Petak, 3.10.2014. u 14:00h, sala 301f, MI SANU
Zajednicki sastanak sa Seminarom za istoriju i filozofiju matematike i mehanike

dr Menso Folkerts, Bayerische Akademie, Munich, Germany
PRAKTICNA RACUNICA U SREDNJEM VEKU I RENESANSI
PRACTICAL ARITHMETIC IN THE MIDDLE AGES AND RENAISSANCE

Abstract: Sitacija u ranom srednjem veku 500-1100. Prevodi na latinski u 12 veku. Uloga univerziteta. Matematika izvan univerziteta, tzv. Abacisticka tradicija. Doprinos Abacisticke tradicije algebri.

(The early Middle Ages (ca. 500 - 1100 AD). The translation into Latin in the 13th century. The Universities. Mathematics outside universities: the abbaco tradition. The contribution of abbaco tradition to algebra).

Petak, 10.10.2014. u 14:00h, sala 301f, MI SANU
Goran Djankovic, Matematicki fakultet, Univerzit u Beogradu
FAMILIJE AUTOMORFNIH $L$-FUNKCIJA I TEORIJA SLUCAJNIH MATRICA
FAMILIES OF AUTOMORPHIC $L$-FUNCTIONS AND RANDOM MATRIX THEORY

Abstrakt: U prvom, uvodnom delu predavanja cemo uvesti L-funkcije pridruzene modularnim (i opstije, automorfnim) formama, diskutovati o znacaju tzv. centralnih vrednosti ovih L-funkcija za aritmetiku i opisati nekoliko kljucnih problema o ovim centralnim vrednostima koji se mogu proucavati metodama analiticke teorije brojeva, kada modularna forma prolazi odreenom familijom. Zatim cemo u drugom delu opisati rezultate vezane za centralne vrednosti nekih familija automorfnih formi na GL(2) i GL(3) i njihovu interpretaciju u terminima teorije slucajnih matrica.

Petak, 24.10.2014. u 14h, sala 301f, MI SANU, BGD
Vesna Manojlovic, FON, Univerzitet u Beogradu i Matematicki Institut SANU
HARMONIC QUASICONFORMAL MAPPINGS IN DOMAINS IN $R^n$

Abstract: This talk is based on certain aspects of $hqc$ mappings in domains in $R^n$. Emphasis is given on a generalization of Pavlovic's characterization of boundary mapping admitting $hqc$ extension to the unit disc, to the multidimensional setting.

Harmonic quasiconformal (briefly, $hqc$) mappings in the plane were studied first by O. Martio in 1968., today they are investigated both in the planar and the multidimensional setting from several different points of view. Among topics considered are: boundary behavior, including Holder and Lipschitz continuity and more general moduli of continuity, behavior with respect to natural metrics, especially quasihyperbolic metric, distortion estimates, bi-Lipschitz properties with respect to different metrics, characterization of boundary maps. Different tools are used : conformal moduli of curve families, Poisson kernels, estimates from the theory of second order elliptic operators, notions of capacity, subharmonic functions, Hilbert's transformation. Both theories of harmonic mappings and quasiconformal mappings are well developed, it is of interest to consider how these results can be strengthened in presence of both harmonicity and quasiconformality. Some of the results are unexpected and elegant, e.g. preservation of boundary modulus of continuity in the unit ball, bi-Lipschitz property with respect to quasihyperbolic metric.

Petak, 31.10.2014. u 14h, sala 301f, MI SANU, BGD
Zajednicki sastanak sa Odeljenjem za Mehaniku i Seminarom za istoriju i filozofiju matematike i mehanike
akademik Teodor Atanackovic, Fakultet tehnickih nauka u Novom Sadu
NAUKA I PSEUDO NAUKA: KAKO DA IH RAZLIKUJEMO I KAKO DA VREDNUJEMO NAUKU

Abstrakt: Izlozicemo nekoliko definicija nauke koje vode do kriterijuma razgranicenja nauke i pseudo nauke. Ogranicicemo se na prirodne nauke. Posebna pa.nja bice posvecena radovima Popera, Kuna i Lakatosa. Analizirace se prednosti i nedostatci pojedinih definicija. Izlozice se i neke od metoda za vrednovanja naucnih rezultata i istrazivaca. Ukazace se na prednosti i nedostatke pojedinih kriterijuma za vrednovanje.