Curve configurations in the projective plane and their characteristic numbers

In this paper we study the concept of characteristic numbers and Chern slopes in the context of curve configurations in the real and complex projective plane. We show that some extremal line configurations inherit the same asymptotic invariants, namely asymptotic Chern slopes and asymptotic Harbourne constants which sheds some light on relations between the bounded negativity conjecture and the geography problem for surfaces of general type. We discuss some properties of Kummer extensions, especially in the context of ball-quotients. Moreover, we prove that for a certain class of smooth curve configurations in the projective plane their characterstic numbers are bounded by $8/3$.Comment: 12 page

Complexity Theory

Computational Complexity Theory is the mathematical study of the intrinsic power and limitations of computational resources like time, space, or randomness. The current workshop focused on recent developments in various sub-areas including arithmetic complexity, Boolean complexity, communication complexity, cryptography, probabilistic proof systems, pseudorandomness and randomness extraction. Many of the developments are related to diverse mathematical fields such as algebraic geometry, combinatorial number theory, probability theory, representation theory, and the theory of error-correcting codes

On the relationship between plane and solid geometry

Traditional geometry concerns itself with planimetric and stereometric considerations, which are at the root of the division between plane and solid geometry. To raise the issue of the relation between these two areas brings with it a host of different problems that pertain to mathematical practice, epistemology, semantics, ontology, methodology, and logic. In addition, issues of psychology and pedagogy are also important here. To our knowledge there is no single contribution that studies in detail even one of the aforementioned area

Real Algebraic Geometry With A View Toward Systems Control and Free Positivity

New interactions between real algebraic geometry, convex optimization and free non-commutative geometry have recently emerged, and have been the subject of numerous international meetings. The aim of the workshop was to bring together experts, as well as young researchers, to investigate current key questions at the interface of these fields, and to explore emerging interdisciplinary applications

Network based data oriented methods for application driven problems

Networks are amazing. If you think about it, some of them can be found in almost every single aspect of our life from sociological, financial and biological processes to the human body. Even considering entities that are not necessarily connected to each other in a natural sense, can be connected based on real life properties, creating a whole new aspect to express knowledge. A network as a structure implies not only interesting and complex mathematical questions, but the possibility to extract hidden and additional information from real life data. The data that is one of the most valuable resources of this century. The different activities of the society and the underlying processes produces a huge amount of data, which can be available for us due to the technological knowledge and tools we have nowadays. Nevertheless, the data without the contained knowledge does not represent value, thus the main focus in the last decade is to generate or extract information and knowledge from the data. Consequently, data analytics and science, as well as data-driven methodologies have become leading research fields both in scientific and industrial areas. In this dissertation, the author introduces efficient algorithms to solve application oriented optimization and data analysis tasks built on network science based models. The main idea is to connect these problems along graph based approaches, from virus modelling on an existing system through understanding the spreading mechanism of an infection/influence and maximize or minimize the effect, to financial applications, such as fraud detection or cost optimization in a case of employee rostering