MISANU

PROGRAM

ODELJENJE ZA MATEMATIKU
MATEMATIČKOG INSTITUTA SANU

Registracija za učešće na seminaru je dostupna na sledećem linku:
https://miteam.mi.sanu.ac.rs/asset/tz97w4Hu4c3unsJ7N.
Ukoliko ste vec registrovani predavanje možete pratiti na sledećem linku (nakon sto se ulogujete):
https://miteam.mi.sanu.ac.rs/asset/WbsehnSL4ZeTPJo6r.
Neulogovani korisnici mogu pratiti prenos predavanja na ovom linku (ali ne mogu postavljati pitanja osim putem chata i ne ulaze u evidenciju prisustva):
https://miteam.mi.sanu.ac.rs/call/T9XDGChhq8aDcNqmz/qw7wIwci2jv2rdg9I9CrXkm7OJhF_LB8DfjXZp4jTFV.

PROGRAM ZA OKTOBAR 2024.

Petak, 04.10.2024. u 14:15, Kneza Mihaila 36, sala 301f i Online
Pavle Blagojević, Matematički institut SANU
MAKFERSONOVA HIPOTEZA O KOMBINATORNIM GRASMANIJANIMA, NOVI POČETAK
Robert Makferson je 1991 godine, oslanjajući se na zajednički rad sa Gelfandom, uveo kombinatorne analoge realnih vektorskih raslojenja i identifikovao asocirane klasifikacione prostore - takozvane Makfersonijane. Takođe on je postavio hipotezu da je uređajni kompleks parcijalno uređenog skupa svih orjentisanih matroida fiksnog ranga jednak realnom Grasmanijanu, barem do na homotopsku ekvivalenciju -takozvana Makfersonovan hipoteza.
Istorija rešavanja Makfersonove hipoteze je kotraverzna. Danijel Bis je 2003, u svojoj publikaciji u "Annals of Mathematics", ustvrdio da je hipotezu rešito u potpunosti. Par godina kasnije Nikolaj Mnjev je, u beleški na platformi arXiv, ukazao na elementarnu ali fatalnu grešku u Bisovom dokazu.
U ovom predavanju ćemo pokazati kao se Makfersonovo preslikavanje može upotrebiti za definisanje dijagrama prostora čiji je kolimit odgovarajući realni Grasmanijan. Koristeći novu konstrukciju dobijamo spektralni niz koji konvergira relanom Grasmanijanu čiji drugi član se iskazuje upotrebom Makfersonijana. Na taj način dobijamo trvđenje da, ako bi idukovani dijagram imao kotraktibilne vrednosti Makfersonova hipoteza bi odmah bila razrešena. Specijalno, mi dobijamo sve poznate rezultate na uniforman način.
Predavanje se zasniva na zajedničkom radu sa Balintom Žigijem.

Petak, 11.10.2024. u 16:00, Kneza Mihaila 36, sala 301f i Online
Pavle Blagojević, Matematički institut SANU
KONVEKSNE EKVIPARTICIJE POMOĆU OPERADA MALIH KOCKI
Pre jedne decenije dve grupe autora, Karasev, Hubard & Aronov i Blagojević & Cigler, su pokalazale da regularne konveksne particije euklidskog prostora na $n$ delova daju rešenje hipoteze Nandakumara & Ramana-Raoa u slučaju kada je $n$ stepen prostog broja.
Sada iteriramo proces regularnih konveksnih particija i delimo euklidski prostor prvo na $n_1$ delova, pa na $n_2$delova, itd. Na taj način dobijamo ekviparticije konveksnog tela na $n=n_1\cdot\ldots\cdot n_k$ delova. Koristeći iterirane particije pokazujemo postojanje novih klasa rešenja problema Nandakumara & Ramana-Raoa u slučaju kada su sve iteracije stepeni istog prostog broja.
Predavanje je bazirano na zajedničkom radu sa Nikolom Sadovekom (https://arxiv.org/abs/2305.10711)

