I will review the classification of vector bundles on P^1. Then I will introduce parabolic bundles and discuss them in the simple cases. I will briefly review the role of parabolic bundles in the geometric Langlands program -- this will be explored in detail in the future talks.
In this semester, we will go over the paper by D. Arinkin and R. Fedorov "An example of the Langlands correspondence for irregular rank two connections on P1." In fact, the goal will be to understand the regular case as well as connections to more modern approaches to Langlands correspondence. In this paper, the authors construct a derived equivalence between certain moduli space of bundles and moduli space of bundles with connections.
In the first talk, I will give an overview of the results.
In the Graph Matching (also known as Network Alignment) problem, the goal is to find a shared vertex labeling (matching) between two observed, unlabelled graphs, focusing on maximizing the alignment of their edges. This problem can be framed as a random instance of the well-known quadratic assignment problem. We explore two versions of graph matching: the seeded version, where partial matching is provided as side information, and the seedless version, where only the input graphs are given.