ὅδε οἶκος, ὦ ἑταῖρε, μνημεῖον ἐστιν ζῴων τῶν σοφῶν ἀνδρῶν, καὶ τῶν ἔργων αὐτῶν

Mathematical Colloquim

PROGRAM

 ODELJENJE ZA MATEMATIKUMATEMATIČKOG INSTITUTA SANU

PROGRAM ZA JUN 2018.

PETAK, 15.06.2018. u 14:15, Sala 301f, MI SANU, Kneza Mihaila 36
Dragan Mašulović, Departman za matematiku i informatiku, Novi Sad
CATEGORICAL RAMSEY THEORY
Generalizing the classical results of F. P. Ramsey from the late 1920's, the structural Ramsey theory originated at the beginning of 1970’s. We say that a class $K$ of finite structures has the Ramsey property if the following holds: for any number $k \ge 2$ of colors and all $A, B \in K$ such that $A$ embeds into $B$ there is a $C \in K$ such that no matter how we color the copies of $A$ in $C$ with $k$ colors, there is a monochromatic copy $B'$ of $B$ in $C$ (that is, all the copies of $A$ that fall within $B'$ are colored by the same color).
Showing that the Ramsey property holds for a class of finite structures $K$ can be an extremely challenging task and a slew of sophisticated methods have been proposed in literature. These methods are usually constructive: given $A, B \in K$ and $k \ge 2$ they prove the Ramsey property directly by constructing a structure $C \in K$ with the desired properties.
It was Leeb who pointed out already in early 1970's that the use of category theory can be quite helpful both in the formulation and in the proofs of results pertaining to structural Ramsey theory. Instead of pursuing the original approach by Leeb (which has very fruitfully been applied to a wide range of Ramsey problems) we proposed in the last few years a set of new strategies to show that a class of structures has the Ramsey property.
In this talk we explicitly put the Ramsey property and the dual Ramsey property in the context of categories of finite structures. We use elementary category theory to generalize some combinatorial results and using the machinery of very basic category theory provide new combinatorial statements (whose formulations do not refer to category-theoretic notions) concerning both the Ramsey property and the dual Ramsey property.

PETAK, 22.06.2018. u 14:15, Sala 301f, MI SANU, Kneza Mihaila 36
Raka Jovanović, Qatar Environment and Energy Research Institute, Hamad Bin Khalifa University, Doha Qatar
METODA PRETRAGE FIKSIRANOG SKUPA
U predavanju će biti predstavljen novi tip metaheuristike koji na jednostavan način dodaje mehanizam učenja na Greedy Randomized Adaptive Search Procedure (GRASP). Osnovna ideja je da se pretraga ne fokusira na specifična rešenja visokog kvaliteta već na elemente koje lokalno optimalna rešenja ovog tipa imaju. Metoda bi bila prvo ilustrovana na primeru trgovačkog putnika, a zatim na dve varijacije problema dominirajućeg skupa sa energijom (Power Dominating Set).

PETAK, 29.06.2018. u 14:15, Sala 301f, MI SANU, Kneza Mihaila 36