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

Seminar for Combinatorics, Geometry, Algebra and Topology

 

PROGRAM


Seminar Kombinatorika, Geometrija, Topologija, Algebra (KGTA)

PLAN RADA ZA DECEMBAR 2017:



UTORAK, 23.01.2018. od 14:00 do 16:00, Matematički fakultet, sala 844 (5. sprat)
Jelena Ivanović, Arhitektonski fakultet Univerziteta u Beogradu
PROST PERMUTO-ASOCIEDAR
Biće reči o familiji prostih politopa koji predstavljaju svojevrsni hibrid dve familije - permutoedara i asociedara. Familiju kombinatornih CW-kompleksa, pod nazivom permuto-asociedri, prvi je uveo Kapranov početkom 90-tih godina. Njihovu realizaciju kao konveksne, ali ne i proste (!), politope dali su V. Rajner i G. Cigler. Kako su i permutoedar i asociedar prosti politopi, bilo je prirodno potražiti familiju prostih hibridnih politopa ovog tipa. U ovom predavanju daćemo konstrukciju ovakve familije. Napomenimo da se ovi objekti prirodno pojavljuju u teoremi koherencije u simetričnim monoidalnim kategorijama. Predavanje se bazira na preprintu, "A simple permutoassociahedron", arXiv:1708.02482, Dj.Baralic, J.Ivanovic, Z.Petric.
Ključne reči: prosti politopi, asocijativnost, komutativnost, koherencija, geometrijska realizacija


UTORAK, 30.01.2018. od 14:00 do 16:00, Matematički fakultet, sala 844 (5. sprat)
Branko Nikolić, Macquarie University, Sydney
METRIC AND (RELATIVISTIC) CAUSAL SPACES VIA ENRICHMENT
We give a short introduction to basics of (enriched) category theory. When the base of enrichment is a monoidal category that is in fact a poset (aka quantale), the definition of an enriched category becomes simpler. We consider two particular quantales consisting of positive real numbers. Categories enriched in the first are generalized metric spaces [1]. The categories enriched in the second can be interpreted as causal preorders that remember intervals (times) between time-like events [2]. Modules between enriched categories enable expressing Cauchy completeness of metric spaces in purely categorical terms; in this sense all event spaces are Cauchy complete. We give sufficient conditions on a monoidal category that ensure that an enriched category is Cauchy complete if and only if idempotents split in its underlying category.

  1. Lawvere, F. W. Metric spaces, generalized logic, and closed categories. Rendiconti del Seminario Matematico e Fisico di Milano 43, 1 (1973), 135–166.
  2. Nikolic, B. Cauchy completeness and causal spaces. arXiv:1712.00560v1 [math.CT] (2017)


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