For studies on singularities over the field of characteristic
zero, we can use many convenient tools: resolutions of
singularities, Bertini’s theorem (generic smoothness), cohomology
vanishing of Kodaira type, and so on. However, in positive...
Emmy Noether was a central figure in the development of abstract
algebra in the early 20th century. Her ideas were profoundly
influential, touching nearly every corner of mathematics. In this
talk, I'll discuss how those ideas have taken new shape...
The Deligne--Simpson problem asks for a criterion of the
existence of connections on an algebraic curve with prescribed
singularities at punctures. We give a solution to a generalization
of this problem to $G$-connections on $\mathbb{P}^1$ with a...
It is well-known that for any finite group $G$, there exists a
closed $3$-manifold $M$ with $G$ as a quotient of the fundamental
group of $M$. However, we can ask more detailed questions about the
possible finite quotients of $3$-manifold groups, e...
