Seminar: Basic Notions, Summer Term 2017

Organisers: João Pedro Ramos, Joris Roos, Tim Seynnaeve, Arik Wilbert, Catharina Stroppel

This seminar is organised by students as a BIGS event. The goal is to present topics from all areas of mathematics in an elementary and informal way. The talks should be accessible to a general mathematical audience.
Everybody (students, postdocs, faculty, guests) is welcome to attend.
Coffee, tea and cookies will be served afterwards.

If you would like to give a talk please contact us. Our e-mail address is basicnotions(at)

For receiving updates and information on upcoming talks, you can also subscribe to our Facebook page.

The seminar will take place Wednesdays 14-16 in room 1.007.

Previous instances of this seminar:
Winter Term 2016/17, Summer Term 2016,
Winter Term 2015/16, Summer Term 2015,
Winter Term 2014/15, Summer Term 2014,
Winter Term 2013/14.

Date Speaker Topic
26.04.2017 Deniz Kus What is representation theory? An introduction via the symmetric group (Abstract)
03.05.2017 Siad DaboulThe five color theorem (Abstract)
10.05.2017 Andreas GerhardusCounting rational curves with quantum gauge theories (Abstract)
Dies Academicus

  • April 26, 2017: Deniz Kus

      What is representation theory? An introduction via the symmetric group

      Abstract. Representation theory is a branch of mathematics that reduces problems in abstract algebra to problems in linear algebra, a subject that is well understood. In the first part of the talk we will present the basic concepts about the representation theory of finite groups: indecomposable objects, simple objects, module homomorphisms, Schur's Lemma and Maschke's theorem. The running example will be the symmetric group. In the second part of the talk we discuss several applications and answer the question why representation theory is important.

  • May 3, 2017: Siad Daboul

      The five color theorem

      Abstract. The four color theorem states that the regions of a planar map can be colored with at most four colors such that all neighboring regions are colored differently. In the first part of the talk I will give a brief introduction to graph theory and finally prove the weaker statement where we allow five colors instead of four. I will then discuss some extensions and provide examples for real world applications of coloring problems that arise in the design of computer chips.

  • May 10, 2017: Andreas Gerhardus

      Counting rational curves with quantum gauge theories

      Abstract. Rational curves in \(\mathbb{C}P^n\) are the images of homogeneous polynomial maps \(\phi: \mathbb{C}P \to \mathbb{C}P^n\). It is a classical problem of enumerative geometry to count the number of rational curves that are contained in a given hypersurface \(X \subset \mathbb{C}P^n\). In this talk I will address this problem for \(X\) being the vanishing locus of a degree \(5\) polynomial in \(\mathbb{C}P^4\), the well studied quintic Calabi--Yau threefold, by using modern methods of mathematical physics. Here, the enumerative problem amounts to counting instantons in a suitable two-dimensional quantum gauge theory. I will demonstrate calculations for the quintic and comment on the generalization to more complicated cases.