In this talk, I will go through some old and new results concerning the rigidity and flexibility of scalar curvature.

The famous knot complement theorem of Gordon and Luecke states that two knots in the three-sphere are equivalent if and only if the complements are homeomorphic. This was proved more than 30 years ago using combinatorial methods. In this talk, we will prove some extended results using techniques from gauge theory. If there is time…

 Invariants withstand transformations and, therefore, represent the essence of objects or phenomena. In mathematics, transformations often constitute a group action. Since the 19th century, studying the structure of various types of invariants and designing methods and algorithms to compute them remains an active area of ongoing research with an abundance of applications, in particular, to…

Invariants withstand transformations and, therefore, represent the essence of objects or phenomena. In mathematics, transformations often constitute a group action. Since the 19th century, studying the structure of various types of invariants and designing methods and algorithms to compute them remains an active area of ongoing research with an abundance of applications, in particular, to…