s z e g e d y b _at_ gmail _dot_ com
MTA Alfréd Rényi Institute of Mathematics
Reáltanoda utca 13-15.
Budapest, Hungary, H-1053
My main research areas are combinatorics and group theory. At the moment,
I am working
in various topics related to limits of discrete structures. This field is connected to combinatorics, ergodic theory and
Limits of combinatorial structures: an analytic
approach that considers large structures as approximations of infinite analytic
objects and creates new connections between analysis, combinatorics, probability theory, group theory and ergodic theory.
- Limits of dense graph sequences, graphons as limits objects, graph homomorphisms, regularity lemma.
D. Kunszenti-Kovacs, L. Lovasz, B. Szegedy. Multigraph limits, unbounded kernels,and Banach space decorated graphs . [arXiv:1406.7846]
L. Lovasz, B. Szegedy. The automorphism group of a graphon.[arXiv:1406.4958]
H. Hatami, S. Janson, B. Szegedy, Graph properties, graph limits and entropy. [arxiv:1312.5626]
G. Elek, B. Szegedy, A measure-theoretic approach to the theory of dense hypergraphs. Adv. Math., 231 (2012).
L. Lovász, B. Szegedy, Finitely forcible graphons, J. Combin Theory B 101 (2011).
L. Lovász, B. Szegedy, Limits of dense graph sequences, J. Comb. Theory B 96 (2006). [Fulkerson prize 2012]
- Local-global limits of bounded degree graph sequences, graphings as limit objects.
H. Hatami, L. Lovász, B. Szegedy, Limits of local-global convergent graph sequences. Geom. Funct. Anal., to appear.
A. Backhausz, B. Szegedy. On large girth regular graphs and random processes on trees. [arXiv:1406.4420]
Higher order Fourier analysis:
a theory of higher order structures in compact abelian groups, which
proves general inverse theorems and regularity lemmas for Gowers uniformity norms.
- Limits of functions on Abelian groups, limit approach to Gowers norms, nilspaces and nilmanifolds.
B. Szegedy, On higher order Fourier analysis, [arxiv:1203.2260].
O. Antolin Camarena, B. Szegedy, Nilspaces, nilmanifolds and their morphisms, [arxiv:1009.3825].
On Sidorenko's conjecture:
roughly speaking, Sidorenko's conjecture says that the density of any given bipartite graph in a
graph with fixed edge density is minimized by the random graph.
- Logarithmic calculus, graph homomorphisms, Sidorenko's conjecture for various bipartite graphs.
B. Szegedy, Relative entropy and Sidorenko's conjecture. [arXiv:1406.6738]
X. Li, B. Szegedy, On the logarithmic calculus and Sidorenko's conjecture, [arxiv:1107.1153].