József Balogh (mathematician)

József Balogh is a Hungarian mathematician who studies graph theory and combinatorics .

Balogh grew up in Mórahalom and went to a special school for mathematics in Szeged. As a student, he won two silver medals at the International Mathematical Olympiads. He studied at the University of Ghent and the University of Szeged, where he received his diploma in mathematics in 1995 with Péter Hajnal (On the existence of MDS-cyclic codes). In 2001 he received his doctorate from the University of Memphis with Béla Bollobás (Graph properties and Bootstrap percolation). As a post-doctoral student he was at ATT Shannon Laboratories in Florham and in 2002 at the Institute for Advanced Study . In 2002 he became Zassenhaus Assistant Professor at Ohio State University and in 2005 Assistant Professor at the University of Illinois at Urbana-Champaign , where he became Associate Professor in 2010 and Professor in 2013.

From 2009 to 2011 he was also an Associate Professor at the University of California, Davis .

Balogh deals with extremal and probabilistic combinatorics (especially graph theory) and bootstrap percolation . The latter models the spread of an infection on a d-dimensional grid, with nodes being infected in each time step where at least r neighbors have already been infected. A randomly chosen initial structure is assumed and Bollobas, Balogh, Hugo Duminil-Copin and R. Morris proved an asymptotic (for large lattices) formula for the threshold probability that the whole lattice will be infected, depending on d and r. He had previously treated the three-dimensional case with r = 3 with Bollobas and Morris.

For 2018 he is invited speaker at the International Congress of Mathematicians in Rio de Janeiro . In 2013/14 he was a Simons Fellow and Marie Curie Fellow and received an NSF Career Grant. In 2016 he received the George Pólya Prize in combinatorics with Robert Morris and Samotij . Wojciech Samotij is one of his students .

Fonts (selection)

with JA Csirik: Index assignment for two-channel quantization, IEEE Transitions on Information Theory, Volume 50, 2004, pp. 2737-2751.

with Noga Alon , Peter Keevash , Benny Sudakov : The number of edge colorings with no monochromatic cliques, J. London Math. Soc., Volume 70, 2004, pp. 273-288. pdf

with B. Bollobas, Robert Morris: Bootstrap percolation in three dimensions. Annals of Probability, Volume 37, 2009, pp. 1329-1380. Arxiv

with Wojtek Samotij: The number of -free graphs, J. Lond. Math. Soc., Volume 83, 2011, pp. 368-388, abstract ${\ displaystyle K_ {s, t}}$
with Béla Bollobás, Michael Krivelevich, Tobias Müller, Mark Walters: Hamilton cycles in random geometric graphs, Annals of Applied Probability, Volume 21, 2011, pp. 1053-1072, Arxiv
with John Lenz: Some Exact Ramsey-Turan Numbers, Bull. Lond. Math. Soc., Volume 44, 2012, pp. 1251-1258. Arxiv
with Bela Bollobas, Hugo Duminil-Copin , R. Morris: The sharp threshold for bootstrap percolation in all dimensions, Trans. Amer. Math. Soc., Volume 364 2012, pp. 2667-2701. Arxiv
with N. Alon, R. Morris, W. Samotij: A refinement of the Cameron-Erdös Conjecture, Proc. London Mathematical Society, Volume 108, 2014, pp. 44-72. Arxiv
with Sarka Petrickova: The number of the maximally triangle-free graphs, Bull. London Math. Soc., Volume 46, 2014, pp. 1003-1006. Arxiv
with Morris, Samotij: Independent sets in hypergraphs, J. AMS, Volume 28, 2015, pp. 669–709, Arxiv 2012
with Hong Liu, Maryam Sharifzadeh, Andrew Treglown: The number of maximal sum-free subsets of integers, Proc. AMS, Volume 143, 2015, pp. 4713-4721, Arxiv 2014
with R. Morris, W. Samotij, L. Warnke: The typical structure of sparse- free graphs., Transactions AMS, Arxiv 2013 ${\ displaystyle K_ {r + 1}}$

Web links

personal data
SURNAME	Balogh, József
BRIEF DESCRIPTION	Hungarian mathematician
DATE OF BIRTH	20th century