Matija Bucic

I am a Veblen Research Instructor at:

Department of Mathematics at		School of Mathematics at
Princeton University and		Institute for Advanced Study

Contact Info:

E-mail address:

matija.bucic

ias.edu

Office address 1:	Department of Mathematics, Princeton University
	Washington Road, Fine Hall 1203, Princeton, 08540
	Phone: +16092584214.
Office address 2:	School of Mathematics, Institute for Advanced Study
	1 Einstein Drive, Simonyi Hall 025, Princeton, 08540

Teaching:

Spring 2022: MAT202 Linear Algebra with Applications.
Fall 2021: MAT377/APC377 Combinatorial Mathematics.

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

Curriculum Vitae: CV
Before coming to IAS and Princeton,
I completed my PhD at ETH Zürich
where my advisor was Benny Sudakov.
My undergraduate and masters studies
were at the University of Cambridge.

Research Papers:

Submitted:

Unit and distinct distances in typical norms

Towards the Erdős-Hajnal conjecture

Towards the Erdős-Hajnal conjecture for P_5-free graphs

Towards the Erdős-Gallai Cycle Decomposition Conjecture

To appear:

Uniform Turan density of cycles

Large independent sets from local considerations

Erdős-Szekeres theorem for multidimensional arrays

Turan numbers of sunflowers

Covering random graphs with monochromatic trees

Published:

Counting H-free orientations of graphs

Tight Ramsey bounds for multiple copies of a graph

The (t-1)-chromatic Ramsey number for paths

The intersection spectrum of 3-chromatic intersecting hypergraphs

Cycles of many lengths in Hamiltonian graphs

Clique minors in graphs with forbidden subgraphs and other restrictions

Universal and unavoidable graphs

Unavoidable hypergraphs

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

Large cliques and independent sets all over the place

Tournament quasirandomness from local counting

List Ramsey numbers

Perfect matchings and derangements on graphs

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

January 2023 - Combinatorics Workshop in Oberwolfach Institute, Germany Towards the Erdős-Hajnal Conjecture (slides)
December 2022 - Graph Theory Workshop at McGill research centre in Barbados, 2022, Towards the Erdős-Hajnal conjecture for P_5-free graphs (board talk)
October 2022 - AMS Special Session on Ramsey Theory, Tight Ramsey bounds for multiple copies of a graph (board talk)
August 2022 - Recent Advances in Probabilistic and Extremal Combinatorics in Ascona, Switzerland New bounds towards the Erdős-Gallai cycle decomposition conjecture (slides).
June 2022 - SIAM Conference on Discrete Mathematics 2022, CMU, Pittsburgh, USA Turan numbers of sunflowers (slides).
April 2022 - Graph Theory Workshop in Oberwolfach Institute, Germany New bounds towards the Erdős-Gallai cycle decomposition conjecture (slides).
January 2022 - Graph Theory Workshop in Oberwolfach Institute, Germany Clique minors in graphs with a forbidden subgraph (slides)
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

September 2021 - Eurocomb 2021 online. The intersection spectrum of 3-chromatic intersecting hypergraphs (slides)
July 2021 - SIAM Conference on Discrete Mathematics 2021 online. Erdős-Szekeres theorem for multidimensional arrays (slides)
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 and Colloquium Talks

February 2023 - UCSD Department of Mathematics Colloquium, Robust Sublinear Expanders (slides) .
February 2023 - IAS Computer Science and Discrete Mathematics Seminar, From Robust Sublinear Expanders to Additive Number Theory via Rainbow Cycle (video).
February 2023 - Rutgers Discrete Math Seminar, Unit and distinct distances in typical norms (board talk)
November 2022 - MIT-Harvard-MSR Combinatorics Seminar, New bounds towards the Erdős-Gallai cycle decomposition conjecture (slides).
November 2022 - Graz Colloquium in Combinatorics, Decomposition Problems (slides).
September 2022 - IAS Computer Science and Discrete Mathematics Seminar, Robust Sublinear Expanders, and an Application Towards the Erdős-Gallai Conjecture (video).
September 2022 - IAS Short Talks, Robust Sublinear Expanders (video).
May 2022 - Graz Combinatorics Seminar, Covering random graphs with monochromatic components (slides).
March 2022 - IAS Computer Science and Discrete Mathematics Seminar, The absorption method, and an application to an old Ramsey problem (video).
March 2022 - Princeton Applied and Computational Matehmatics Colloquium, Two classical decomposition problems (board talk).
March 2022 - Discrete Mathematics and Algebra Seminar at University of Delaware, Tight Ramsey bounds for multiple copies of a graph (board talk).
January 2022 - Birmingham Combinatorics and Probability Seminar, Tight Ramsey bounds for multiple copies of a graph (board talk)
November 2021 - Rutgers Discrete Math Seminar, Tight Ramsey bounds for multiple copies of a graph (board talk)
November 2021 - Oxford Discrete Mathematics and Probability Seminar, Turan numbers of sunflowers (slides) (video)
October 2021 - Princeton Discrete Math Seminar, Tight Ramsey bounds for multiple copies of a graph (board talk)
March 2021 - Mittagsseminar at ETH Zürich, Large cliques and independent sets all over the place (slides, short version)
November 2020 - Combinatorics seminar at Tel Aviv University, The intersection spectrum of 3-chromatic intersecting hypergraphs (slides, long version)
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)
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

Mentoring:

I am supervising Robert Rubin, for a Junior Paper, resulting in the publication: "Ramsey numbers of nK_4", in preparation.
I had a pleasure of supervising Pablo Blanco, for a Summer Research Project, resulting in the following publication:
Towards the Erdős-Hajnal Conjecture for P_5-free graphs, submitted.

I had a pleasure of supervising George Bentley for his Junior Paper titled: "On unavoidable r-uniform hypergraph".
I had a pleasure of (co)supervising Domagoj Bradac, for his Master Thesis, resulting in the following publication:
Covering Random Graphs with Monochromatic Trees, accepted in RSA.
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. Proceedings of London Mathematical Society,
3. Transactions of American Mathematical Society,
4. Proceedings of American Mathematical Society,
5. American Mathematical Monthly,
6. Combinatorica,
7. Random Structures and Algorithms,
8. Journal of Combinatorial Theory Series B,
9. Advances in Combinatorics,
10. Journal of Combinatorial Theory Series A,
11. Combinatorics, Probability and Computing,
12. SIAM Journal on Discrete Mathematics,
13. European Journal of Combinatorics,
14. Journal of Graph Theory,
15. Electronic Journal of Combinatorics,
16. Discrete Applied Mathematics,
17. Discrete Mathematics and
18. Utilitas Mathematica.
I organised a Minisymposium titled: "Extremal Problems Involving Colouring" at SIAM DM 2021. Conference website.
I organised a Minisymposium titled: "Extremal Problems Involving Colouring" which was accepted at SIAM DM 2020 (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 had a great pleasure of leading the Croatian team to the IMO 2018. IMO website.
I have been awarded an ETH medal for my PhD Thesis (examiners were: Benny Sudakov and Michael Krivelevich): Local to global phenomenon and other topics in probabilistic and extremal combinatorics.
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
I had a great pleasure of participating in MPS Conference on High-Dimensional Expanders hosted by the Simons Foundation in New York.
I had a great pleasure of leading the Croatian team to the IMO 2018. IMO website.