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

Mathematical Colloquim

 

PROGRAM


ODELJENJE ZA MATEMATIKU
MATEMATIČKOG INSTITUTA SANU

                      


PROGRAM ZA OKTOBAR 2019.


Petak 11.10.2019. u 18:00, sala 301f, MISANU, Kneza Mihaila 36
Ilijas Farah, York University, Canada
ULTRAPROIZVODI I ALGEBRE OPERATORA
Operacije uzimanja ultraproizvoda i ultrastepena se obichno povezuju sa logikom, mada su nezavisno otkrivene u kontekstu operatorskih algebri. Ovo predavanje će da bude pregled ultraproizvoda i njihovih primena u logici, kombinatorici, sa posebnim osvrtom na njihovu ulogu u programu klasifikacije C*-algebri. Prethodno predznanje logike ili algebri operatora nije neophodno za ovo predavanje.
Zajednički sastanak sa Seminarom za logiku




Petak, 18.10.2019. u 14:15, sala 301f, MISANU, Kneza Mihaila 36
Slavko Moconja, Matematički fakultet, Beograd
REMZIJEVA TEORIJA I TOPOLOŠKA DINAMIKA ZA TEORIJE PRVOG REDA
Na predavanju ćemo razmotriti nekoliko svojstava Remzijevog tipa za teorije prvog reda, kao i neke osobine Elisove i Kim-Pilajeve Galoaove grupe teorije koje ta svojstva povlače. Cilj predavanja nije da ulazimo u detalje, pokušaćemo da opišemo globalnu sliku, svi neophodni pojmovi biće definisani, i sem poznavanja neki osnovnih koncepata teorije modela, posebna predznanja nisu neophodna. Rezultati koje ćemo predstaviti su deo zajedničkog istraživanja sa Kšištofom Krupinjskim i Džungukom Lijem.
Zajednički sastanak sa Seminarom za logiku




Utorak, 22.10.2019. u 15:30, sala 301f, MISANU, Kneza Mihaila 36
Danko Jocić, Matematički fakultet, Beograd
INEQUALITIES FOR (σ-ELEMENTARY OPERATORS AND GENERAL) INNER PRODUCT TYPE TRANSFORMERS IN NORM IDEALS OF COMPACT OPERATORS
Inner product type (i.p.t.) transformers represent a class of transformers on the space B(H) of bounded Hilbert space operators of the form ∫Ω *A**t **⊗ **B**t **dµ*(*t*): *B*(*H*) *→ **B*(*H*) : *X **→* ∫Ω *A* *t **X B**t **dµ*(*t*) Beside elementary operators, double operator integrals (DOI), introduced and developed by Birman and Solomyak, represent the most investigated class of i.p.t. transformers, contributing to deep results in perturbation theory and differentiability properties of operator valued functions. Necessary and sufficient conditions for DOI to induce a bounded transformer on every norm ideal of compact operators were characterized by Peller, implying that such transformers admit a representation (1) for some square integrable families {At}, t ∈ Ω and {Bt}, t ∈ Ω. of bounded Hilbert space operators, such that each of them consists of mutually commuting normal operators. Recently, some new Cauchy-Schwarz Q and Q* norm inequalities for i.p.t. transformers are obtained, reducing normality and commutativity conditions only to one of families {At}, t ∈ Ω or {Bt}, t ∈ Ω . This complements some previous Cauchy-Schwarz Schatten norm inequalities for i.p.t. transformers, obtained without any requirement of normality or commutativity for considered families of operators. Different applications of the above inequalities include means inequality for operator monotone functions, Young and Heinz norm inequalities, as well as Grüss-Landau norm inequalities for i.p.t. transformers. Some applications of refined Cauchy-Schwarz operator inequality for i.p.t. transformers will also be presented.






Odeljenje za matematiku je opsti matematicki seminar namenjen sirokoj publici. Predavanja su prilagodjena matematicarima i onima koji zele da to postanu.


Zoran Petric, Odeljenje za matematiku Matematickog instituta SANU