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

Mathematical Colloquim

 

PROGRAM


ODELJENJE ZA MATEMATIKU

MATEMATICKOG INSTITUTA SANU
                       OPSTI MATEMATICKI SEMINAR

NA MATEMATICKOM FAKULTETU U BEOGRADU



-- PROGRAM ZA OKTOBAR 2004 --

Petak, 22. oktobar 2004. u 14h, sala 2, MI SANU:

Mirjana Vukovic, Prirodno-matematicki fakultet, Sarajevo
NAJOPSTIJE GRADUIRANE STRUKTURE NAZVANE PARAGRADUIRANIM

Sadrzaj. Dobro je poznato da su klasicne graduirane strukture (grupe, prsteni i moduli) objekti kategorije koja nije zatvorena u odnosu na direktni proizvod i direktnu sumu.
Cilj novog koncepta, uvedenog u zajednickim radovima ([3], [4] i [5] ) i monografskom radu ( [6] ), M. Krasnera i mene, bio je uvesti pojam ekstra - i para - graduacije, kao i struktura koje smo naz-vali ekstra - i para - graduiranim koje generaliziraju klasicne graduirane strukture u smislu Bour-bakia, kao i neke ranije rezultate M. Krasnera i M. Chadeyras (vidi [1] i [2]) i koje imaju osobinu da su direktni proizvod i direktna suma familije paragraduiranih: grupa prstena i modula opet paragradui-rane grupe, prsteni i moduli, od kojih je druga homogena podgrupa one prve. I proizvod i suma bice ekstragradirane strukture: grupe, prsteni i moduli, ukoliko se polazna familija sastoji od ekstragradui- ranih grupa, prstena, odnosno modula. Medjutim to va^Ţi za graduirane grupe samo u trivijalnom slu- caju, tj kada je najvise jedna od polaznih graduiranih grupa sa netrivijalnom graduacijom.
Tako se u nacim radovima prosiruju brojni klasicni rezultati i otvara sasvim nova grana istrazivanja u kojoj postoji veliki broj otvorenih pitanja.

[1] M.Chadeyras, Essai d'une théorie noetherienne homogčne pour les anneaux commutatifs dont la graduation est aussi générale que possible. Suppl. Bull. Soc. Math. France, Mémoire, 22 (1970), 1-143.
[2] M.Krasner, Anneaux gradués généraux, Colloque d' algčbre, Université Rennes 1, (1980), 209-308.
[3] M.Krasner Structures paragraduées, (groupes, anneaux, modules) I, Proc. Japan Acad. et M.Vukovic, 62 (1986), Ser. A, No. 9, 350-352.
[4] M.Krasner Structures paragraduées, (groupes, anneaux, modules) II, Proc. Japan Acad. et M.Vukovic, 62 (1986), Ser. A, No. 10, 389-391.
[5] M.Krasner Structures paragraduées, (groupes, anneaux, modules) III, Proc. Japan Acad. et M.Vukovic, 63 (1987), Ser. A, No. 1, 10-12.
[6] M.Krasner Structures paragraduées, (groupes, anneaux, modules), Queen' s Papers in Pure et M.Vukovic, and Applied mathematics, No.77, Queen' s University, Kingston, Ontario, Canada (1987 ), p.163
[7] M.Vukovic, Structures graduées et paragraduées, Prepublication de l'Institut Fourier, Univer- sité de Grenoble, No. 536, St Martin d'Heres (2001), p. 1 - 40. ( http://www-fourier.ujf-grenoble.fr/prepublications.html)

Sreda, 27. i cetvrtak, 28. oktobar 2004. u 16h, sala 2 MI SANU:

Stevo Todorcevic, Matematicki institut SANU
VON NEUMANNOV PROBLEM O POSTOJANJU I KONTROLI MERE, I i II

Sadrzaj. Daje se pregled jednog problema koji je Von Neuman postavio 1937. godine, a i prikaz skorasnjeg parcijalnog resenja tog problema.

