Petak, 05. novembar 2004. u 18h, sala 718 MF BG:

Aleksandar Ivic, Rudarsko-geoloski fakultet, Beograd
O DOKAZU KUREPINE HIPOTEZE O LEVOM FAKTORIJELU

Sadrzaj. U predavanju se izlaze dokaz D. Barsky-B. Benzaghou (upravo objavljen u casopisu "Journal de Théorie des Nombres de Bordeaux") o znamenitoj Kurepinoj hipotezi iz 1971: ako je p neparan prost broj, onda p ne deli 0! + 1! + ... + (p-1)!. Metode dokaza se zasnivaju na funkciji generatrisi za tzv. Bell-ove brojeve iz kombinatorike, kao i na osobinama ekstenzija konacnog polja sa p elemenata.

Petak, 12. novembar 2004. u 14h, sala 2 MI SANU:

Silvija Ghilezan, Institut za matematiku, FTN, Novi Sad
KONSTRUKTIVNA INTERPRETACIJA KLASICNE LOGIKE

Sadrzaj. U vezi izmedu lambda-racuna sa tipovima I intuicionisticke logike tipovi predstavljaju formule, a lambda termi predstavljaju dokaze. Ova veza se uglavnom odnosi na prirodno dedukcijske sisteme. Na slican nacin lambda-mu racun predstavlja konstruktivnu interpretaciju klasicne logike. Postoje dve verzije lambda-mu racuna: jedna odgovara prirodno dedukcijskoj, a druga sekventnoj formulaciji klasicne logike. Razmatracemo neke specificne redukcijske osobine sekventnog lambda-mu racuna.

Petak, 19. novembar 2004. u 14h, sala 2 MI SANU:


EVALUACIJA NAUCNIH REZULTATA. KRITERIJUMI ZA IZBORE U ZVANJA.

Kritike na racun rada komisija Ministarstva su vrlo ceste. Uoceno je da su ponekad i rezultat nedovoljne informisanosti. Molimo koleginice i kolege da iznesu svoja kriticka razmisljanja i da tako pomognu Komisiji za matematiku i mehaniku kao i Komisiji za izbore u zvanja da formulišu dobre predloge za Ministarstvo nauke.

Petak, 26. novembar 2004. u 14h, sala 2, MI SANU:

Pavle Blagojevic, Matematicki institut SANU
TOPOLOGY OF PARTITION OF MEASURES BY FANS AND THE SECOND OBSTRUCTION

Abstract. The simultaneous partition problems are classical problems of the combinatorial geometry which have the natural flavor of the equivariant topology. The $k$-fan partition problems have attracted a lot of attention [1,2,3] and forced some hard concrete combinatorial calculations in the equivariant cohomology [4]. These problems can be reduced, by a beautiful scheme of [2], to a typical question of the existence of a $D_{2n}$ equivariant map $f:V_2(R^3) -> W_{n-} \cup A(\alpha)$, where $V_2(R^3)$ is the space of all orthonormal 2-frames in $R^3$ and $W_{n-} \cup A(\alpha) is the complement of the appropriate arrangement. We introduce the target extension scheme which allow us to use the equivariant obstruction theory as a tool for proving that: for every two proper measures on the sphere $S^2$, and any $\alpha =(a,a+b,b) \in R^3_{>0}$, there exists an partition of theses measures by a 3-fan.
The significance of these results, among other, is that, beside negative results [4], the equivariant obstruction theory can pull off some positive results, which were not attained by other means.

[1] J. Akiyama, A. Kaneko, M. Kano, G. Nakamura, E. Rivera-Campo, S. Tokunaga, and J.Urrutia, Radial perfect partitions of convex sets in the plane. In Discrete and Computational Geometry (J. Akiyama et al. eds.), Lect. Notes Comput. Sci. 1763, pp. 1--13. Springer, Berlin 2000.

[2] I.Bárány, J.Matoušek, Simultaneous partitions of measures by k-fans, Discrete Comp. Geometry, 25 (2001), 317--334.

[3] I.Bárány, J. Matoušek, Equipartitions of two measures by a 4-fan, Discrete Comp. Geometry 27 (2001), 317-334

[4] P. Blagojevic, S. Vrecica, R. Živaljevic Computational Topology of Equivariant Maps from Spheres to Complement of Arrangements, arXiv:math.AT/0403161

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