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 probability theory.

**Recent work**

** 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. [arxiv:1205.4356].

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].