07.11.2017 um 16:15 Uhr in 69/125:
Grace Itunuoluwa Akinwande (Universität Osnabrück)
Random Simplicial Complexes
Random simplicial complexes are higher dimensional generalizations of random graphs. In particular, the aim is to get limit theorems for the Vietoris-Rips complex. In this talk, I'll introduce the Gilbert graph and discuss previous results on it. I'll then generalize these to higher dimensional simplicial complexes.
22.11.2017 um 16:15 Uhr in 69/125:
Ilia Pirashvili (Universität Osnabrück)
From Toric Varieties to Topos Points - A brief Introduction to the Geometry of Monoids
In this talk, we will give a very short and non-formal introduction to toric varieties and then move on to monoid schemes, which enable us to generalise the former. It will end with the introduction of a new type of "geometry" that one can do with monoids, where prime ideals will be replaced with topos points. These two construcitons agree in the finitely generated case, but already in the simplest non-finitely generated case, there are significantly more topos points than prime ideals. This might be especially interesting for the multiplicative monoids of commutative rings.
24.11.2017 um 16:15 Uhr in 69/125:
Prof. Dr. Walter Ferrer (University of the Republic, Uruguay)
Observability: From Subgroups to Actions and Adjunctions
The exploration of the notion of observability exhibits transparently the rich interplay between
algebraic and geometric ideas in geometric invariant theory. We will talk about the concept of observable subgroup introduced in the 1960s with the purpose of studying extensions of representations from an affine algebraic subgroup to the whole group. It can be considered as an intermediate step in the notion of reductivity (semisimplicity) and it has been recently generalized to the concept of observable action of an affine algebraic group on an affine variety. We will also talk about the related concept of observable adjunction.
28.11.2017 um 16:15 Uhr in 69/125:
Timo de Wolff (TU Berlin)
Discrete Structures Related to Nonnegativity
Deciding nonnegativity of real polynomials is a fundamental problem in real algebraic geometry and polynomial optimization, which has countless applications. Since this problem is extremely hard, one usually restricts to sufficient conditions (certificates) for nonnegativity, which are easier to check. For example, since the 19th century the standard certificates for nonnegativity are sums of squares (SOS), which motivated Hilbert’s 17th problem. A maybe surprising fact is that both polynomial nonnegativity and nonnegativity certificates re closely related to different discrete structures such as polytopes and point configurations. In this talk, I will give an introduction to nonnegativity of real polynomial with a focus on the combinatorial point of view.
12.12.2017 um 16:15 Uhr in 69/125:
Manh Toan Nguyen (Universität Osnabrück)
Central simple algebras: From linear algebra to motives
The theory of central simple algebra (CSA) belongs to the classical directions of linear algebra. Appearing in the late 19th century in the works of Frobenius and Wedderburn, this theory received brilliant developement in the works of Brauer, Hasse, Noether, at al. primarily in connection with class field theory. Nowaday, CSAs has found numerious applications in algebra, algebraic geometry, arithmetics, diophantine geometry and derived algebraic geometry.
In this talk, I will give an introduction to this theory with many examples. I will explain how to associate CSAs with certain interesting class of algebraic varieties - the Severi-Brauer varieties, in connection with Galois cohomology. In the end, I will discuss about the relation between higher algebraic K-theory of a CSA and algebraic cycles on the associated Severi-Brauer variety.