arXiv subjects

Jeonghoon So

Publications and source records attributed to Jeonghoon So.

4 recordsLinked to original sources

arXiv2026

Fundamental Groups of Genus-$0$ Quadratic Differential Strata via Exchange Graphs

We investigate how exchange-graph techniques can be used to study the topology of strata of meromorphic quadratic differentials. The exchange graph provides natural generators for the fundamental group. By extending the combinatorics of triangulations to weighted mixed-angulations, we generalise the familiar relations arising in the simple-zero case and introduce an additional relation that appears only around higher-order zeroes. In the genus-zero case with four singularities, we show that these relations suffice to give explicit presentations of the fundamental group.

math.GT↗

arXiv2023

A smooth compactification of spaces of stability conditions: the case of the $A_{n}$-quiver

We propose a notion of multi-scale stability conditions with the goal of providing a smooth compactification of the quotient of the space of projectivized Bridgeland stability conditions by the group of autoequivalence. For the case of the 3CY category associated with the $A_n$-quiver this goal is achieved by defining a topology and complex structure that relies on a plumbing construction. We compare this compactification to the multi-scale compactification of quadratic differentials and briefly indicate why even for the Kronecker quiver this notion needs refinement to provide a full compactification.

math.AG↗

arXiv2022

Quadratic differentials as stability conditions: collapsing subsurfaces

We introduce a new class of triangulated categories, which are Verdier quotients of three-Calabi-Yau categories from (decorated) marked surfaces, and show that its spaces of stability conditions can be identified with moduli spaces of framed quadratic differentials on Riemann surfaces with arbitrary order zeros and arbitrary higher order poles. A main tool in our proof is a comparison of two exchange graphs, obtained by tilting hearts in the quotient categories and by flipping mixed angulations associated with the quadratic differentials.

math.GT↗

arXiv2019

S-hypersimplices, pulling triangulations, and monotone paths

An $S$-hypersimplex for $S \subseteq \{0,1, \dots,d\}$ is the convex hull of all $0/1$-vectors of length $d$ with coordinate sum in $S$. These polytopes generalize the classical hypersimplices as well as cubes, crosspolytopes, and halfcubes. In this paper we study faces and dissections of $S$-hypersimplices. Moreover, we show that monotone path polytopes of $S$-hypersimplices yield all types of multipermutahedra. In analogy to cubes, we also show that the number of simplices in a pulling triangulation of a halfcube is independent of the pulling order.

math.CO↗