David Swinarski
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View article: The worst destabilizing 1-parameter subgroup for toric rational curves with one unibranch singularity
The worst destabilizing 1-parameter subgroup for toric rational curves with one unibranch singularity Open
Kempf proved that when a point is unstable in the sense of Geometric Invariant Theory, there is a ``worst'' destabilizing 1-parameter subgroup $λ^{*}$. It is natural to ask: what are the worst 1-PS for the unstable points in the GIT proble…
View article: Computation of GIT quotients of semisimple groups
Computation of GIT quotients of semisimple groups Open
We describe three algorithms to determine the stable, semistable, and torus-polystable loci of the GIT quotient of a projective variety by a reductive group. The algorithms are efficient when the group is semisimple. By using an implementa…
View article: Some singular curves in Mukai's model of $\overline{M}_7$
Some singular curves in Mukai's model of $\overline{M}_7$ Open
Mukai showed that the GIT quotient $\operatorname{Gr}(7,16) /\!/ \operatorname{Spin}(10)$ is a birational model of the moduli space of Deligne-Mumford stable genus 7 curves $\overline{M}_7$. The key observation is that a general smooth gen…
View article: Modelling elevator traffic with social distancing in a university classroom building
Modelling elevator traffic with social distancing in a university classroom building Open
Social distancing standards implemented during the COVID-19 pandemic may have negative effects on vertical traffic. We describe a model and use it to predict the elevator traffic under social distancing in a university classroom building, …
View article: Software for computing conformal block divisorson M0,n
Software for computing conformal block divisorson M0,n Open
We introduce the packages LieTypes.m2and ConformalBlocks.m2for Macaulay2.LieTypes.m2contains basic types for working with Lie algebras and Lie algebra modules.ConformalBlocks.m2computes ranks and first Chern classes of vector bundles of co…
View article: Equations of Riemann surfaces with automorphisms
Equations of Riemann surfaces with automorphisms Open
We present an algorithm for computing equations of canonically embedded Riemann surfaces with automorphisms. A variant of this algorithm with many heuristic improvements is used to produce equations of Riemann surfaces $X$ with large autom…
View article: PD‐L1 expression in non‐small cell lung carcinoma: Comparison among cytology, small biopsy, and surgical resection specimens
PD‐L1 expression in non‐small cell lung carcinoma: Comparison among cytology, small biopsy, and surgical resection specimens Open
BACKGROUND One immunotherapeutic agent for patients with advanced non‐small cell lung carcinoma, pembrolizumab, has a companion immunohistochemistry (IHC)‐based assay that predicts response by quantifying programmed death‐ligand 1 (PD‐L1) …
View article: On the $S_n$-invariant F-conjecture
On the $S_n$-invariant F-conjecture Open
By using classical invariant theory, we reduce the $S_{n}$-invariant F-conjecture to a feasibility problem in polyhedral geometry. We show by computer that for $n \le 19$, every integral $S_{n}$-invariant F-nef divisor on the moduli space …