The log canonical threshold plays a fundamental role in
algebraic geometry, especially birational geometry and Mori theory.
Recently the problem of classifying foliations on algebraic
varieties has been revolutionized by introducing ideas from
Mori...
To understand the birational geometry of a projective variety
$X$, one seeks to describe all rational contractions from $X$. From
an algebraic perspective, information about all these contractions
are encoded in the ring formed by all sections of...
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...
