34 citations · 108 across the 17 of their papers we have counts for
23 papers
Hadwiger's classification theorem on the sphere via signed orthoscheme decompositions
Martin Lotz
We give an elementary and combinatorial proof of the spherical Hadwiger theorem, which states that every continuous, rotation-invariant valuation on the space of closed convex cone…
Monotone invariant valuations on convex cones
Martin Lotz
We classify the monotone $\SOn d$-invariant valuations, , on the space of all closed convex cones. They are precisely the linear combinations of the conic intrinsic volumes…
Khovanskii's Bezout-type Theorem for Pfaffian Functions: A Self-Contained Proof, and Applications
Martin Lotz, Abhiram Natarajan
We present a direct and self-contained proof of Khovanskii's Bezout-type bound for the number of nondegenerate solutions of a system of Pfaffian equations. We isolate the ingredien…
Tubular Neighbourhoods of Pfaffian Sets and Applications to Neural Networks
Paul Lezeau, Martin Lotz
We derive bounds for the volume of tubular neighbourhoods of smooth Pfaffian hypersurfaces, generalising known results for algebraic varieties. The bounds are given in terms of the…
Partitioning Theorems for Sets of Semi-Pfaffian Sets, with Applications
Martin Lotz, Abhiram Natarajan, Nicolai Vorobjov
We generalize the seminal polynomial partitioning theorems of Guth and Katz to a set of semi-Pfaffian sets. Specifically, given a set of -dimensional s…
Sharp phase transitions in Euclidean integral geometry
Martin Lotz, Joel A. Tropp
The intrinsic volumes of a convex body are fundamental invariants that capture information about the average volume of the projection of the convex body onto a random subspace of f…