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More about this group

ombinatorics is the study of discrete structures, which are as ubiquitous in mathematics as they are in our everyday lives.

They are studied for their intrinsic beauty as well as their many important practical applications, for example to networking, optimisation, and statistical physics to name just a few.

Moreover, problems of a combinatorial nature arise in many areas of pure mathematics, notably in group theory, probability, topology and number theory.

While research into combinatorics at Bristol spans a wide range of topics, our main focus is currently on probabilistic and arithmetic combinatorics. In the former area, we work towards an improved understanding of random graphs and percolation as well as random walks on groups.

Under the broad heading of arithmetic combinatorics we study problems in combinatorial geometry, for example related to incidences of points and lines, and their applications to the so-called sum-product problem over various fields.

At the same time, we use a relatively recent fusion of Fourier-analytic and combinatorial techniques to identify and quantify both additive and multiplicative structure in sets of integers, connecting this area of research closely to parts of analytic number theory.

The interface with theoretical computer science, in particular coding theory, as well as the study of dynamical systems via ergodic theory are also of interest to members of the group.

Our regular Combinatorics Seminar meets on Thursday afternoons and benefits from sponsorship from the Heilbronn Institute.