Mathematical Colloquim
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^Þi 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 homogène 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' algèbre,
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.
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.