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", Journal of Physics A: Mathematical and Theoretical 57 108001 (2024), arxiv, doi
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
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
– 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
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
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