Seminar

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.

Abstract: We introduce and analyse a fully-mixed formulation for the coupled problem arising in the interaction between a free fluid and a poroelastic medium. The flows in the free fluid and poroelastic regions are governed by the Navier-Stokes and Biot equations, respectively, and the transmission conditions are given by mass conservation, balance of stresses, and the Beavers-Joseph-Saffman law.

The QQ systems are systems of polynomial equations that arise in various geometric settings, including the enumerative geometry of Nakajima varieties and elements of the (deformed)  geometric Langlands correspondence. These equations are related to the integrable models of spin chain type, linked to quantum groups and Yangians. Specifically, the solutions to the QQ-system equations characterize the spectrum of these integrable models via the so-called Bethe ansatz equations.