Alessio Sgubin - WebPage

Study Resources

About me Study resources Seminars and Conferences Other stuff

What to find on this page

This is the menu from which to navigate all study resouces I have collected over the years.

On the left side you can find a list of courses, organized by year.

What to find on this page

This is the menu from which to navigate all study resouces I have collected over the years.

On the left side you can find a list of courses, organized by year.

Analysis 1

Here you can find a summary of all the theory we studied in this course (in Italian).

Fact Summary

Computer Labs

In this page we collect all the stuff we've done in LCMC, a computational laboratory.

Oldest WebPage Formula

Geometry 1

Here you can find a summary of all the theory we studied in this course (in Italian).

Fact Summary

Analysis 2

Here you can find the lecture notes (in Italian) for the Analysis 2 course given by Pietro Majer in 2022.

Honestly, this is one of my most precious works given the time and effort put into it, with the help of my friend Andrea Rocca!

Guida Galattica per Analisti

Elements of Probability and Statistics

Here you can find some scans of the longer proofs we had to study.

Long Proofs

Geometry 2

Given the vastness of this course, I decided to collect all the results in the following file (in Italian). It may be useful to prepare the oral exam!

Fact Summary

Groups and Representations

This course has a special place in my heart: it was the first opportunity to get to know combinatorics!

Here you can find some notes that I used to prepare for the exam. If you want some real lecture notes, look up Michele D'Adderio's lecture notes on the elearning page of the course!

Some notes...

Elements of Algebraic Topology

During that year, I've written some lecture notes (in Italian).

Beware: there are MANY mistakes, eventually I will correct them all...

Lecture Notes

Physics 2

Here you can find a formulary for the written exam.

Fomulary

Physics 3

Here you can find two versions of a formulary for the written exam (joint work with Andrea Rocca).
As you can see, the NSFW version has some more explanations and stuff, bring the other to the exam!

Formulary NSFW Formulary SFW

Rational Mechanics

Too many formulae to remember? Here you can find something to help memorize them...

Formulary

Bachelor's Thesis

In my Bachelor's Thesis I got to know some group representation theory and poset topology. In particular, I focused on two nice constuctions between simplicial complexes and finite posets.
From there, I get into poset (co)homology, EL-shellability and I explain how the action of the symmetric group translates to an action on the homology groups.
In the end, you can also find a study-case, the Boolean Algebra, which has a pretty nice combinatorial description.

Here you can find my work (in Italian)!

Bachelor's Thesis Thesis Presentation

Do you like the template? You can download it clicking on the button below!

Thesis Template

Some photos from my Bachelor's Degree discussion...

Waiting for the photos to be printed...

Institutions of Mathematical Analysis

The lecture notes for Analysis 2 took all Andrea Rocca's and my energy. We ended up making just a summary (in Italian) of all results seen during the semester.

Fact Summary

Algebraic Geometry C

During my fourth year I partially transitioned to taking notes on a tablet. Why don't publish my notes alltogether?

Lecture Notes

Topological Persistence: theory and applications

For this PhD course I was tasked with studying and presenting a published article on topological persistence.

To be more specific, the paper studies the so-called "space of Barcodes". In this context, barcodes encode information on persistence homology and - for example - they can be used as input in some machine learning pipelines.
There is a neat description that, through Coxeter group theory, links these barcode spaces with simplicial complexes and the double cosets of $A_n$.

Here you can find the material (in Italian) I used to present this work.

Presentation

Probability

Here you can find some notes, collecting all the results we've seen.

Fact Summary Fact Summary (Booklet)

Tutoring at Faculty of Physics ~ Geometry and Linear Algebra (2023 - 2024)

Here you can find all the material I wrote for the students in Physics that attended the course Geometry and Linear Algebra (2023 - 2024).

Notes on an exercise (25_11_2023)

Tutoring at Faculty of Mathematics ~ Arithmetic (2024 - 2025)

Here you can find all the material I wrote for the students in Mathematics that attended the course Arithmetic (2024 - 2025).

Notes on cyclic groups (07_11_2024)