## Blog

Welcome to my Blog. My name is Lucas and currently I am graduate student in mathematical physics at the Pennsylvania State University. I started this website and blog to give an overview of what I am doing. My original plan was to post at least once per month. However, I am not doing this.

You can read more about me, add my feed or subscribe to my newsletter.

After a long time of being very inactive concerning my website, I recently decided to blog more regularly on topics of mathematical physics. For this, it is very important to be able to write formulae and other mathematical expressions which is usually done using . To test if my latex compiler works, I will start with one of the wonderful Stokes’ theorem that combines topology and differential geometry: Given a manifold with a boundary , we have

where

is a

-form.

We published a paper based on my Bachelor’s thesis – submitted in July 2011 at Humboldt University. You can read it on arXiv or PRD.

**What did we do?**

We analysed the __efficiency__ of new __analytical expressions__ for __tree-level__ __amplitudes__ in __massless__ __QCD__. To give an idea what this means, you have to read the last sentence backwards (almost word for word):

**QCD**

QCD stands for Quantum Chromo Dynamics and is a quantum field theory to describe the fundamental particles of matter, namely quarks and their interaction through gluons. Protons and Neutrons (in the nucleus of every atom) are built from quarks. Understanding QCD is crucial to understand the behavior of matter on high energies, for example in high energy experiment at the Large Hadron Collider (LHC) at CERN.
**Massless**

Quarks are not massless (otherwise we would not feel gravity). However, on high energies the mass is negligible compared to the high-energy in their momentum: a bullet shot with a canon will still fall down, but as approximation for a few meters we can assume that it follows almost a straight line. In the same way, we can neglect mass if a particle is accelerated to a very high speed and momentum.
**Amplitudes**

For many experiments in high-energy physics we want to know how likely it is that accelerated particles scatter and produce new particles. This can be answered by calculating a probability distribution which depends on the absolute value of a complex quantity called scattering amplitude. Roughly speaking, a (scattering) amplitude is the function that allows us to calculate the probability of a scattering event to happen and it depends on the properties of the particles involved.
**Tree-level**

Calculating scattering amplitudes is difficult: Even with computer there is no way to calculate scattering amplitudes to arbitrary precision. Instead we have to use a perturbation series of very complicated expressions. Feynman found a way to represent these complicated expressions by simple diagrams called Feynman diagrams and the perturbation series
**Analytical exprressions**

Calculation of such amplitudes is mainly done through a numerical recursion that repeats certain steps a number of times to get a numerical result. In contrast to this, an analytical expression is one formula describing how you get a numerical value by just applying certain operations (like addition, multiplication, squareroots etc.) and is mathematically speaking a function with explicit form. In our case, we have such analytical expressions for the tree-level amplitudes, even though they are very long and complicated.
**Efficiency**

In order to predict certain outcomes of a scattering experiment one needs to predict probabilities by calculating the amplitudes for different possible processes. Because even on tree-level (leading order) one finds a huge number of possible processes one has to evaluate thousands and millions of amplitudes which makes efficiency very important: the less time one evaluation of an amplitude takes the more realistic is it to make certain predictions. Our whole analysis has the goal to compare the efficiency of just evaluating our analytical expressions with one commonly used numerical procedures (called Berends-Giele) that use a recursion to approximate the value. Furthermore, we compared the precision of the different approaches.

**What did we get?**

As expected before, our implementation of the analytical formulae (the main work of my bachelor thesis) is faster for the first two orders (MHV and NMHV). The third order (NNMHV) that I implemented, as well, becomes slower than the Berends-Giele approach as the number of involved particles increases. I did not implement higher orders because it was clear that higher orders will be slower than Berends-Giele. Finally, the accuracy of the analytical formulae was a bit higher than using the Berends-Giele scheme.

German Christmas Candies

I decided to return to Europe for the two weeks of winter break to see my girlfriend and to celebrate Christmas in Germany. Furthermore, I wanted to realize a long dream: to celebrate New Year in Berlin!

In the following list you see a short order of events:

- Flight: Dakar-Madrid and Madrid-Paris (22.12/23.12)
- Trainride: Paris-Mannheim (24.12)
- Christmas in Freinsheim (24.12-29.12)
- Visiting Cologne, Essen and Hagen (29.12-31.12)
- New Year in Berlin (31.12-3.1)
- Flight: Berlin-Paris (3.1)
- Relaxing in Paris (3.1-5.1)
- Flight: Paris-Madrid and Madrid-Dakar (5.1)

Over the break I did not do much work and focused on enjoying a good time. However, during the last week I was ill which enabled me to do at least some computer work. On the weekend when I felt better we had some meetings to discuss the progress of different projects.

