Basic Notion Seminar
The Basic Notion Seminar shall give people with different mathematical backgrounds the opportunity to present their favourite mathematical topic in a relaxed and informal ambient.
Either a research result or a general introduction of an area of interest are welcomed as subject. The talk should be presented in a simple way so that as many people as possible can understand it. The style of the presentation is left to the speaker. It can be either a beamer or blackboard presentation of about 60 min. This can be followed by questions and discussions in a relaxed atmosphere, supported by coffee, cookies etc.
The main goal of the seminar is to bring together people with different mathematical backgrounds and give them the opportunity to gain knowledge about areas which are not directly related to their research. Moreover the seminar shall provide a platform to practice presentations in a relaxed ambient.
The seminar is intended for professors, postdocs, PhDs and interested students. Participants are not supposed to get credit points or cover any teaching duties. Every participation is on a voluntarily basis. It is possible to subscribe to give a talk via email to the organizers or at the meetings.
Schedule
Room: IA 1/63
Time: 16:30  17:30

23th October: Fabian Korthauer "Varieties and schemes for nonalgebraic people"

6th November: Murat Saglam “Gromov's nonsequeezing theorem”

20th November: Floyd Zweydinger “Subset Sum and its application to Cryptanalysis”

11th December: Bernd Stratmann "When does a complex manifold fit best to its algebra of holomorphic functions or what is a Stein manifold?"

18th December: Viktoriya Ozornova "Can we multiply vectors in R^3?"

8th January: Jorret Bley "KempfNess Theory"

22th January: Leon Barth "Tilings and affine Weyl groups"
Abstracts
Fabian Korthauer: "Varieties and schemes for nonalgebraic people"
Varieties and schemes are the central objects of study in algebraic geometry and they provide a powerful though beautiful language. In my talk I intend to present these including various concrete examples starting with the basic definition of an affine variety. After looking at some examples I plan to introduce some selected facts from the classical theory of algebraic varieties, state the definition of a scheme and describe its connections to the classical notion of a variety.
At least 75 % of the talk is supposed to be accessible to an audience with a general mathematical preknowledge.
Murat Saglam “Gromov's nonsequeezing theorem”
I will discuss pseudoholomorphic curves in almost complex manifolds and as an application this tool I will present the celebrated nonsqueezing theorem of Gromov, which is one of the milestones of modern symplectic topology.
Floyd Zweydinger “Subset Sum and its application to Cryptanalysis”
Though the SubSet Sum (SSS) is a well known NPComplete (NPC) problem
its application to cryptanalysis is less known. In this talk I want to
discuss the problem itself, its application to various cryptosystem
(lattice, LWEbased) and finally the history of algorithms solving SSS.
The algorithms I'm going to present are the Schroeppel Shamir (1980) and
HowgraveGraham Joux (2010).
Bernd Stratmann "When does a complex manifold fit best to its algebra of holomorphic functions or what is a Stein manifold?"
We develop a first definition of a Stein manifold from what might fail the algebra of holomorphic functions to describe the underlying manifold entirely. We succeed with nonobviously equivalent definitions where we only touch on aspects of the equivalence. Finally, we state the nowadays used cohomological definition and show its immense power to establish properties of Stein manifolds in few examples.
Viktoriya Ozornova "Can we multiply vectors in R^3?"
We know that R^2 can be given a multiplication making it into a field, namely into the field of complex numbers. There is also a multiplication on R^4 making it into a noncommutative field, the quaternions. What about R^3? And how long can we keep going, say with R^6 or R^8 or R^16? It turns out that one way to settle such questions is using algebraic topology and actually motivated a number of developments in algebraic topology, some of which I will try to outline.
Jorret Bley "KempfNess Theory"
We will introduce a Theorem by Kempf and Ness that connects the theory of GITquotients by complex reductive groups and the theory of geometric quotients by the maximal compact subgroup. Then we will discuss how this is used in the theory of Hamiltonian group actions on Kähler manifolds.
Leon Barth "Tilings and affine Weyl groups"
Let W be a Weyl group acting on an Euclidean vector space V and let C be a Weyl chamber. Waldspurger proved in 2005 that the images (id  w)(C) for w in W are pairwise disjoint and their union is the closed cone spanned by the positive roots. Based on this, Meinrenken proved in 2009, that the images of (id  w)(A) of the fundamental alcove A for elements w in the affine Weyl group are disjoint and their union is V, which gives rise to a nontrivial tiling.