Student conference for Mathematics 2016 - Poster

Student conference for Mathematics 2016. The student conference aims to connect undergraduate and postgraduate students from both Bulgaria and abroad by building a friendly atmosphere in which they can exchange knowledge. The ultimate long-term goal of the conference is to become an annual meeting which is part of the academic environment of the Faculty of Mathematics and Informatics in Sofia University.

In the fascinating world of arithmetic geometry the central objects of study are varieties. One of the interesting questions that many authors consider is whether a variety has a k-rational or integral point. The formulae in the middle right illustrate how one can study the latter question in terms of the Brauer-Manin obstruction. On top of them is situated the commutative diagram which defines the fibre product of schemes, a generalisation of varieties. Under them we have a transition to algebraic topology and in particular to topological modular forms. One can see the descent spectral sequence for computing the homotopy groups of the connective cover of the spectrum of topological modular forms. On the bottom right is the natural ring homomorphism from the homotopy groups of the sphere spectrum to the homotopy groups of the tmf spectrum.