Zachary Lihn

activity

20232026

collaborators

6 papers

math.DG2026

Tetrahedral points and classification of Almgren-minimizing sets in $R^{3}$

Michele Caselli, Zachary Lihn

We prove that a two-dimensional Almgren-minimizing set in three dimensions which is sufficiently close in Hausdorff distance to a tetrahedral cone contains an interior tetrahedral…

math.DG2026

$L^{2}$ Curvature Bounds for Area-Minimizing Currents Mod(2)

Zachary Lihn

We prove \emph{a priori} interior $L^{2}$ bounds for the second fundamental form of area-minimizing currents modulo $2$ in every dimension $n \geq 2$ and arbitrary codimension. The bo…

math.DG2026

Stationary varifolds with singularities II

Camillo De Lellis, Jonas Hirsch, Zachary Lihn +1

For every dimension $m \geq 3$ , we show the existence of an open set $U \subset R^{m + 1}$ , a smooth Riemannian metric $g$ on it, and an integral $m$ -dimensional stationary var…

math.AG2024

Intersections of Real Symmetric Hypersurfaces

Samuel Lidz, Zachary Lihn, Adam Melrod

We prove a symmetric version of Bézout's theorem. More precisely, we show that the symmetric orbit type of a transverse intersection of complex symmetric hypersurfaces in projectiv…

math.QA2023

Automata and one-dimensional TQFTs with defects

Paul Gustafson, Mee Seong Im, Remy Kaldawy +2

This paper explains how any nondeterministic automaton for a regular language $L$ gives rise to a one-dimensional oriented Topological Quantum Field Theory (TQFT) with inner endpoi…

math.AG2023

Realizing a Fake Projective Plane as a Degree 25 Surface in $P^{5}$

Lev Borisov, Zachary Lihn

Fake projective planes are smooth complex surfaces of general type with Betti numbers equal to that of the usual projective plane. Recent explicit constructions of fake projective…

Tetrahedral points and classification of Almgren-minimizing sets in R3

L2 Curvature Bounds for Area-Minimizing Currents Mod(2)

Stationary varifolds with singularities II

Intersections of Real Symmetric Hypersurfaces

Automata and one-dimensional TQFTs with defects

Realizing a Fake Projective Plane as a Degree 25 Surface in P5

Tetrahedral points and classification of Almgren-minimizing sets in $R^{3}$

$L^{2}$ Curvature Bounds for Area-Minimizing Currents Mod(2)

Realizing a Fake Projective Plane as a Degree 25 Surface in $P^{5}$