Certifying zeros of polynomial systems using interval arithmetic
We establish interval arithmetic as a practical tool for certification in numerical algebraic
geometry. Our software HomotopyContinuation. jl now has a built-in function certify, which …
geometry. Our software HomotopyContinuation. jl now has a built-in function certify, which …
[PDF][PDF] An invitation to positive geometries
T Lam - arXiv preprint arXiv:2208.05407, 2022 - arxiv.org
arXiv:2208.05407v1 [math.CO] 10 Aug 2022 Page 1 AN INVITATION TO POSITIVE
GEOMETRIES THOMAS LAM Abstract. This short introduction to positive geometries, targeted …
GEOMETRIES THOMAS LAM Abstract. This short introduction to positive geometries, targeted …
Momentum amplituhedron for N= 6 Chern-Simons-matter Theory: Scattering amplitudes from configurations of points in Minkowski space
T Łukowski, J Stalknecht - Physical Review Letters, 2023 - APS
In this Letter, we define the Aharony-Bergman-Jafferis-Maldacena loop momentum
amplituhedron, which is a geometry encoding Aharony-Bergman-Jafferis-Maldacena planar …
amplituhedron, which is a geometry encoding Aharony-Bergman-Jafferis-Maldacena planar …
The Geometry of Cosmological Correlators
P Benincasa, G Dian - arXiv preprint arXiv:2401.05207, 2024 - arxiv.org
We provide a first principle definition of cosmological correlation functions for a large class of
scalar toy models in arbitrary FRW cosmologies, in terms of novel geometries we name {\it …
scalar toy models in arbitrary FRW cosmologies, in terms of novel geometries we name {\it …
Adjoints and Canonical Forms of Tree Amplituhedra
We consider semi-algebraic subsets of the Grassmannian of lines in three-space called tree
amplituhedra. These arise in the study of scattering amplitudes from particle physics. Our …
amplituhedra. These arise in the study of scattering amplitudes from particle physics. Our …
Lorentzian polynomials, Segre classes, and adjoint polynomials of convex polyhedral cones
P Aluffi - Advances in Mathematics, 2024 - Elsevier
We consider polynomials expressing the cohomology classes of subvarieties of products of
projective spaces, and limits of positive real multiples of such polynomials. We study the …
projective spaces, and limits of positive real multiples of such polynomials. We study the …
Explicit smooth real algebraic functions which may have both compact and non-compact preimages on smooth real algebraic manifolds
N Kitazawa - arXiv preprint arXiv:2304.02372, 2023 - arxiv.org
In our previous work, we have constructed explicit smooth real algebraic functions which
may have both compact and non-compact preimages on smooth real algebraic manifolds …
may have both compact and non-compact preimages on smooth real algebraic manifolds …
Natural real algebraic maps of non-positive codimensions with prescribed images whose boundaries consist of non-singular real algebraic hypersurfaces satisfying …
N Kitazawa - arXiv preprint arXiv:2303.10723, 2023 - arxiv.org
We present new real algebraic maps of non-positive codimensions with prescribed images
whose boundaries consist of explicit non-singular real algebraic hypersurfaces satisfying so …
whose boundaries consist of explicit non-singular real algebraic hypersurfaces satisfying so …