Seminar for Geometry, education and visualization with applications
PROGRAM
MATEMATIČKI INSTITUT SANU
Seminar geometriju, obrazovanje i vizualizaciju sa primenama
PLAN RADA ZA MART 2020.
ČETVRTAK, 05.03.2020. u 17:15, Matematički institut SANU, sala 301f
Ivan Dimitrijević, Matematički Fakultet Beograd
COSMOLOGICAL SOLUTIONS OF A NEW NONLOCAL GRAVITY MODEL
In this talk, we present modification of GR extending $R - 2\Lambda$ by nonlocal term $\sqrt{R - 2\Lambda} \mathcal{F}(\Box)\sqrt{R - 2\Lambda}$, where $\mathcal{F}(\Box)$ is an analytic function of the d’Alembert operator $\Box$. The choice of $\mathcal{F}(\Box)$ in the analytic form is motivated by existence of analytic expressions with $\Box$ in string field theory and $p$-adic string theory.
We have found some exact cosmological solutions of the corresponding equations of motion without matter and with $\Lambda\neq 0$. One of these solutions is $a(t) = A t^{\frac 23} e^{\frac{\Lambda}{14}t^2}$, which contains properties similar to an interplay of the dark matter and the dark energy.
For this solution we computed some cosmological parameters which are in good agreement with their values in the standard $\Lambda$CDM model. This nonlocal gravity model has not the Minkowski space solution. Also, some constraints on function $\mathcal{F}(\Box)$ are obtained.
ČETVRTAK, 12.03.2020. u 17:15, Matematički institut SANU, sala 301f
Tijana Šukilović, Matematički Fakultet Beograd
HAJZENBERGOVA EKSTENZIJA
Na predavanju će biti predstavljena konstrukcija kojom se n-dimenziona Liova algebra proširuje za dve dimenzije tako da je jedna nova ne-nula Liova zagrada upravo Hajzenbergova. Može se pokažati da je ovakvo proširenje takodje Liova algebra. Ova konstrukcija je u nešto opširnijem obliku prvi put opisao Mabarakzyanov 1963. godine u radu kojem klasifikuje rešive Liove algebre nižih dimenzija.
U nedostatku boljeg termina, konstrukciju ćemo nazvati Hajzenbergova ekstenzija.
Na predavanju će biti razmatrana specijalna svojstva koje imaju algebre dobijene opisanom ekstenzijom, a posebna pažnja će biti posvećena 4-dimenzionom slučaju.
Sednice seminara odrzavaju se u zgradi Matematickog instituta SANU, Knez Mihailova 36, na trecem spratu u sali 301f.
Rukovodilac Seminara dr Stana Nikcevic
