Seminar for Combinatorics, Geometry, Algebra and Topology
PROGRAM
Seminar Kombinatorika, Geometrija, Topologija, Algebra (KGTA)
PLAN RADA ZA JUL 2026:
Četvrtak, 02.07.2026. u 12:15, Kneza Mihaila 36, sala 301f i Online
Rade Živaljević, MI SANU
EKVIANGULARNE BAZE (MUBs) I EKVIANGULARNI POLITOPI (COMPLEMENTARITY POLYTOPES)
“Mutually unbiased bases” (MUBs) u konačno dimenzionalnim, kompleksnim Hilbertovim prostorima, kao i asocirani “complementarity polytopes” (CPs), su medju centralnim temama savremene kvantne fizike (kvantne teorije informacija).
Naglašavajući geometrijsku tačku gledišta, (MUBs) ovde preimenujemo u “Uzajamno ekviangularne baze“ (ili kratko “Ekviangularne baze“), dok (CPs) “prevodimo“ kao “Ekviangularni politopi”. U predavanju ćemo razmotriti neke od najinteresatnih osobina ovih objekata (iz ugla matematilara).
Neposredni povod je vrlo interesantni, multidisciplinarni prepint: Stefan Joka, Mutualy unbiased bases and orthogonal Latin squares, https://arxiv.org/abs/2511.03537, ali je akcent u predavanju pre svega na dijalogu i razmeni ideja između fizičara i matematičara (namenjenih “svim studentima I najtalentovanijim profesorima”).
Četvrtak, 09.07.2026. u 12:15, Kneza Mihaila 36, sala 301f i
Online
Seonghyeon Yu, Ajou University, Republic of Korea
FULL SUBCOMPLEXES OF BIER SPHERES AND THEIR APPLICATIONS IN TORIC TOPOLOGY
A simplicial sphere is a simplicial complex whose geometric realization is homeomorphic to a sphere, and a full subcomplex of a simplicial sphere is the subcomplex induced by a subset of its vertex set. These objects appear naturally in toric topology. For instance, the combinatorics of a simplicial sphere gives rise to spaces such as (real) moment-angle complexes and (real) toric spaces. Moreover, the topology of these spaces can often be studied through the full subcomplexes of the underlying simplicial spheres.
A Bier sphere is a simplicial sphere, defined as the deleted join of a simplicial complex and its Alexander dual. In this talk, we discuss the homotopy types of full subcomplexes of Bier spheres. As applications, we obtain computations of the bigraded Betti numbers of Bier spheres and the cohomology of associated real toric manifolds.
Četvrtak, 16.07.2026. u 12:00, Faculty of Mathematics, room 830, V floor
Seonghyeon Yu, Ajou University, Republic of Korea
SMALL COVERS OVER BIER SPHERES OF THE SKELETA OF A SIMPLEX
A Bier sphere is defined as the deleted join of a simplicial complex and its Alexander dual. Although Bier spheres are not polytopal in general, those arising from the skeleta of a simplex are known to be polytopal. Their polytopality allows us to consider small covers whose orbit spaces are the corresponding dual simple polytopes. In this talk, we will discuss the classification of small covers over these Bier spheres up to Davis-Januszkiewicz equivalence. As applications, we determine their homeomorphism types in one case and compute their rational Betti numbers in the other cases.
Predavanja imaju pregledni karakter i namenjena su najširem krugu slušalaca
