Petak, 17.04.2015. u 14:00h, sala 301f, MI SANU
Natasa Krejic, Prirodno-matematicki fakultet, Novi Sad
NUMERICAL METHODS FOR DISTRIBUTED OPTIMIZATION

We consider a connected network with n nodes, each of which has access to a local function. The objective of all nodes is to minimize the aggregate cost function. In this paper we propose a distributed Newton-like method for minimisation of the objective function which exploits the specific structure of the penalty reformulation. The Hessian matrix is approximated by its diagonal part, taking the advantage of the problem structure, which allow us to compute the inverse in a distributed manner. The remaining part of the Hessian is used to correct the right hand side of the quasi Newton equation, to preserve as much of the second order information, as possible. The method exhibits linear convergence under a set of standard assumptions for the functions and the network architecture. The numerical results confirm the efficiency of the proposed method.

Petak, 24.04.2015. u 14:00h, 301f MI SANU
Marko Stosic, Matematicki Institut SANU
HOMOLOSKE INVARIJANTE CVOROVA I PRIMENE U TEORIJI BROJEVA

Rezime: Homoloske invarijante cvorova su se prvi put pojavile pre 15 godina, i od tada je ova oblast veoma aktivna sa velikim brojem znacajnih rezultata u raznim oblastima. Kao i u slucaju "klasicnih" invarijanti cvorova, i homoloske invarijante su blisko povezane sa velikim brojem, a priori, razlicitih oblasti kako matematike (topologija, kvantne grupe, teorija reprezentacija, homoloske algebre, kombinatorika, fon-Nojmanove algebre, ...) tako i fizike (statisticka fizika, kvantna teorija polja, teorija struna). U ovom predavanju bice dat jedan kratak pregled osnovnih ideja ove oblasti i nekih od najznacajnijih rezultata, kao i neke od najaktuelnijih i iznenadjujucih primena, pre svega u teoriji brojeva.