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My research focuses on problems that have a geometric flavor and have roots in analysis, probability and combinatorics. Recently, I have worked on the stability of geometric inequalities, covering systems, random polynomials and Ramsey Theory.
From 2024, I have been a Lecturer in Pure Mathematics at King's College London (in the Analysis group). From 2022 to 2024, I was 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) kcl (dot) ac (dot) uk
Selected publications
A. Figalli, P. van Hintum, M. Tiba
Sharp Quantitative Stability for the Prékopa-Leindler and Borell-Brascamp-Lieb Inequalities
arXiv:2501.04656 (2024)
A. Figalli, P. van Hintum, M. Tiba
Sharp quantitative stability of the Brunn-Minkowski inequality (for arbitrary sets)
arxiv:2310.20643 (2023)
P. Balister, B. Bollobás, R. Morris, J. Sahasrabudhe, M. Tiba
Flat Littlewood polynomials exist
Annals of Math. 192 (3), 2020, pp 977-1004.
P. van Hintum, H. Spink, M. Tiba
Sharp quantitative stability of the planar Brunn-Minkowski inequality
J. Eur. Math. Soc. (JEMS), 26, 2024, no. 2, pp. 695–730.
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. 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), 26, 2024, no. 1, pp. 75–109.
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. 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, M. Campos, S. Griffiths, E. Hurley, R. Morris, J. Sahasrabudhe, M. Tiba
Upper bounds for multicolour Ramsey numbers
arXiv:2410.17197 (2024)
A. Figalli, P. van Hintum, M. Tiba
Sharp stability of the Brunn-Minkowski inequality via optimal mass transportation
arXiv:2407.10932 (2024)
Stability of Geometric inequalities
A. Figalli, P. van Hintum, M. Tiba
Sharp Quantitative Stability for the Prékopa-Leindler and Borell-Brascamp-Lieb Inequalities
arXiv:2501.04656 (2024)
A. Figalli, P. van Hintum, M. Tiba
Sharp quantitative stability of the Brunn-Minkowski inequality (for arbitrary sets)
arxiv:2310.20643 (2023)
P. van Hintum, H. Spink, M. Tiba
Sharp quantitative stability of the planar Brunn-Minkowski inequality
J. Eur. Math. Soc. (JEMS), 26, 2024, no. 2, pp. 695–730.
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
A. Figalli, P. van Hintum, M. Tiba
Sharp stability of the Brunn-Minkowski inequality via optimal mass transportation
arXiv:2407.10932 (2024)
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.
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.
Ramsey Theory
P Balister, B Bollobás, M Campos, S Griffiths, E Hurley, R Morris, J Sahasrabudhe, M Tiba
Upper bounds for multicolour Ramsey numbers
arXiv:2410.17197 (2024)
S David, I Hartarsky, M Tiba,
Strong Ramsey games in unbounded time
European Journal of Combinatorics, 86 (2020), Article 103096
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), 26, 2024, no. 1, pp. 75–109.
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
Discrete Brunn-Minkowski conjectures
P van Hintum, P Keevash, M Tiba.
On Ruzsa's discrete Brunn-Minkowski conjecture
Accepted in Proceedings of the AMS (2024)
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.
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)
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
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
T Chau, D Ellis, M Tiba
Intersections of iterated shadows
arxiv 2024
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