# ~alvin

Personal website of Alvin Šipraga.

I was a mathematics student at the University of Copenhagen until August
2015. Before that, I was at the University of Bath. After doing
some stuff at the University of
Vienna, I now work at ~~Pipetop~~
SHFT.

email: alvin@pqrs.dk

## Algebraic geometry

I wrote my Master's thesis—entitled The Nash problem—between February and
July 2015, in which I studied the theory of arc spaces and the so-called Nash
problem on singular varieties. I successfully defended on the 28th of August
2015, which involved some brief
presentation slides.

## Convex analysis

In 2013 I did a project on convex analysis as part of my final year at
Bath, the results of which can be found below:

**Convex sets in Euclidean
space** — a set of (potentially lecture-) notes that give a
thorough introduction to the notion of convex sets in finite dimensional
Euclidean space. This was my final "report", with some typo
corrections.
- Presentation notes with
(unhelpfully) the same title, giving a rough overview of the stuff studied.
It also includes a proof for
*Helly's theorem* for up to uncountably
infinite families of convex sets (the above notes offer only a proof for
finite such families). I gave this as a presentation at the end of the
semester.
- Original scan of the
above presentation notes. This includes some diagrams that are absent in
the LaTeXed version above.

In November 2013 I gave more or less the
same presentation to the KU
mathematics student colloquium.

## Deep inference

During the summer of 2012 I worked on a research project at the University
of Bath Department of Computer Science in the area of proof theory. It was
under the supervision of Anupam Das
and Alessio Guglielmi. I wrote
some software as part of it, and also
a **paper**
discussing the results and method.

In December 2012 I delivered a presentation (printable version)
discussing the project and its findings to the
Mathematical foundations of computation group at Bath.

## Miscellaneous

I maintain the following websites and webpages:

## PGP public key

pgp 1024D/3AA70853
: B18D D089 D243 7F09 A6AD 5D45 A32D FD30 3AA7 0853