Predavanje: Dynamics of meromorphic vector fields on the Riemann sphere

U petak 06.05. od 12h u dvorani B3-17 PMF-a

dr. sc. Martin Klimeš

Fakultet elektrotehnike i računarstva
Sveučilište u Zagrebu

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DYNAMICS OF MEROMORPHIC VECTOR FIELDS ON THE RIEMANN SPHERE

Predavanje je organizirano u sklopu redovitog kolokvija Znanstvenog razreda SMD-a.

Pozivamo sve zainteresirane da prisustvuju.

Sažetak: The talk will offer a brief overview on the dynamics of real-time flow of rational vector fields in one complex variable on CP^1, of their bifurcations, and, if time allows, of the structure of their moduli space. The real phase portrait is also known as the horizontal foliation of the dual meromorphic differential form (Abelian differential), and a great deal of the theory has a natural generalization also for horizonal foliations of meromorphic quadratic differentials on compact Riemann surfaces. No prior knowledge of dynamics needed.

Predavanje: o incidencijskim grafovima 2-dizajna

U petak 25.03. od 12h u dvorani B3-17 PMF-a

prof. dr. sc. Sanja Rukavina

Fakultet za matematiku
Sveučilište u Rijeci

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O INCIDENCIJSKIM GRAFOVIMA 2-DIZAJNA.

Predavanje je organizirano u sklopu redovitog kolokvija Znanstvenog razreda SMD-a.

Pozivamo sve zainteresirane da prisustvuju.

Sažetak

Predavanje: where groups = graphs = topology

U petak 11.03. od 12h u dvorani B3-17 PMF-a

prof. Mathew Timm

s Bradly University i splitskog PMF-a

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where groups = graphs = topology.

Predavanje je organizirano u sklopu redovitog kolokvija Znanstvenog razreda SMD-a.

Pozivamo sve zainteresirane da prisustvuju.

Sažetak predavanja:
A group is non-Hopfian if it has proper quotients which are isomorphic to itself. The Baumslag-Solitar groups [Baumslag, G., Solitar, D., 1962] were the first known examples of 2 generator, 1 relator non-Hopfian groups. They, and the broader class of generalized Baumslag-Solitar (GBS) groups, have since become test beds for various sorts of conjectures in group theory. The class of GBS groups is intimately connected to a class of graphs, the GBS graphs, and a class of topological spaces, the GBS complexes. We explore those connections and, we hope, provide a justification for the title chosen for this talk.

Predavanje: On Locally Spherical Regular Hypertopes

U petak, 10. rujna 2021. u 12h u dvorani B3-17 PMF-a

prof. Asia Ivić Weiss

Department of Mathematics and Statistics
York University

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On Locally Spherical Regular Hypertopes

Predavanje je organizirano u sklopu redovitog kolokvija Znanstvenog razreda SMD-a.

Pozivamo sve zainteresirane da prisustvuju predavanju.

Sažetak:
Defining a hypertope as a thin, residually connected incidence geometry, we show how the concept generalizes the concept of a polytope. In this talk we present the characterization of the automorphism groups of regular hypertopes, summarize the classication of universal locally spherical regular hypertopes, and give examples of fine ones. In particular, given any irreducible Coxeter group C of hyperbolic type with non-linear diagram and rank at least 4, whose maximal parabolic subgroups are finite, we show how to construct an infinite family of locally spherical regular hypertopes of hyperbolic type whose Coxeter diagram is the same as that of C.

Predavanje: Pakiranja malih grafova u fulerene i u druge poliedre

U petak, 09. srpnja 2021. u 12:00 u dvorani B3-17 PMF-a

prof. dr. sc. Tomislav Došlić

s Građevinskog fakulteta Sveučilišta u Zagrebu

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Pakiranja malih grafova u fulerene i u druge poliedre

Predavanje je organizirano u sklopu redovitog kolokvija Znanstvenog razreda SMD-a.

Pozivamo sve zainteresirane da prisustvuju predavanju.

Sažetak:

Sparivanja i pakiranja u grafovima služe kao korisni modeli za procese adicije i adsorpcije malih molekula na strukturiranim supstratima. U predavanju ćemo promatrati takva pakiranja u fulerenskim grafovima i sličnim poliedrima. Posebno će nas zanimati granični slučajevi, tj. slučajevi najveće i najmanje efikasnosti te slučaj kad ostatak grafa dopušta savršeno sparivanje.

Predavanje: Spatial statistics in materials science

U petak, 18. lipnja 2021. u 12:00 u dvorani B3-17 PMF-a

Jakub Stanek, phd

sa Karlovog Sveučilišta u Pragu

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Spatial statistics in materials science

Predavanje je organizirano u sklopu redovitog kolokvija Znanstvenog razreda SMD-a.

Pozivamo sve zainteresirane da prisustvuju predavanju.

Sažetak:

Spatial statistics is a special part of statistics which focuses on various geometrical objects of random shapes and/or positions. It has many practical applications, e.g. in biology (presence of plants or trees), medicine (distinguishing different types of tissues), material sciences (structures of various materials) etc. This talk concerns the last mentioned branch, namely three applications of spatial statistics in material science will be presented. First, there will be shown a parametric model of three phases in a material, where each phase forms a connected component. Such a kind of material occurs e.g. in anodes of solid oxide fuel cells. The second application introduces the mathematical definition of two structural characteristics which describe transport properties in porous or composite materials, the estimators of these two characteristics and their properties. The last application concerns a method of reconstruction of grains of polycrystalline materials based on incomplete 3DXRD data. The method uses cross-entropy optimization to find such a Laguerre tessellation that minimizes the discrepancy between centers of mass as well as sizes of the cells from the Laguerre tessellation and those of the grain data measured by 3DXRD. Although all the above-mentioned applications touch physics, the talk will focus mainly on their mathematical aspects.

Predavanje: Geometrija motivirana kvantizacijom gauge polja

U petak, 06. ožujka 2020. u 12:00 u dvorani B3-17 PMF-a

dr. sc. Damjan Pištalo

sa Sveučilišta u Zadru

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Geometrija motivirana kvantizacijom gauge polja

Predavanje je organizirano u sklopu redovitog kolokvija Znanstvenog razreda SMD-a.

Pozivamo sve zainteresirane da prisustvuju predavanju.


Sažetak:

Od osamdesetih godina, kad je kvantna teorija polja formulirana u jeziku vektorskih svežnjeva, uočavaju se njeni geometrijski aspetkti: djelovanje gauge simetrija podsjeća na strukturu Liejevog, odnosno Lie beskonačno algebroida, rezolucija kritičnog lokusa Lagrangiana ima strukuturu diferencijalno graduirane sheme, itd.
Ipak, premda je kvantizacija gauge polja motivirala razvoj homotopske (derivirane) geometrije, geometrija još uvijek nije u potpunosti opisala strukturu gauge simetrija.
U ovom predavanju ću skicirati povijesni razvoj priče (Faddeev-Popov; Becchi-Rouet-Stora-Tyutin; Batalin-Vilkovisky), a potom reći nešto o modernijim geometrijskim inetrpretacijama iz perpektive svog rada.