30.05.2018 um 17:15 Uhr in Raum 69/125
Prof. Dr. Ngô Việt Trung (Institute of Mathematics Hanoi, Vietnam)
Depth of powers of homogeneous ideals
Let I be an arbitrary homogeneous ideal in in a polynomial ring R. Brodmann showed that the function depth R/It = dim R - pd R/It (where pd is the projective dimension) is always a constant for t >> 0. In other word, it is a convergent function. Subsequent works have indicated that this function may behave wildly. Herzog and Hibi conjectured that any convergent non-negative numerical function is the depth function of powers of a homogeneous ideal. We will solve this conjecture by showing that any convergent non-negative numerical function is the depth function of powers of a monomial ideal. The lecture is about the basic ideas of the solution, which are rather elementary and should be understandable for everybody.
06.06.2018 um 17:15 Uhr in Raum 69/125
Prof. Dr. Sylvie Roelly (Universität Potsdam)
Random Sphere Packing
We consider a system of hard balls in Euclidean space, undergoing random dynamics and interacting via a mutual attraction force. Such stochastic evolutions converge asymptotically in time towards equilibrium states, which are connected with the famous geometry problem of close-packing of equal spheres.