Monopoles and Landau-Ginzburg Models
Montag, 11.1.21, 16:00-17:00, vSR318 (Kasparov)
Multiplication of BPS states in VOAs from string theory
Freitag, 15.1.21, 14:15-15:15, vSR217 (Steinitz)
In the first part of the talk, I will state some generalities about vertex operator algebras (VOAs). This includes a brief outline of how studying these mathematical objects is justified by their importance to conformal field theory.\n\nThe second part will contain segments of my PhD thesis project. This will make use of a generalized version of VOAs, which is needed, for instance, to formalize those field theories occurring in string theory. The project aims at a mathematically rigorous definition of an algebra structure on states of minimal energy -- so-called Bogomol'nyi-Prasad-Sommerfield (BPS) states --, which was first introduced by Harvey and Moore. While a significant amount of generalization is still work in progress or beyond the scope of the talk, I will try and demonstrate the main concept in the case of torus compactifications.
Simple Singularities and Their Symmetries
Montag, 18.1.21, 16:15-17:15, bbb Konferenzraum 1 (PW Konferenz3210)
We will study simple singularities from various points of view.\nIn the first part, I will give an introduction to the theory of unfoldings. We will see how to use unfoldings to analyse and resolve singularities. An important tool therein will be the Jacobian algebra. \nThen, we will review blowups which provide a different method to resolve singularities. Here, the type of a singularity is determined by the appearance of its exceptional divisor. \nIn both cases, the associated objects allow for actions of symmetry transformations. In the last part of the talk, we will study how to translate between the different perspectives.
On certain lattice polarized K3 surfaces
Montag, 25.1.21, 16:15-17:15, vSR318 (Kasparov)
Let M be an even non-degenerate lattice of signature (1,t). A complex K3 surface X is M-polarized, if there exists a primitive lattice embedding of M into its Picard group Pic(X). \n\nVia such a polarization of the Picard group one is able to encode certain properties of the members of the family of M-polarized K3 surfaces. In this talk we will focus on Kummer surfaces which correspond to the product of two elliptic curves. We will discuss which kind of polarization, i.e. which lattice M, leads to those special Kummer surfaces. \n\nThe bigger picture that these polarized K3 surfaces fit into was described by Dolgachev’s influential paper „Mirror symmetry for lattice polarized K3 surfaces“. We will sketch some of Dolgachev’s insights and give an idea how they can be applied to the Kummer surfaces mentioned above.