Science – Znanost

I am interested in topology geometry, mathematical physics and fundamenta.

Doctoral dissertation
Upotpunjeni Hopfovi algebroidi, in Croatian language, defended on October 20, 2017 ♫♪♬♫ mentor: Zoran Škoda
Completed Hopf algebroids, Doctoral presentation, English translation of the doctoral presentation in Croatian language

Publications
  1. S. Meljanac, Z. Škoda, M. Stojić, Lie algebra type noncommutative phase spaces are Hopf algebroids, Letters in Mathematical Physics, 107:3, 475-503 (2017) arxiv, doi
  2. Z. Škoda, M. Stojić, Hopf algebroids with balancing subalgebra, Journal of Algebra, 598:445-469 (2022) arxiv, doi
  3. M. Stojić, Scalar extension Hopf algebroids, Journal of Algebra and Its Applications (2023) arxiv, doi
  4. Z. Škoda, M. Stojić, Comment on "Twisted bialgebroids versus bialgebroids from a Drinfeld twist", accepted for publication in Journal of Physics A: Mathematical and Theoretical, arxiv

Submitted articles under review
  5. Z. Škoda, M. Stojić, Enveloping algebra is a Yetter-Drinfeld module algebra over Hopf algebra of regular functions on the automorphism group of a Lie algebra, under review for Georgian Mathematical Journal, arxiv

Preprints
  6. M. Stojić, Internal Hopf algebroid, arxiv
  7. M. Stojić, Z. Škoda, Examples of scalar extension Hopf algebroids over a universal enveloping algebra, preprint
  8. M. Stojić, Construction of algebras given by generators and infinite sum relations, preprint

Lists of publications and preprints: arXiv, ORCID, google scholar, bib.irb.hr

Projects
Quantum Current Algebras and Their Representation Theory, Croatian Science Foundation installation research project, Jan 1, 2020 - Dec 31, 2021
I am the topologist entrusted with completions of algebraic structures.
– Dimension and Shape Theory, 2011 - 2013

I was at IHÉS for three months as an invited researcher, from Oct 1 to Dec 31, 2019. ♬

Conferences
Noordung forum: Building European Blockchain Infrastructure, Center Noordung - Center vesoljskih tehnologij Hermana Potočnika Noordunga, Vitanje, Slovenia, Apr 23, 2019
39th Winter School Geometry and Physics, Srni, Czech Republic, January 12-19, 2019
   Contributed talk: Completed Hopf algebroid over U(g) of formal differential operators on a Lie group G
Dubrovnik VIII – Geometric Topology, Geometric Group Theory & Dynamical Systems, Dubrovnik, Croatia, June 22-26, 2015
Manifolds, K-theory, and Related Topics, Dubrovnik, Croatia, June 23-27, 2014
Dubrovnik VII – Geometric Topology, Dubrovnik, Croatia, June 26 - July 3, 2011

Contributed talks in international conferences
The symmetric monoidal category indprofinVect of ind-pro-finite-dimensional vector spaces, International Topology Seminar Ljubljana-Maribor-Zagreb, University of Maribor, Slovenia, 2019
Completed Hopf algebroid over U(g) of formal differential operators on a Lie group G, 39th Winter School Geometry and Physics, Srni, Czech Republic, January 12-19, 2019

Other talks
The category indproVect of filtered cofiltered vector spaces, series of six talks from dissertation at Topology Seminar, PMF-MO, Zagreb, 2017
Automorphic sets and quandles in geometry and topology, series of two talks from literature at Topology Seminar, PMF-MO, Zagreb, 2014
From Maxwell equations to Gauge theory, series of two talks from literature at Topology Seminar, PMF-MO, Zagreb, 2012
Knot invariants; Knot quandle and knot group; Free quandle; Homology of knot complement; Seifert surfaces; Infinite cyclic covering of knot complement, series of six talks from diploma thesis Alexander polynomial at Topology Seminar, PMF-MO, Zagreb, 2010

Diploma thesis
Alexanderov polinom, mentor: profesor Šime Ungar
siječanj 2010. diplomirana inženjerka matematike, smjer: teorijska matematika

mono no aware.