Concretely, I am currently involved in the following activities for 2013:

**Preparation: Summer School in Quantum Information Theory**

Together with Robert Jonsson I will teach a course on quantum information theory at the beginning of August: the school is offered for talented highschool students (German: Deutsche Schülerakademie) I am very excited about this opportunity.
**Writing: Lecture Notes on Shape Dynamics**

I started to write some lecture notes on my current research that I would like to finish soon. You find the current version on the course page of my Sunday lectures.
**Production: AIMS Movie**

We still have to film some student interviews, some intro animations and a conversation with Neil Turok, founder of AIMS. Morgan, Pavel and I are optimistic to finish a version within the next month.
**Launch: African Opportunity Network**

Yannick, Pavel and I were working hard to launch the official website for the African Opportunity Network.
**Lobbying: PSI Alumni Conference 2014**

The PSI Alumni Committee is thinking about lobbying for a re-union of four generations of PSI in the form of an scientific conference at Perimeter Institute in 2014.
**Preparation: Internship at Global Public Policy Institute in Berlin**

At the end of April I will begin an internship at GPPi in Berlin and I try to start reading about public policy and relevant stakeholders to get grasp on this unknown field.
**Research: Perturbative approach to Shape Dynamics**

With Tim Koslowski I am continuing a collaboration from my Master’s thesis and I am spending the remaining time beside my tutor job and other activities on tricky calculations involving tons of Poisson brackets.

I am very excited what else 2013 will bring. My plans reach until the 17th of August when Robert’s and my summer school on quantum information ends – what I will do next or where I will hopefully begin my PhD is open. Stay tuned…

The last couple of weeks were very intense, but after I reached maximal stress level last week it is getting more relaxed as the application deadlines for the American universities approach. There were a lot of things going on since I wrote my last post:

- Video Production

We worked on our video production for which we interviewed the director of the IRD, the French institute for research in development. The IRD supports AIMS Sénégal since the beginning and its current director Michel Laurent is also member of AIMS’ executive board. Morgan and I went to Dakar where the annual board meeting took place to use the opportunity to film some interviews with Mr. Laurent and other board members.
- GRE Test

I traveled to Boston where I wrote the two compulsory GRE tests for my applications: The General GRE and the GRE Subject Test for Physics. I don’t have my results yet, but at the moment I’m just relieved that it is over. Especially, as I had the feeling that learning for the GRE used some resources that I would have preferred to spend otherwise (see next projects).
- Turning AIMS bilingual

Back from Boston we had a very interesting discussion among the AIMS tutors how to implement bilingualism at AIMS: up to now many students can speak both, English and French, but those who could not on their arrival did not proceed as much as they could have. A competent language teacher is missing. I suggested for next year that we could advertise the position internationally to find a highly dynamical and committed language teacher and change the student selection to balance the numbers of native speakers in English and French (currently most students have a French background).
- African Opportunity Network

Yannick, Pavel and I started to work on the website of a new project supporting African students pursuing a career in mathematical sciences. When professor Banyaga from PennState University taught at AIMS Sénégal he gave also a talk on the problems of African applicants at Western Universities: they are not used to the sort of application and especially good recommendation letters are difficult to get as many African professors do not know how to write good reference letters. Yannick, one of our very committed students, asked if there exists a support network to guide talented Africans through Western application procedures. We could not find anything and so we are going to start it: we want to bring professors from all over the world together with African students to guide during their first steps into modern research (Master’s and PhD).

For Christmas I will return to Germany and celebrate New Year in Berlin.

Two weeks ago, I started to work with Morgan Pascal and Pavel Chvykov on an Outreach Video for AIMS Sénégal. Our plan is go into post-production in January 2013, but until then there is some work to do: We have to schedule interviews, present our concepts to the students and employees of AIMS Sénégal and to organize a fast computer to actually do video editing. But we are on a good way:

- In our first week we interviewed, Tanja Fröhlich, representative of the German Ministry of Education and research, that supports AIMS Sénégal by funding a research center for applied mathematics.
- Last week, we filmed Clarisse Uwizeye, a student of this year, who wrote a song about the wonderful atmosphere at the institute. We hope that we can use parts of this great music in our movie. Furthermore, Neil Turok is planning to use the footage for his presentations about the AIMS idea. You can watch the song.

Günter Nooke, German Chancellor’s G8 Personal Representative for Africa in the Federal Ministry for Economic Cooperation and Development, visits AIMS Sénégal

I didn’t expect to meet any Germans during my time in Sénégal: I wanted to learn French. However, since I arrived no less than four German institutions sent their representatives to AIMS Sénégal to get an impression of Neil Turok’s idea “building science in Africa”. It was interesting to meet German institutions from this perspective, as an employee of an institute that they support.

The German institutions decided to fund a research center for applied mathematics based at AIMS Sénégal. For this five shortlisted candidates of a faculty position paid by the Alexander-von-Humboldt Foundation were invited to interview sessions and talks.

We are excited to see when the research center is going to start.

This is the first post and a first test of my blog. I’m very excited to see it starting. The goal is to post once a months to provide up-to-date information about what I’m just doing.

At the moment, I’m working on my homepage, learn for the GRE (in order to apply for US PhD programs) and last, but not least (in fact, my major occupation) I’m teaching mathematics at the African Institute for Mathematical Sciences in Sénégal.