Petak, 18.10.2024. u 14:15, Kneza Mihaila 36, sala 301f i Online
Stanislav Speranski, Steklov Mathematical Institute of RAS
CONCERNING DOŠEN'S LOGIC N AND SOME OF ITS EXTENSIONS
The idea of treating negation as a modality manifests itself in various logical systems, especially in Došen's propositional logic N, whose negation is weaker than that of Johansson's minimal logic. Among the interesting extensions of N are the propositional logics N* and Hype; the former was proposed by Cabalar, Odintsov and Pearce as a framework for studying foundations of well-founded semantics for logic programs with negation, while the latter has recently been advocated by Leitgeb as a basic system for dealing with hyperintensional contexts, but was first described by Moisil in 1942. We shall look at predicate versions of N and N*, and talk about a simple Routley-style semantics for Leitgeb's predicate version of Hype. The corresponding strong completeness results will be presented. Also, the disjunction property and the existential property will be discussed. In addition, we shall see what happens when we add the contraposition axiom to several important extensions of N.
Zajednički sastanak sa Logičkim seminarom.

Četvrtak, 24.10.2024. u 17:15, Kneza Mihaila 36, sala 301f i Online
Zoran Grujić, The University of Alabama at Birmingham
SPATIAL INTERMITTENCY AND TURBULENT DISSIPATION IN 3D VISCOUS AND HYPER-VISCOUS NAVIER-STOKES FLOWS
The problem of whether a singularity can form in an initially smooth viscous, incompressible flow described by the homogeneous (no external force) 3D Navier-Stokes (NS) equations has been a fundamental open problem in mathematical physics. A key obstacle to progress has been super-criticality of the system, i.e., there is a scaling gap between the energy level and the scaling invariant level. A manifestation of this super-criticality can be seen in the realm of the hyper-viscous flows described by the hyper-dissipative (HD) NS system. Here, the negative Laplacian is replaced by the negative Laplacian to the power (say $\beta$) greater than 1. It has been known since the fundamental work of J.L. Lions in 1960s that the HD NS system is regular for any $\beta$ greater or equal to 5/4, while what happens in the super-critical regime ($1 < \beta < 5/4$) has remained a mystery. (At 5/4, the energy level and the scaling-invariant level coincide.)
The main goal of this lecture is to present a novel mathematical framework suitable for encoding the spatial intermittency of turbulent flows and the mechanism of turbulent dissipation for the purpose of the analysis of the possible singularity formation in the NS and HD NS flows. In particular, mathematical evidence of criticality of the NS dissipation ($\beta = 1$) will be given – namely, the approximately self-similar blow-up (a prime candidate for the formation of a singularity) is ruled out as soon as $\beta$ is greater than 1.
Zajednički sastanak sa Odeljenjem za mehaniku i Geometrijskim seminarom.

Petak, 25.10.2024. u 14:15, Kneza Mihaila 36, sala 301f i Online
Margaret Bayer, University of Kansas
GRAPHS AND RECONSTRUCTION OF POLYTOPES
How much combinatorial information is needed to determine the face lattice of a convex polytope? The talk will survey results on this question. An old result by Blind and Mani, and Kalai, shows that the graph of a simple d-polytope determines the combinatorial type of the d-polytope. More recent work of Doolittle, et al., extends the result on simple polytopes to polytopes with few nonsimple vertices. The d/2-skeleton of a simplicial d-polytope determines the combinatorial type of the polytope (Perles), and this has been extended (by Dancis) to simplicial manifolds. Also considered will be the question of dimensional ambiguity: when is a k-complex the k-skeleton of polytope of different dimensions. In particular, results by Espenschied on the graphs of crosspolytopes will be discussed.
Zajednički sastanak sa CGTA seminarom.

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

Zoran Petrić, Odeljenje za matematiku Matematickog instituta SANU