Rob Morris
IMPA (Instituto de Matemática Pura e Aplicada)
Pesquisador Titular (Full Professor)
Estrada Dona Castorina, 110
Jardim Botânico
Rio de Janeiro, Brasil
office: 310
e-mail: rob(at)impa(dot)br
About me:
My research focuses on probabilistic combinatorics and related areas. In particular, I’m interested in random graphs and processes, Ramsey theory, monotone cellular automata, combinatorial number theory, and extremal graph theory. Before coming to Rio, I was a Research Fellow of Murray Edwards College, Cambridge, a post-doc in Tel Aviv, Tokyo and at IMPA, a PhD student of Béla Bollobás at the University of Memphis, and an undergraduate at Christ's College, Cambridge.
Recent papers (since 2020):
P. Balister, B. Bollobás, M. Campos, S. Griffiths, E. Hurley, R. Morris, J. Sahasrabudhe and M. Tiba
Upper bounds for multicolour Ramsey numbers
submitted : pdfM. Campos, S. Griffiths, R. Morris and J. Sahasrabudhe
An exponential improvement for diagonal Ramsey
submitted : pdf videosP. Balister, B. Bollobás, R. Morris and P. Smith
Universality for monotone cellular automata
submitted : pdfP. Balister, B. Bollobás, R. Morris and P. Smith
The critical length for growing a droplet
Mem. Amer. Math. Soc., to appear : pdfR. Morris, W. Samotij and D. Saxton
An asymmetric container lemma and the structure of graphs with no induced 4-cycle
J. Europ. Math. Soc., 26 (2024), 1655-1711 : pdfP. Balister, B. Bollobás, R. Morris, J. Sahasrabudhe and M. Tiba
The structure and number of Erdős covering systems
J. Europ. Math. Soc., 26 (2024), 75-109 : pdfM. Campos, P. van Hintum, R. Morris and M. Tiba
Towards Hadwiger's conjecture via Bourgain Slicing
IMRN, 10 (2024), 8282-8295 : pdfL. Aragão, M. Collares, J.P. Marciano, T. Martins and R. Morris
A lower bound for set-colouring Ramsey numbers
Random Structures Algorithms, 64 (2024), 157-169 : pdfP. Balister, B. Bollobás, R. Morris and P. Smith
Subcritical monotone cellular automata
Random Structures Algorithms, 64 (2024), 38-61 : pdfB. Bollobás, H. Duminil-Copin, R. Morris and P. Smith
Universality for two-dimensional critical cellular automata
Proc. London Math. Soc., 126 (2023), 620-703 : pdfP. Balister, B. Bollobás, R. Morris, J. Sahasrabudhe and M. Tiba
On the Erdős Covering Problem: the density of the uncovered set
Invent. Math. 228 (2022), 377–414 : pdfM. Campos, M. Collares, R. Morris, N. Morrison and V. Souza
The typical structure of sets with small sumset
IMRN, 2022, 11011–11055 : pdfP. Balister, B. Bollobás, R. Morris, J. Sahasrabudhe and M. Tiba
The Erdős–Selfridge problem with square-free moduli
Algebra & Number Theory 15 (2021), 609-626 : pdfM. Campos, L. Mattos, R. Morris and N. Morrison
On the singularity of random symmetric matrices
Duke Math. J., 170 (2021), 881-907 : pdfP. Balister, B. Bollobás, R. Morris, J. Sahasrabudhe and M. Tiba
Flat Littlewood Polynomials Exist
Ann. Math., 192 (2020), 977-1004 : pdfG. Fiz Pontiveros, S. Griffiths and R. Morris
The triangle-free process and the Ramsey numbers
Mem. Amer. Math. Soc., 263 (2020), 125pp : pdf Appendix : pdf
Probabilistic combinatorics:
J. Balogh, R. Morris and W. Samotij
Independent sets in hypergraphs
J. Amer. Math. Soc., 28 (2015), 669-709 : pdfR. Morris and D. Saxton
The number of -free graphs
Adv. Math., 298 (2016), 534-580 : pdfJ. Balogh, R. Morris, W. Samotij and L. Warnke
The typical structure of sparse -free graphs
Trans. Amer. Math Soc., 368 (2016), 6439-6485 : pdf
Graph theory / Ramsey theory:
G. Fiz Pontiveros, S. Griffiths, R. Morris, D. Saxton and J. Skokan
The Ramsey number of the clique and the hypercube
J. London Math. Soc., 89 (2014), 680-702 : pdfP. Allen, J. Böttcher, S. Griffiths, Y. Kohayakawa and R. Morris
The chromatic thresholds of graphs
Adv. Math., 235 (2013), 261-295 : pdfN. Alon, J. Balogh, B. Bollobás and R. Morris
The structure of almost all graphs in a hereditary property
J. Combin. Theory, Ser. B, 101 (2011), 85-110 : pdf
Combinatorial number theory:
P. Balister, B. Bollobás and R. Morris
The sharp threshold for making squares
Ann. Math., 188 (2018), 49-143 : pdfN. Alon, J. Balogh, R. Morris and W. Samotij
A refinement of the Cameron-Erdős conjecture
Proc. London Math. Soc., 108 (2014), 44-72 : pdfB. Green and R. Morris
Counting sets with small sumset and applications
Combinatorica, 36 (2016), 129-159 : pdf
Bootstrap percolation:
I. Hartarsky and R. Morris
The second term for two-neighbour bootstrap percolation in two dimensions
Trans. Amer. Math Soc., 372 (2019), 6465-6505 : pdfB. Bollobás, H. Duminil-Copin, R. Morris and P. Smith
The sharp threshold for the Duarte model
Annals of Probability, 45 (2017), 4222-4272 : pdfJ. Balogh, B. Bollobás, H. Duminil-Copin and R. Morris
The sharp threshold for bootstrap percolation in all dimensions
Trans. Amer. Math Soc., 364 (2012), 2667-2701 : pdfJ. Balogh, B. Bollobás and R. Morris
Bootstrap percolation in three dimensions
Annals of Probability, 37 (2009), 1329-1380 : pdf
Probability theory:
F. Martinelli, R. Morris and C. Toninelli
Universality results for kinetically constrained spin models in two dimensions
Commun. Math. Phys., 369 (2019), 761-809 : pdfD. Ahlberg, S. Griffiths, R. Morris and V. Tassion
Quenched Voronoi percolation
Adv. Math., 286 (2016), 889-911 : pdfD. Ahlberg, E. Broman, S. Griffiths and R. Morris
Noise Sensitivity in Continuum Percolation
Israel J. Math., 201 (2014), 847-899 : pdfR. Morris
Zero-temperature Glauber dynamics on
Prob. Theory Rel. Fields, 149 (2011), 417-434 : pdf
Books / surveys / course notes:
F. Botler, M. Collares, T. Martins, W. Mendonça, R. Morris, G. Mota
Combinatória
XXXIII Colóquio Brasileiro de Matemática (SBM/IMPA): pdfP. Balister, B. Bollobás, R. Morris, J. Sahasrabudhe and M. Tiba
Erdős covering systems
Acta Mathematica Hungarica, 161 (2020), 540-549 : pdfJ. Balogh, R. Morris and W. Samotij
The method of hypergraph containers
Proc. ICM, Rio de Janeiro, 2018 : pdfR. Morris
The method of hypergraph containers
Notes from mini-courses given at a summer school at USP, the Ramsey DocCourse in Prague, and the XVI Escuela de Verano en Matemáticas Discretas: pdfR. Morris
Monotone cellular automata
Surveys in Combinatorics 2017, Cambridge University Press : pdfR. Morris
Bootstrap percolation and other automata
European J. Combin., 66 (2017), 250-263 : pdfR. Morris and R. Imbuzeiro Oliveira
Extremal and probabilistic combinatorics
XXVII Colóquio Brasileiro de Matemática (SBM/IMPA) : pdf videos
Postdocs:
- Simon Griffiths (2010-13)
- Gonzalo Fiz Pontiveros (2011-13)
- David Saxton (2012-14)
- Paul Smith (2012-14 and 2017-18)
- Nathan Kettle (2013-14)
- Neal Bushaw (2014)
- Mauricio Collares (2015-16)
- Teeradej Kittipassorn (2015-17)
- Julian Sahasrabudhe (2017-19)
- Natasha Morrison (2018-19)
- Taísa Martins (2018-19)
- Marius Tiba (2021-22)
PhD Students:
- Mauricio Collares (graduated 2015)
- Daniel Blanquicett (graduated 2019)
- Walner Mendonça (graduated 2020)
- Luiz Moreira (graduated 2020)
- Pedro Araújo (graduated 2021)
- Letícia Mattos (graduated 2021, Prêmio CAPES de tese)
- Marcelo Campos (graduated 2023, Prêmio CAPES de tese)
- Lucas Aragão (graduated 2024)
- Zhifei Yan (expected 2025)
- Gabriel Dahia (expected 2025)
- João Pedro Marciano (expected 2026)
- Rafael Filipe dos Santos (expected 2026)
- Danni Peng (expected 2026)
- Vitoria Aparecida (expected 2027)
- Xinbu Cheng (expected 2027)
Masters Students:
- Pedro Araújo (graduated 2017)
- Victor Souza (graduated 2019)
- Marcelo Campos (graduated 2020)
- Zhifei Yan (graduated 2021)
- João Pedro Marciano (graduated 2023)
- Bruno Alejandro Andrades Albornoz (expected 2025)
- Sebastião Fróes Nachtergaele Gomes Navarro (expected 2025)
- Monica Martinez Sanchez (expected 2025)
- Joseph Altamirano (expected 2025)
Awards:
- 2024: The Leroy P. Steele Prize for Seminal Contribution to Research (AMS)
- 2023: The Elon Lages Lima Prize (SBM)
- 2022: Elected to the Brazilian Academy of Sciences
- 2018: Invited speaker, International Congress of Mathematicians
- 2018: The Delbert Ray Fulkerson Prize (AMS)
- 2017: Prize of the Mathematical Congress of the Americas (MCA)
- 2017: Prize of the Brazilian Mathematical Society (SBM)
- 2016: Prize of the Mathematical Union of Latin America and the Caribbean (UMALCA)
- 2016: The SIAM George Pólya Prize in Combinatorics
- 2015: European Prize in Combinatorics