Teaching – Nastava

Uvod u diferencijalnu geometriju


Nastava prijašnjih semestara

Kompleksna analiza
Materijali za vježbe, 38 stranica
    1. Kompleksni brojevi i funkcije
        1.1. Kompleksni brojevi
        1.2. Geometrija kompleksne ravnine
        1.3. Derivacija kompleksne funkcije
        1.4. Elementarne funkcije
    2. Nizovi i redovi kompleksnih funkcija
        2.1. Nizovi i redovi kompleksnih brojeva
        2.2. Redovi potencija
        2.3. Integral kompleksne funkcije
        2.4. Taylorov red
        2.5. Laurentov red
        2.6. Singulariteti
    3. Teorem o reziduumima i primjene
        3.1. Reziduumi
        3.2. Teorem o reziduumima
        3.3. Rouchéov teorem
        3.4. Računanje integrala funkcija realne varijable pomoću reziduuma
Zanimljivosti
– Daniel, Viallet, The geometrical setting of gauge theories of the Yang-Mills type, Reviews of Modern Physics, Vol. 52, No. 1, January 1980
Non-technical introduction to Gauge theory
– Richard Feynman, QED: The Strange Theory of Light and Matter, wikipedia
– Frederic P. Schuller, A thorough introduction to the theory of general relativity, WE-Heraeus International Winter School on Gravity and Light ♡ 24 predavanja
Circle Packing: A Mathematical Tale, AMS Notices
– Alexandru Scorpan, The Wild World of Four Manifolds, AMS, 2005.
– LaTeX online editor and documentation: www.overleaf.com

Matematika 1 i 2 za kemičare

Linearna algebra 1 (nastavnički smjer)

Konstruktivne metode u geometriji
Materijali za vježbe, 13 stranica
Algebarska metoda, zadaci s rješenjima i dodatnim uputama
        Interaktivni html s konstrukcijom & ggb:
            1. KMG-2-1-geometrijska-sredina.html & ggb
            2. KMG-2-Zadatak-2.2.html & ggb
Dodatni materijali
– Dvije konstrukcije: EG-konstrukcije.pdf
– D. Palman, Geometrijske konstrukcije, Element, Zagreb 1996.
Popis zadataka s vježbi, 2014/15, 4 stranice

Elementarna geometrija
– How to relax with geometry: breathe-in-and-out.gif
– Stereometrija, neki zadaci s vježbi: EG-stereometrija-4-8-9-10-11-15-16.pdf, EG-stereometrija-14-17-18-19.pdf

Analitička geometrija

Vektorski prostori
Materijali za vježbe, 25 stranica
    1. Ponavljanje linearne algebre
    2. Jordanova forma
    3. Funkcije operatora
    4. Unitarni prostori

Strukture podataka i algoritmi
Materijali za vježbe, 44 stranice, po knjizi: Aho, Hopcroft, Ullman, Data Structures and Algorithms, 2nd Edition, Addison-Wesley, Reading MA, 1987.
    1. Uvod
    2. Općenita lista (List)
    3. Stog (Stack)
    4. Red (Queue)
    5. Uređeno stablo (Tree)
    6. Binarno stablo (BinaryTree)
    7. Općeniti skup (Set)
    8. Rječnik (Dictionary)
    9. Prioritetni red (PriorityQueue)
    10. Preslikavanje (Mapping)
    11. Binarna relacija (Relation)
    12. Oblikovanje algoritama
Computer programming
– Kernighan, Ritchie, C Programming Language, 2 ed.
– Pointers: Pointer uses, Making pointers safer, Dangling pointer
Undefined behaviour
Technical debt
Design / metodology
Poka-yoke, Toyota Production System, Lean Software Development, Kanban, Scrum, Kanban vs. Scrum, REST
Abstract Data Types, OOP
– Sedgewick, Algorithms in C, Part 2, 1990
. Ch.3 Elementary Data Structures, Ch.4 Abstract Data Types, Ch.5 Recursion and Trees – dobar uvodni opis kako graditi ADT
– Hanson, C Interfaces and Implementations: Techniques for Creating Reusable Software, 1996. – detaljnije o ADT
Abstract Data Types, Java (Software Construction, MIT)
Problem Solving with Algorithms and Data Structures, Python

Elementarna matematika I
shu ha ri: wikipedia entry, Alistair Cockburn on Shu Ha Ri
– How To Count Past Infinity: youtube
– Teorija skupova, skripta profesora Vukovića: Hilbertov hotel, kardinalni brojevi, ordinalni brojevi, hipoteza kontinuuma
EM-indukcija-neki-zadaci-scan.pdf
Relacije.pdf
– Grothendieck: wikipedia entry, Grothendieck describes two styles in mathematics: opening the nut and the rising sea is one
Kongruencije.pdf
EM-Rastav-na-parcijalne-razlomke.pdf

Elementarna matematika II


Sada gledam-čitam-pohađam:
– Frederic P. Schuller, A thorough introduction to the theory of general relativity, WE-Heraeus International Winter School on Gravity and Light ♡ 24 predavanja
Access to further material on www.gravity-and-light.org/lectures and www.gravity-and-light.org/tutorials
– Chan Hong-Mo, Tsou Sheung Tsun, Some Elementary Gauge Theory Concepts, Lecture Notes in Physics, World Scientific, 1993

Zadnja promjena: Martina Stojić,