I will discuss a dictionary between the quantities in the
spectrum of the string theory compactified on the Calabi-Yau and
object in the Calabi-Yau. I will also discuss some properties.
A few months ago, I decide to attempt to formalize one of my own
papers using the Lean4 theorem prover. I will report on this
experiment. (The Lean code can be found there: https://github.com/smorel394/TS1)
A $\mathrm{GL}$-variety $X$ is an (infinite-dimensional) affine
variety with an action of the infinite general linear group
$\mathrm{GL}$ such that the coordinate ring of $X$ is a
polynomial $\mathrm{GL}$-representation and generated by
finitely...
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...
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...
