# An introduction to Symplectic Geometry

During the last two weeks I gave in the seminar series of our work group two talks about Symplectic Geometry and its relations to physics. The first part consists of a basic introduction to the language of Symplectic Geometry and fixes the used notation. Since I had only one talk for the introduction I refer to the given literature for further details.
The second part is dedicated to the applications and results of Sympletic Geometry to Physics. Most importantly we talked about Gromov's theorem from 1985 which can be interpreted as the mathematical analog of the uncertain principle of quantum mechanics

As always I have prepared a little handout of everything that I have presented. You can find it here. In case you find any mistake of do have a suggestion, don't hesitate to write me an email.

# Irreducible representations of $\text{SU}_2(\mathbb{C})$

Today I gave a talk with the header:  'Irreducible representations of $\text{SU}_2(\mathbb{C})$'  in the Proseminar: Ausgewählte Kapitel der linearen Algebra, organized by Prof. Dr. I. Burban.

I explained how to construct these presentations and I also proved, that these presentations are indeed irreducible. Unfortunately, the handout that I have created is only available in german. You can find it here.

# Mathematics - curse or blessing?!

With the begining of this semester I also started my bachelor in the topic of mathematics.
By studying  a lot of very dry definitions of algebraic sets and topological features of closed set the question emerges:

Do we need all of this as theoretical physicists?!

I.e. does "nature" really care about e.g. closed or open sets?
This was and is an absolute non-trival question. Most physicists would argue that these mathematical concepts only emerge from our logical understanding as a human. But on the other side: Humanity has build up logical concepts from watching at nature itself. Consider for example the integer numbers $\mathbb{N}$. These arise naturally from counting stuff like apples or so.
But the question is then, what is couting? It is the ability to see similarities between two things and to say, that these two or more objects are equal. This then give us naturally the concept of $\mathbb{N}$ in order to specialize how many "equal" things there are.

This was just ment to give a little example of how mathematical concepts arise from nature and this is also the reason why I think that mathematics is much more a blessing as a cure for any theoretical physicists. It gives the ability to "see" structures, similarities and relations between objects and theories, that somehow might look completly different.
Due to this face I would encourage everyone, who would love to work in theoretical physics, to put his effort a little bit more towards mathematics. Of course one should not lose his mind in the big sea of defintions, lemma and propositions but being a little bit more rigorious about math will benifit a lot. At least that is was I think and I hope to get from my studies in these fields.

# SnarXiv.org

During the last week I found an interesting and funny page, called snarXiv where a computer generates arbitrarily headers and abstracts for scientific papers.  Sometimes it is really hard to distinguish between real and fake.

For all of those who want to test yourselves, here is a snarXiv vs arXiv-Quiz where you have to choose which title is a fake and which one is not.
Have fun with it:)

Best wishes
Alessandro

# Be welcome on my blog

This is my first attempt to create my own blog about my research in theoretical physics.
The main idea is to start some discussion about the topics I will present by using the comment function.

At the moment I am in my Master at the University of Cologne, where I have chosen Quantum Gravity as my main area of research.
Therefore I will post some of my ideas and thoughts about the concepts I will explore and hopefully build.

Non of the things I will presented have to be final or correct. They are only attempts to give a starting point for discussions.

Have fun on my page

Best wishes
Alessandro