Pedro Núñez

[Here is a picture of myself]

I am a PhD student in mathematics at the University of Freiburg under the supervision of Prof. Stefan Kebekus. I am working on algebraic geometry, mainly on birational geometry but also interested in derived categories.

Email:
pedro.nunez [at] math.uni-freiburg.de

Address:
University of Freiburg
Mathematical Institute (Office 420)
Ernst-Zermelo-Straße 1
79104 Freiburg im Breisgau, Germany

Preprints

A note on semiorthogonal decompositions for Fano fibrations [arXiv:2002.10987].

Scripts for seminar talks

Zariski Cancellation, for a seminar on insightful examples organized by Dr. Oliver Braunling at the Uniersity of Freiburg (WS 20/21).

Hitchin--Kobayashi correspondence, for a seminar on Higgs bundles organized by Dr. Andriy Haydys at the University of Freiburg (SS 20).

Condensed Abelian Groups, for a seminar on condensed mathematics organized by Dr. Johan Commelin at the University of Freiburg (WS 19/20).

Projective bundle formula, for a seminar on characteristic classes of topological vector bundles organized by Dr. Fabian Hebestreit at the University of Bonn (WS 18/19).

Riemann--Roch theorem for surfaces, for a seminar on the classifcation of algebraic surfaces organized by Prof. Luca Tasin at the University of Bonn (SS 18).

Bachelor and Master theses

Derived categories of Fano fibrations, Master's thesis written under the supervision of Prof. Luca Tasin and Dr. Pieter Belmans at the University of Bonn (SS 19).

Blow-ups in algebraic geometry, Bachelor's thesis written under the supervision of Prof. Nikita Semenov at the Ludwig-Maximilians-University of Munich (SS 17).

Computer stuff

Push and pull GitHub repositories from the terminal. For example, if you wish to push your repository "homework" to GitHub, then type "push homework changes" on the terminal and press enter, where changes is the desired commit message.

All local repositories are assumed to be on a same folder (~/git in my case). If not, some small changes would be necessary. It is also assumed that we can connect to GitHub with SSH, which avoids being asked for username and password every time you want to push or pull repositories (thanks to Stefan Kebekus and Johan Commelin for this suggestion).
Create a variable containing your GitHub username in your .bashrc:
```
# Variables
GITHUBUSERNAME=yourusername
```

Add the following "push" function to your .bashrc:


# Functions
push() {
    # Push local changes on a repository to GitHub
	# By default, all files are added
	# Unnecessary files can be avoided with .gitignore
    # First argument is the name of the repository
	# If no arguments, then push dotfiles
    # Remaining arguments are used as a commit message
	# If at most one argument, then use "Some updates" as commit message
    if [ $# = 0 ]; then
    	cd ~/git/dotfiles;
	git add .;
	git commit -m "Some updates";
	git push origin master;
	cd;
    elif [ $# = 1 ]; then
    	cd ~/git/$1;
	git add .;
	git commit -m "Some updates";
	git push origin master;
	cd;
    else
    	cd ~/git/$1;
	git add .;
	git commit -m "${*:2}";
	git push origin master;
	cd;
    fi
}

Add the following "pull" function to your .bashrc:


pull() {
    # Pull changes from GitHub to your local folder
    # First argument is the name of the repository
	# If no arguments, then pull dotfiles
    if [ $#= 0 ]; then
    	cd ~/git/dotfiles;
	git pull origin master;
	cd;
    else
    	cd ~/git/$1;
	git pull origin master;
	cd;
    fi
}

New documents from templates: type "new X Y" on the terminal and press enter to create a new latex document named Y from template X. This will create a folder named Y inside ~/git containing the new main.tex and a new private GitHub repository named Y as well. A new alias will also be created, so that when we type Y in the terminal and press enter, our text editor opens the corresponding main.tex file.

