A 2-design D with parameter (v,k,λ) is a point-line rank 2 geometry whose point set P is of size v and lines are k-subsets of P known as blocks such that each pair of points is contained in exactly λ blocks. A design is called symmetric if the number of points and blocks are equal, in other words, points and blocks play the same role. A group of automorphisms of a design consists of permutations of points mapping blocks to blocks and preserving the incidence relation. An automorphism group G of D is called flag-transitive if it is transitive on the set of flags of D. If G is primitive on the point set P, then G is said to be point-primitive. In this talk, we give a survey on recent studies on symmetric designs admitting flag-transitive and point-primitive almost simple automorphism groups with socle projective special unitary groups.
