Marius Tiba
My research focuses on combinatorics and its connections with metric geometry, analysis and combinatorial number theory. Recently, I have worked on the stability of geometric inequalities, covering systems and random polynomials.
Starting in 2022, I have been a Titchmarsh research fellow at the Mathematical Institute, University of Oxford. From 2021 to 2022, I was visiting Rob Morris at IMPA (Instituto Nacional de Matemática Pura e Aplicada) in Rio de Janerio, Brazil as a post-doc of excellence. I did my PhD under the supervision of Béla Bollobás at the University of Cambridge, defending in September of 2021.
My email is Marius (dot) Tiba (at) maths (dot) ox (dot) ac (dot) uk.
Selected publications
A. Figalli, P. van Hintum, M. Tiba
Sharp quantitative stability of the Brunn-Minkowski inequality (for arbitrary sets)
arxiv
P. van Hintum, H. Spink, M. Tiba
Sharp quantitative stability of the planar Brunn-Minkowski inequality
J. Eur. Math. Soc. (JEMS) Accepted.
P. van Hintum, H. Spink, M. Tiba
Sharp stability of Brunn-Minkowski for homothetic regions
J. Eur. Math. Soc. (JEMS) 24, 2022, pp 4207–4223.
P. van Hintum, H. Spink, M. Tiba
Sets in Z^k with doubling 2^k+\delta are near convex progressions
Advances in Mathematics, 413, 2023, pp 108830.
P. Balister, B. Bollobás, R. Morris, J. Sahasrabudhe, M. Tiba
On the Erdős Covering Problem: the density of the uncovered set
Inventiones Math. 228, 2022, pp 377–414.
P. Balister, B. Bollobás, R. Morris, J. Sahasrabudhe, M. Tiba
The structure and number of Erdős covering systems
J. Eur. Math. Soc. (JEMS) Accepted.
P. Balister, B. Bollobás, R. Morris, J. Sahasrabudhe, M. Tiba
The Erdős-Selfridge problem with square free moduli
Algebra and Number Theory ,15, 2021, 609-626
P. Balister, B. Bollobás, R. Morris, J. Sahasrabudhe, M. Tiba
Flat Littlewood polynomials exist
Annals of Math. 192 (3), 2020, pp 977-1004.
Stability of Geometric inequalities
A. Figalli, P. van Hintum, M. Tiba
Sharp quantitative stability of the Brunn-Minkowski inequality (for arbitrary sets)
arxiv
P. van Hintum, H. Spink, M. Tiba
Sharp quantitative stability of the planar Brunn-Minkowski inequality
J. Eur. Math. Soc. (JEMS) Accepted.
P. van Hintum, H. Spink, M. Tiba
Sharp stability of Brunn-Minkowski for homothetic regions
J. Eur. Math. Soc. (JEMS) 24, 2022, pp 4207–4223.
P van Hintum, H Spink, M Tiba,
Sharp L1 Inequalities for Sup-Convolution
Discrete Analysis, 2023
Discrete Brunn-Minkowski conjectures
P van Hintum, P Keevash, M Tiba.
On Ruzsa's discrete Brunn-Minkowski conjecture
arxiv 2023
P. van Hintum, H. Spink, M. Tiba
Sets in Z^k with doubling 2^k+\delta are near convex progressions
Advances in Mathematics, 413, 2023, pp 108830.
Covering Systems
P. Balister, B. Bollobás, R. Morris, J. Sahasrabudhe, M. Tiba
On the Erdős Covering Problem: the density of the uncovered set
Inventiones Math. 228, 2022, pp 377–414.
P. Balister, B. Bollobás, R. Morris, J. Sahasrabudhe, M. Tiba
The structure and number of Erdős covering systems
J. Eur. Math. Soc. (JEMS) Accepted.
P. Balister, B. Bollobás, R. Morris, J. Sahasrabudhe, M. Tiba
The Erdős-Selfridge problem with square free moduli
Algebra and Number Theory ,15, 2021, 609-626
P. Balister, B. Bollobás, R. Morris, J. Sahasrabudhe, M. Tiba,
Covering intervals with arithmetic progressions,
Acta Mathematica Hungarica, 161 (2020), pages 197–200
P. Balister, B. Bollobás, R. Morris, J. Sahasrabudhe, M. Tiba,
Acta Mathematica Hungarica, 161 (2020), pages 540–549
Littlewood Polynomials
P. Balister, B. Bollobás, R. Morris, J. Sahasrabudhe, M. Tiba
Flat Littlewood polynomials exist
Annals of Math. 192 (3), 2020, pp 977-1004.
Restricted Sumsets
B. Bollobás, I. Leader, M. Tiba
Large sumsets from small subsets
Israel Journal of Mathematics, (2023).
B. Bollobás, I. Leader, M. Tiba
Large sumsets from medium-sized subsets subsets
arxiv:2206.09366.
B. Bollobás, I. Leader, M. Tiba
A strengthening of Freiman's 3k-4 theorem
Bull of the London Math Soc 55 (2023), 2363-2381.
P. Balister, B. Bollobás, I. Leader, M. Tiba
Random Translates in Minkowski Sums
arXiv:2309.00103 (2023)
Hadwiger and Bourgain slicing conjectures
M Campos, P van Hintum, R Morris, M Tiba.
Towards Hadwiger's Conjecture via Bourgain Slicing
International Mathematics Research Notices, 2023.
Others
H Spink, M Tiba.
Judiciously 3-partitioning 3-uniform hypergraphs
Random Structures and Algorithms 56, 2020, pp 1205-1221
H Spink, M Tiba,
Multicolour chain avoidance in the boolean lattice
European Journal of Combinatorics, 87 (2020), Article 103135
S David, I Hartarsky, M Tiba,
Strong Ramsey games in unbounded time
European Journal of Combinatorics, 86 (2020), Article 103096
V Dvořák, P van Hintum, M Tiba,
Improved bound for Tomaszewski's problem
SIAM Journal on Discrete Mathematics, 34 (4), 2020, 2239-2249
S David, H Spink, M Tiba
Geometric symmetric chain decompositions
Under Review at the European Journal of Combinatorics
arXiv:1703.10954, 2017
S David, H Spink, M Tiba,
Symmetric chain decompositions of products of posets with long chains
The Electronic Journal of Combinatorics, 25 (2018), Issue 1, Article P1.69
V Dvořák, P van Hintum, A Shaw, M Tiba,
Radius, Girth and Minimum Degree
J. of Graph Theory, 100, 2022, pp 470-488
