Mathematical Colloquim
PROGRAM
ODELJENJE ZA MATEMATIKU MATEMATIČKOG INSTITUTA SANU |
PROGRAM ZA APRIL 2015.
NAPOMENA: Predavanja ce se odrzavati u Sali 301f na trecem spratu Matematickog instituta SANU, Knez-Mihailova 36 (zgrada preko puta SANU).
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.
Stevan Pilipovic, Odeljenje za matematiku Matematickog instituta SANU