Petak, 29. oktobar 2004. u 14h, sala 718, MF Bgd.:

Prof. Günter M. Ziegler, Institut für Mathematik, MA 6-2, TU Berlin, Germany
ON THE COMBINATORICS OF THE 3-SPHERE

Abstract. Triangulations and cell decompositions of thetwo-dimensional sphere can be understood in terms ofthree-dimensional polyhedra. The corresponding theory isclassical, visually accessible, and quite complete ---due to Tutte, Steinitz, and many others.Triangulations and cell decompositions of thethree-dimensional sphere pose much bigger problemsto us. In this lecture we shall thus treat questions like
`How many triangulations are there (with $n$ vertices, say)?''
`Do most of these correspond to convex polytopes?''
`How can the vertex-/ edge-/ face-numbersbe characterized?''
Our (partial) answers to such questions involve a niceinterplay of combinatorial ideas, new geometric constructions,advanced visualization tools,as well as differential geometric and topological components.\newpage

OBAVESTENJA

Sa prof. Zieglerom u Beograd dolaze i dva njegova saradnika koji ce odrzati predavanja u okviru Seminara Geometrija, topologija, algebra na Matematickom fakultetu u cetvrtak, 28. oktobra.

Torsten Schoneborn (TU Berlin):
The Topological Tverberg Theorem and winding numbers

The Topological Tverberg Theorem claims that any continuous map of a$(q-1)(d+1)$-simplex to~$\mathbf{R}^d$ identifies points from $q$ disjointfaces. (This has been proved for affine maps, for $d\le1$, and if $q$is a prime power, but not yet in general.)The Topological Tverberg Theorem can be restricted to maps of the$d$-skeleton of the simplex. We further show that it is equivalent toa `Winding Number Conjecture'' that concerns only maps of the$(d-1)$-skeleton of a $(q-1)(d+1)$-simplex to~$\mathbf{R}^d$.`Many Tverberg partitions'' arise if and only if there are`many $q$-winding partitions.''The $d=2$ case of the Winding Number Conjecture is a problem aboutdrawings of the complete graphs $K_{3q-2}$ in the plane.We investigate graphs that are minimal with respect to thewinding number condition.

Stephan Hell (TU Berlin): On the number of Tverberg partitions in the prime power case

In 1966, Helge Tverberg showed that any set of $(d+1)(q-1)+1$ pointsin $d$-dimensional Euclidean space admits a partition into $q$ subsetssuch that the intersection of their convex hulls is non-empty. Suchpartitions are called Tverberg partitions; the result is best possible:For less than $(d+1)(q-1)+1$ points the statement does not hold.Another natural question is to ask for a lower bound for the number ofTverberg partitions. How many Tverberg partitions are there for agiven set of points? Gerard Sierksma conjectured that there are atleast $((q-1)!)^d$ many for $(d+1)(q-1)+1$ points in $d$-dimensionalEuclidean space. The conjecture is still not proved. In this talk wewill show how to extend the currently best known lower bound, byAleksandar Vu\v{c}i\'c and Rade \v{Z}ivaljevi\'c, from the case ofprime $q$ to the prime power case.


Rukovodioci Odeljenja za matematiku Matematickog instituta SANU i Opsteg matematickog seminara na Matematickom fakultetu u Beogradu, Stevan Pilipovic i Sinisa Vrecica predlazu zajednicki program rada naucnih sastanaka.

Predavanja ce se odrzavati na Matematickom Institutu (sala 2), petkom sa pocetkom u 14 casova. Odeljenje za matematiku je opsti seminar sa najduzom tradicijom u Institutu.

Svakog meseca, jedno predavanje ce biti odrzano na Matematickom Fakultetu u terminu koji ce biti posebno odredjen.

Molimo sve zainteresovane ucesnike u radu naucnih sastanaka da posebno obrate paznju na vreme odrzavanja svakog sastanka. Na Matematickom fakultetu su moguce izmene termina.

Obavestenje o programu naucnih sastanaka ce biti objavljeno na oglasnim tablama MI (Beograd), MF (Beograd), PMF (Novi Sad), PMF (Nis) i PMF (Kragujevac).

Odeljenje za matematiku Matematickog instituta SANU

Stevan Pilipovic

Opsti matematicki seminar na Matematickom fakultetu u Beogradu,

Sinisa Vrecica


Ako zelite da se obavestenja o Vasim naucnim skupovima pojave u Newsletter of EMS (European Mathematical Society) i na Internetu na lokaciji EMS, onda se obratite na emsvesti@mi.sanu.ac.yu gde cete dobiti format obavestenja.