We prove results in the direction of showing that for some affine curves, Baker's method applied to finite étale covers is insufficient to determine the integral points. This is joint work with Aaron Landesman.

#
Conference on 100 Years of Noetherian Rings

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...