# Zoran Skoda za studente

This page is for the students of mathematics or theoretical physics at the University of Zagreb. Students from Zadar, Department of teacher’s education, please consult pages zadarmat1, zadarmat2, zadarmat3, zadarmat4, zadarodgoj vjstat or zadarmatstat.

The following is for students (in Zagreb) who need mentorship or advice

Some advice for (math or physics) students in Zagreb possibly needing my help or interested to do some study/research/work (say diploma thesis, PhD thesis, short research, course) with me or looking for other professional advice I can give.

1. You can get some feeling from the description of the courses I taught in graduate school (postdiplomski, matematika, Zagreb): Homotopy in various categories (November 2009-March 2010), Geometry of connections and integrability (2011/2012), and Spaces with structure sheaf (2012/2013) (Prostori sa strukturnim snopom), Homotopy of CW complexes (2014/2015), Neabelova kohomologija (2017/2018). I have been teaching in the title of the adjunct assistant professor (tj. u naslovnom znanstveno-nastavnom zvanju docenta iz matematike). So far 6 math and one physics students finished diploma thesis with me and one a PhD diploma. I was helping unofficially on advising several more diploma and graduate students, some in physics, some in math. I have a couple of PhD students at the moment in Zagreb and comentor one physics PhD student at the University of Luxembourg.

2. In general, I am very interested in having more interaction with students genuinely interested in mathematics or mathematical physics research at all levels, starting with advanced undergraduate. My contact data (email etc.) can be found on my IRB homepage. Please contact me, if possible, before you want to start some work, so we can plan timely. You can also contact me for advice on literature in the fields of my expertise, even if you do not plan to work with me.

3. Internet became a media for much of the communication, for search of literature and it has its own communities in mathematics and physics for various levels which you may be interested to follow. One list of mathematics resources is nlab:math resources.

5. Students from Split can also interact on some of the similar topics, especially in category theory and topology with Igor Baković. He will be glad to have his own students or to share mentorship of students with me. Some of the similar topics at the research level are often discussed at the internet site $n$-category cafe: http://golem.ph.utexas.edu/category and much of the wiki system of nlab is dedicated to such topics.

6. It is difficult sometimes to translate mathematics between various languages, and in particular the Croatian mathematical terminology is underdeveloped. Few words of my interest are listed in the dictionary here. I expect you can decently read English. Being able to read a bit of math in Russian or French is very useful in mathematics, but you can live without them most of the time.

7. This page belongs to my personal part of nlab, the wiki site dedicated to (higher) categorical point of view to pure mathematics and mathematical physics. If you feel confident enough in some of the similar topics please contribute to nlab.

8. I am currently an active member of a mathematical physics group in Zagreb. My main affiliation is now at the University of Zadar as a docent; I am also finishing some last older project with collaborators at the Institute Ruđer Bošković, or within the project with University of Hradec Králové where I have part time appointment as an associate professor of mathematics.

## Topics you can study with me

1. Well, depending on level, there are more or less choices; that means that for higher level there is less choices as it is harder for me to be competent enough to lead you; at lower levels I can be far more broad. If you ask me about Ph.D. thesis topic, it will have to be close to my main topics, for example in noncommutative algebraic geometry or some neighboring field. If you ask about diploma then most of the modern geometry, topology, algebra and mathematical physics can do; and maybe few pieces of math outside these 4 broad areas. See essay geotop on basic outline how modern geometry, topology and homotopy theory are structured.

2. More specifically, for diploma thesis in mathematics I can give topics about fundamentals of some aspects of differential geometry, of algebraic geometry, of some aspects of category theory, homotopy theory, and so on. I am also fond of topics in noncommutative algebra like quantum groups and noncommutative algebraic geometry, but also of the noncommutative geometry of the, say, Alain Connes, flavour.

3. Four of the more ambitious diploma projects suggested have their own webpage: diplomski higher gauge theories, and the page under construction diplomski Feynman integrals and semiclassical limit, both mainly for physics students, though mathematicians are also welcome; diplomski kohomologija snopova about the sheaf cohomology, and diplomski Spectra and reconstruction theorems, both for math majors. Physics students can also choose a topics related to physics on noncommutative spaces or study of noncommutative spaces per se. One of the possible physics topics could be the Differential geometry of gauge theories and another is Geometric quantization and groupoids. Aspiring mathematical physicists should by any means for the beginning learn the geometric material from very basic book by Schutz, Geometric methods of mathematical physics and could look a bit at the list books and reviews in mathematical physics. A physics student of mine recently defended a diploma on factorization algebras in the context of quantum field theory. The diploma had also touched on the topics of Batalin-Vilkovisky formalism in quantum field theory, a topic which is increasingly in the sphere of my interest.

4. Recently I revived some of my old interests in computer science, including working on some practical project involving machine learning. If you are interested in theoretical computer science or some trends in software, especially usage of machine learning in modern applications I can offer a diploma in this area; possibilities include some topics in computational linguistics. A hot topic is now also security, where I could offer a diploma on quantum security (regarding that number theoretical encryption will soon be breakable by quantum computers), most notably the lattice encryption algorithms. Another exciting new topics related to encryption is the blockchain technology.

5. Mathematics department asks us to submit offers for diploma topics for 2018/2019 soon, so if you have some own suggestion/interest you want to tell me about, you can talk to me before I announce my choices. Some possibilities of the topic include diplomski kvazideterminante and also Higher gauge theories.

## My old anouncement at math dept forum 24. 7. 2007.

Nudim mentorstvo za znanstveno orijentirane diplomske, magistarske ili doktorske, radove za moguću rektorovu nagradu ili nezavisne znanstvene publikabilne radove iz moderne matematičke tematike, posebno algebre (Hopfove algebre, nekomutativna lokalizacija, nekomutativni prsteni, Moritina teorija, homološka algebra), teorije kategorija (posebno monade, monoidalne kategorije, kategorijska djelovanja, grupoidi, dg-algebre, bikategorije, fibrirane kategorije, Tannakine dualnosti, ekvivarijantnost u kategorijskom kontekstu), teorije snopova i stogova (uključujući orbistrukosti), diferencijalne geometrije, Liejeve teorije, kvantne grupe, algebarska geometrija (sheme, formalne grupe itd.), i naročito, nekomutativna algebarska geometrija.

Student treba biti entuzijast spreman za često sastajanje radi matematičke diskusije i služiti se barem literaturom na engleskom, ne smije biti isključiv prema raznim matematičkim disciplinama. Esej o geometrijskom mišljenju u matematici

je dobra ilustracija naprednije slike iz one vrste matematike koju bih mogao predložiti. Vidi također opis nekih mogućih tema na