Petak, 08.06.2012. u 14h sala 301f, MI SANU
Vladimir Rakočević, Prirodno-matematički fakultet, Univerzitet u Nišu
INVERTIBILNOST RAZLIKE I ZBIRA IDEMPOTENATA I KO-EP ELEMENTI

Rezime. Dobijeni su ekvivalentni uslovi za invertibilnost f - g i f + g gde su f i g idempotenti u prstenu sa jedinicom, i date su primene na ogranicene linearne operatore na Banahovim i Hilbertovim prostorima. Dokazali smo da se u prstenovima, mnogi ranije korisceni uslovi koji se odnose na konacno-dimenzionalnost prostora, nejednakosti za rang matrica, norm topologiju ogranicenih linearnih operatora ili osobine u C*-algebrama, mogu dokazati jednostavnim algebarskim argumentima.

Navedeni rezultati uglavnom su objavljeni u zajednickim radovima sa J. Kolihom. Nedavno objavljeni su rezultati sa J. Benitezom, koji nastavljaju prethodna istrazivanja. U njima su definisani i izucavani ko-EP elementi, kao dualni pojam za poznate EP elemente.

Četvrtak, 28.05.2012. u 13h sala 301f, MI SANU
Maria Chudnovsky, Department of Industrial Engineering and Operations Research Department of Mathematics, Columbia University
COLORING SOME PERFECT GRAPHS

Abstract: A graph G is called perfect if for every induced subgraph H of G, the chromatic number and the clique number of H are equal. After the recent proof of the Strong Perfect Graph Theorem, and the discovery of a polynomial-time recognition algorithm, the central remaining open question about perfect graphs is finding a combinatorial polynomial-time coloring algorithm. (There is a polynomial-time algorithm known, using the ellipsoid method). Recently, we were able to find such an algorithm for a certain class of perfect graphs, that includes all perfect graphs admitting no balanced skew-partition. The algorithm is based on finding special "extremal" decompositions in such graphs; we also use the idea of "trigraphs". This is joint work with Nicolas Trotignon, Theophile Trunck and Kristina Vuškovic.