Science – Znanost
I am interested in topology ♥ geometry, mathematical physics and fundamenta.
Doctoral disertation
– 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
– S. Meljanac, Z. Škoda, M. Stojić, Lie algebra type noncommutative phase spaces are Hopf algebroids, Letters in Mathematical Physics, 107:3, 475-503 (2017)
– Z. Škoda, M. Stojić, Hopf algebroids with balancing subalgebra, Journal of Algebra, 598:445-469 (2022) arxiv/1610.03837, doi
– M. Stojić, Scalar extension Hopf algebroids, accepted for publication in Journal of Algebra and its Applications, (2023) arxiv/2208.11696
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
I am the topologist entrusted with completions of algebraic structures.
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
Other talks
– The symmetric monoidal category indprofinVect of ind-pro-finite-dimensional vector spaces, Topology
Seminar Ljubljana-Maribor-Zagreb, University of Maribor, Slovenia, 2019
– The category indproVect of filtered-cofiltered vector spaces, short series of talks at Topology Seminar,
PMF-MO, Zagreb, 2017
– Automorphic sets and quandles in geometry and topology, short series of talks from literature at Topology Seminar,
PMF-MO, Zagreb, 2014
– From Maxwell equations to Gauge theory, short series of talks from literature at Topology Seminar, PMF-MO, Zagreb,
2012
– Alexander polynomial, short series of talks from diploma thesis 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
Kompleksna analiza – utorak 12-14, A101
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
Uvod u diferencijalnu geometriju – utorak 16-18, 006
Matematika 1 i 2 za kemičare – petak 8-11, A2, KO
Nastava prijašnjih godina
Linearna algebra 1 (nastavnički smjer) – petak 15-18
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
Proteklih godina ukupno: Elementarna geometrija (8 godina), Konstruktivne metode u geometriji (7 godina), Strukture podataka i algoritmi (5 godina), Elementarna matematika I (4 godine), Elementarna matematika II (5 godina), Diskretna matematika, Uvod u matematiku, Vektorski prostori (2 godine), Analitička geometrija, Mjera i integral
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
Titled "A thorough introduction to the theory of general relativity", the lectures introduce the mathematical and physical foundations of the theory in 24 self-contained lectures. The material is developed step by step from first principles and aims at an audience ranging from ambitious undergraduate students to beginning PhD students in mathematics and physics. Satellite Lectures (see other videos on this channel) by Bernard F Schutz (Gravitational Waves), Domenico Giulini (Canonical Formulation of Gravity), Marcus C Werner (Gravitational Lensing) and Valeria Pettorino (Cosmic Microwave Background) expand on the topics of this central lecture course and take students to the research frontier. 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