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, where my director of studies was Imre Leader .

Research Papers

M. Bucic, B. Sudakov, Tuan Tran; Erdős-Szekeres theorem for multidimensional arrays, submitted.
M. Bucic, E. Long, A. Shapira, B. Sudakov; Tournament quasirandomness from local counting, submitted.
M. Bucic, P. Devlin, M. Hendon, D. Horne, B. Lund; Perfect matchings and derangements on graphs, submitted.
M. Bucic, E. Jahn, A. Pokrovskiy, B. Sudakov; 2-factors with k cycles in Hamiltonian graphs, submitted.
N. Alon, M. Bucic, T. Kalvari, E. Kuperwasser, T. Szabó; List Ramsey numbers , submitted.
M. Bucic, D. Korándi, B. Sudakov; Covering random graphs by monochromatic trees and Helly-type results for hypergraphs, submitted.
M. Bucic, S. Letzter, B. Sudakov; Multicolour bipartite Ramsey number of paths, The Electronic Journal of Combinatorics 26 (2019), P3.60.
M. Bucic, M. Kwan, A. Pokrovskiy, B. Sudakov; Halfway to Rota's basis conjecture, submitted.
We also wrote a companion note to this paper: On Kahn's basis conjecture.
M. Bucic, S. Heberle, S. Letzter, B. Sudakov; Monochromatic trees in random tournaments, accepted, Combinatorics, Probability and Computing.
M. Bucic, M. Kwan, A. Pokrovskiy, B. Sudakov, T. Tran, A. Z. Wagner; Nearly-linear monotone paths in edge-ordered graphs, accepted in Israel Journal of Mathematics.
M. Bucic, M. Ornik, U. Topcu; Graph-Based Controller Synthesis for Safety-Constrained, Resilient Systems, 56th Annual Allerton Conference on Communication, Control, and Computing.
M. Bucic, B. Lidicky, J. Long, A. Z. Wagner; Partition problems in high dimensional boxes, Journal of Combinatorial Theory, Series A 166 (2019), 315-336 https://doi.org/10.1016/j.jcta.2019.02.011.
M. Bucic, S. Letzter, B. Sudakov; Three colour bipartite Ramsey number of cycles and paths, Journal of Graph Theory 92.4 (2019), 445-459, https://doi.org/10.1002/jgt.22463.
M. Bucic, S. Letzter, B. Sudakov, Tuan Tran; Minimum saturated families of sets, Bulletin of the London Mathematical Society 50.4 (2018), 725-732, https://doi.org/10.1112/blms.12184.
M. Bucic, S. Letzter, B. Sudakov; Directed Ramsey number for trees, Journal of Combinatorial Theory, Series B 137 (2019), 145-177 https://doi.org/10.1016/j.jctb.2018.12.006.
M. Bucic, S. Letzter, B. Sudakov; Monochromatic paths in random tournaments, Random Structures and Algorithms 54.1 (2019), 69-81, http://dx.doi.org/10.1002/rsa.20780.
M. Bucic - An Improved Bound for Disjoint Directed Cycles, Discrete Mathematics 341.8 (2018), 2231–2236, https://doi.org/10.1016/j.disc.2018.04.027.

Invited Talks

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, Covering graphs by monochromatic trees and Helly-type results for hypergraphs (slides)
August 2017 - Eurocomb 2017 in Vienna, Austria,
August 2017- Random Structures and Algorithms 2017 in Gniezno, Poland,

Seminar Talks

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

Autumn 2019 - teaching assistant, course organiser Algebraic Methods in Combinatorics
Spring 2019 - teaching assistant, course organiser Graph Theory
I had a pleasure of (co)supervising Michelle Sweering, for her Semester project:
Combinatorial Perspective on the Log-rank Conjecture
Spring 2018 - teaching assistant Graph Theory
I had a great pleasure of (co)supervising Sven Heberle, for his Master Thesis resulting in the following publication:
Monochromatic trees in random tournaments

Miscellaneous

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 to lead 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