mathematical essay, which was awarded the Woods prize 2014, the topic was proposed by Imre Leader: Evolution of Random Graphs