7 papers
Structure-Adaptive Tree Field Integrators
Millend Roy, Soham Samal, Ivan Zelich +1
We present a new class of near-linear algorithms for efficiently integrating general tensor fields defined on trees with distance dependent kernels, the Structure-Adaptive Tree Fie…
The Miracle of Flatness in Algebraic Geometry
Ivan Zelich
This thesis studies various aspects of flatness in algebraic geometry. We first study flatness in the context of semi-rings. We prove some discreteness results for a derived groupi…
Affineness of the maximal étale locus
Ivan Zelich
In this paper we will prove a strong version of the celebrated purity of the ramification locus theorem in algebraic geometry. Our key input is a Tor-independence result for global…
Indivisible Sequences and Descendability
Ivan Zelich
We introduce the notion of indivisible sequences and show that to any indivisible sequence we can associate faithfully flat ring maps that are not de…
Faithfully flat ring maps are not descendable
Ivan Zelich
We construct a faithfully flat algebra over the infinite polynomial ring on an algebraically closed field that is not descendable.
Almost Witt Vectors
Ivan Zelich
Our main goal in this paper is to prove results for Witt vectors in the almost category. We finish with an application to almost purity, in particular offering a new proof for rank…
Triangles with Vertices Equidistant to a Pedal Triangle
Xuming Liang, Ivan Zelich
In this paper, we present a synthetic solution to a geometric open problem involving the radical axis of two strangely defined circumcircles. The solution encapsulates two generali…