Arkadiusz Ploski TITLE Numerical semigroups and plane curve singularities (I) ABSTRACT We give a short survey of results related to the singularities of irreducible plane algebroid curves (branches) defined over an algebraically closed field of arbitrary characteristic. We recall the characterization of the semigroup of values associated with a branch due to Bresinsky and Augermüller, the Abhyanhar–Moh irreducibility criterion and the Merle–Granja factorization theorem. Then we state a conjecture on the Milnor number in characteristic p. BIBLIOGRAPHY [1] E. Garcia Barroso, A. Ploski. An approach to plane algebroid branches, Revista Mat. Compl. vol 1 (28), pp. 227–251, 2015 [2] E. Garcia Barroso, A. Ploski. The Milnor number of plane irreducible singularities in positive characteristic, Bull. London Math. Soc. 48(1), pp. 94–98, 2016