All templates are assumed to be inside ~/git/templates. For instance, to create a new template "article":


cd ~/git/templates
mkdir article
cd article
touch main.tex
touch main.bib
echo "\documentclass{article}" >> main.tex
echo "\begin{document}" >> main.tex
echo "This is a new article!" >> main.tex
echo "\bibliography{main}" >> main.tex
echo "\end{document}" >> main.tex

Add the following function to your .bashrc:


new() {
    # Create a new latex document with the corresponding git repository
    # First argument is the name of the template
    # Second argument is the name of the new folder and repository
    cd ~/git;
    mkdir $2;
    cd $2;
    touch README.md;
    cp ~/git/templates/$1/main.tex main.tex;
    git init;
    git add .;
    git commit -m "First commit";
    hub create -p $GITHUBUSERNAME/$2;
    git push origin master;
    cd;
    echo "alias $2=\"cd ~/git/$2; vim main.tex\";" >> .bash_aliases;
    source .bash_aliases;
}

Access books and articles from the terminal. For example, if you want to open Hartshorne's Algebraic Geometry book, just type "b har77" on the terminal and press enter. Your pdf reader opens the requested book. The naming of the files is the same as the alphabetic bibliography style in latex.

In your home folder, create a folder "refs" and inside of it create three folders "papers", "books" and "notes".
Place your pdfs in the corresponding folder and name them with the first three letters of the author and the last two digits of the publishing year (e.g. "har77.pdf"). If there are several authors, replace the first three letters by one initial for each author in alphabetical order, so for example Kollár and Mori's Birational Geometry of Algebraic Varieties from 1998 would be "km98.pdf". If there are two references with the same name, start using letters (e.g. "laz04a.pdf" and "laz04b.pdf"). Djvu files will also work as long as they are supported by your reader.

In your .bashrc, create three functions "b()", "p()" and "n()" for books, papers and notes respectively. The one for books, for example, would be as follows:


b() {
    # Open some book in the book folder
    # If single author: "first three letters of name"+"last two digits of year"
    # If two or more authors: "initial letters of authors"+"last two digits of year"
    xdg-open ~/refs/books/$1* & exit;
}

Compile latex within Vim: on any mode, pressing F2 saves the changes and compiles and pressing F5 saves, compiles and opens the output pdf file.

In your .vimrc, add the following lines:


nnoremap <F2> <Esc>:w<CR>:! latexmk -pdf main.tex<CR> 
inoremap <F2> <Esc>:w<CR>:! latexmk -pdf main.tex<CR>
vnoremap <F2> <Esc>:w<CR>:! latexmk -pdf main.tex<CR>
nnoremap <F5> <Esc>:w<CR>:! latexmk -pdf main.tex<CR>:! xdg-open main.pdf &<CR>
inoremap <F5> <Esc>:w<CR>:! latexmk -pdf main.tex<CR>:! xdg-open main.pdf &<CR>
vnoremap <F5> <Esc>:w<CR>:! latexmk -pdf main.tex<CR>:! xdg-open main.pdf &<CR>

If you want to use vim in Termux from an Android device (Logitech's K380 keyboard makes this very convenient), you may also add the following substitute of <F5>:


nnoremap <F6> <Esc>:w<CR>:! latexmk -pdf main.tex<CR>:! termux-open main.pdf &<CR>
inoremap <F6> <Esc>:w<CR>:! latexmk -pdf main.tex<CR>:! termux-open main.pdf &<CR>
vnoremap <F6> <Esc>:w<CR>:! latexmk -pdf main.tex<CR>:! termux-open main.pdf &<CR>

If you also want a shortcut to clean the auxiliary files generated by latexmk, you can add the following lines:


nnoremap <F10> <Esc>:w<CR>:! latexmk -c<CR>
inoremap <F10> <Esc>:w<CR>:! latexmk -c<CR>
vnoremap <F10> <Esc>:w<CR>:! latexmk -c<CR>

Disclaimer: