PROGRAM

Seminar Kombinatorika, Geometrija, Topologija, Algebra (KGTA)

PLAN RADA ZA SEPTEMBAR 2018:

UTORAK, 18.09.2018. od 14:00 do 16:00, Matematički fakultet, sala 844 (5. sprat)
Rade Živaljević, Matematički institut SANU
SIMPLEKTIČKA GEOMETRIJA I GEOMETRIJSKA KOMBINATORIKA
Permutoedri i drugi konveksni politopi se prirodno pojavljuju u nekim rezultatima i otvorenim problemima simplektičke geometrije i topologije. Konfiguracioni prostori poligona (polygonal linkages) analiziraju se i metodama simplektičke geometrije (simplektička redukcija) i kombinatorne topologije. U ovom preglednom predavanju, namenjenom najširem krugu slušalaca, pomenućemo neke od najinteresantnijih interakcija ovih oblasti (Hornova teorema o ermitovim matricama, abelova teorema o konveksnosti (Atiyah, Guillemin-Sternberg), hipoteza (Viterbo) o simplektičkim kapacitetima konveksnih tela, kohomologija prostora poligona, itd.).


ČETVRTAK, 20.09.2018. 13:30, Matematički institut SANU, sala 301f, Knez Mihailova 36
Pierre-Louis Curien, IRIF, pi.r2 team (CNRS, University Paris Diderot, and Inria)
ALGEBRAIC STRUCTURES ON FACES OF POLYTOPES
(joint work with Emily Burgunder (Insitut de Mathématiques de Toulouse) and Bérénice Delcroix-Oger (IRIF))
This work is at the crossing point of operad theory and combinatorics. We study families of polytopes (including simplices, associahedra, hypercubes, permutohedra), whose faces are in one to one correspondence with inductively defined tree-like combinatorial objects called constructs (defined in previous work of Dosen and Petic). We define natural operations on constructs, that are variations on the notion of shuffling, and show that in all our examples we get the structure of a (-1)-tridendriform algebra (a notion that will be introduced in the talk), and that our four basic examples give respectively rise to free algebras over specific operads.

Predavanja imaju pregledni karakter i namenjena su najširem krugu slušalaca