The classical version of Bézout's Theorem gives an integer-valued count of the intersection
points of hypersurfaces in projective space over an algebraically closed field. Using work of …

We provide a geometric interpretation of the local contribution of a line to the count of lines
on a quintic threefold over a field k of characteristic not equal to 2, that is, we define the type …

We prove that both the local and global 𝔸 1-degree of an endomorphism of affine space can
be computed in terms of the multivariate Bézoutian. In particular, we show that the Bézoutian …

We prove that the local A 1-degree of a polynomial function at an isolated zero with finite
separable residue field is given by the trace of the local A1-degree over the residue field …

We explore extensions of tropical methods to arithmetic enumerative problems such as A 1-
enumeration with values in the Grothendieck–Witt ring and rationality over Henselian valued …

Smooth algebraic plane quartics over algebraically closed fields of characteristic different
than two have 28 bitangent lines. Their tropical counterparts often have infinitely many …

Recently, the first and third author proved a correspondence theorem which recovers the
Levine-Welschinger invariants of toric del Pezzo surfaces as a count of tropical curves …

Over the complex numbers, there are 92 plane conics meeting 8 general lines in projective 3-
space. Using the Euler number and local degree from motivic homotopy theory, we give an …

We compare two partitions of real bitangents to smooth plane quartics into sets of 4: one
coming from the closures of connected components of the avoidance locus and another …

We study real bitangents of real algebraic plane curves from two perspectives. We first show
that there exists a signed count of such bitangents that only depends on the real topological …