Rob Morris


IMPA (Instituto Nacional de Matemática Pura e Aplicada)

Pesquisador Associado (Associate Professor)

   

Estrada Dona Castorina, 110

Jardim Botânico

Rio de Janeiro, Brasil

  

office: 310

e-mail: rob(at)impa(dot)br

    

About me:


My research is mainly in the areas of extremal and probabilistic combinatorics. In particular, I’m interested in random graphs and processes, extremal graph theory, monotone cellular automata, percolation, Ramsey theory, and additive combinatorics. 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.


Selected Publications:


J. Balogh, R. Morris and W. Samotij

Independent sets in hypergraphs

J. Amer. Math. Soc., 28 (2015), 669-709 : pdf


G. Fiz Pontiveros, S. Griffiths and R. Morris

The triangle-free process and the Ramsey number R(3,k)

Mem. Amer. Math. Soc., to appear : pdf    Appendix : pdf


P. Balister, B. Bollobás and R. Morris

The sharp threshold for making squares

Ann. Math., 188 (2018), 1-95 : pdf


B. Bollobás, H. Duminil-Copin, R. Morris and P. Smith

Universality of two-dimensional critical cellular automata

Proc. London Math. Soc., to appear : pdf


Graph theory / Ramsey Theory:


R. Morris, W. Samotij and D. Saxton

An asymmetric container lemma and the structure of graphs with no induced 4-cycle

submitted : pdf


R. Morris and D. Saxton

The number of C_{2k}-free graphs

Adv. Math., 298 (2016), 534-580 : pdf


J. Balogh, R. Morris, W. Samotij and L. Warnke

The typical structure of sparse K_{r+1}-free graphs

Trans. Amer. Math Soc., 368 (2016), 6439-6485 : pdf


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 : pdf


P. Allen, J. Böttcher, S. Griffiths, Y. Kohayakawa and R. Morris

The chromatic thresholds of graphs

Adv. Math., 235 (2013), 251-295 : pdf


N. 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


Sum-free sets:


N. Alon, J. Balogh, R. Morris and W. Samotij

A refinement of the Cameron-Erdős conjecture

Proc. London Math. Soc., 108 (2014), 44-72 : pdf


N. Alon, J. Balogh, R. Morris and W. Samotij

Counting sum-free sets in abelian groups

Israel J. Math., 199 (2014), 309-344 : pdf


B. Green and R. Morris

Counting sets with small sumset and applications

Combinatorica, 36 (2016), 129-159 : pdf


Bootstrap percolation:


J. 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 : pdf


J. Balogh, B. Bollobás and R. Morris

Bootstrap percolation in three dimensions

Annals of Probability, 37 (2009), 1329-1380 : pdf


I. Hartarsky and R. Morris

The second term for two-neighbour bootstrap percolation in two dimensions

submitted : pdf


F. Martinelli, R. Morris and C. Toninelli

Universality results for kinetically constrained spin models in two dimensions

submitted : pdf


B. Bollobás, H. Duminil-Copin, R. Morris and P. Smith

The sharp threshold for the Duarte model

Annals of Probability, 45 (2017), 4222-4272 : pdf


R. Morris

Zero temperature Glauber dynamics on Z^d

Prob. Theory Rel. Fields, 149 (2011), 417-434 : pdf


J. Balogh, B. Bollobás and R. Morris

Majority bootstrap percolation on the hypercube

Combin. Probab. Computing, 18 (2009), 17-51 : pdf


J. Gravner, A. Holroyd and R. Morris

A sharper threshold for bootstrap percolation in two dimensions

Prob. Theory Rel. Fields, 153 (2012), 1-23 : pdf


J. Balogh, B. Bollobás and R. Morris

Bootstrap percolation in high dimensions

Combin. Probab. Computing, 19 (2010), 643-692 : pdf


Probability theory: 


D. Ahlberg, S. Griffiths, R. Morris and V. Tassion

Quenched Voronoi percolation

Adv. Math., 286 (2016), 889-911 : pdf


D. Ahlberg, E. Broman, S. Griffiths and R. Morris

Noise Sensitivity in Continuum Percolation

Israel J. Math., 201 (2014), 847-899 : pdf

 

Some papers from my PhD thesis:


J. Balogh, B. Bollobás and R. Morris

Hereditary properties of ordered graphs

Topics in Discrete Mathematics, 179-213, Alg. Combin., 26, Springer, Berlin, 2006 : pdf


J. Balogh, B. Bollobás and R. Morris

Hereditary properties of partitions, ordered graphs and ordered hypergraphs

European J. Combin., 27 (2006), 1263-1281 : pdf


J. Balogh, B. Bollobás and R. Morris

Hereditary properties of tournaments

Electronic J. Combin., 14 (2007), Research Paper 60, 25pp : pdf


H. Liu, N. Prince and R. Morris

Highly connected multicoloured subgraphs of multicoloured graphs

Discrete Math., 308 (2008), 5096-5121 : pdf


H. Liu, N. Prince and R. Morris

Highly connected monochromatic subgraphs of multicoloured graphs

J. Graph Theory, 61 (2009), 22-44 : pdf


List of all publications 


Surveys / course notes:


R. Morris and R. Imbuzeiro Oliveira

Extremal and probabilistic combinatorics 

XXVII Colóquio Brasileiro de Matemática (SBM/IMPA) : pdf


R. Morris

The method of hypergraph containers

Notes from mini-courses given in 2016 at a summer school at USP and the Ramsey DocCourse in Prague : pdf


R. Morris

Monotone cellular automata

Surveys in Combinatorics 2017, Cambridge University Press : pdf


R. Morris

Bootstrap percolation and other automata 

European J. Combin., 66 (2017), 250-263 : pdf


Awards:        


2018: Invited speaker, International Congress of Mathematicians


2018: The Delbert Ray Fulkerson Prize (AMS)


2018: Elected an affiliated member of the Academia Brasileira de Ciências (ABC)


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