Seminars Sorted by Series

Abstract: 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...

Abstract: 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...

Abstract: 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...

Abstract:

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...

Abstract: 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)

Abstract: 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.

Abstract:

Motivated by applications in Invariant Theory, Hilbert introduced an approach to describe the structure of modules by free resolutions. Hilbert's Syzygy Theorem shows that minimal free resolutions over a polynomial ring are finite. Most...

Abstract: 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.