23 citations · 77 across the 9 of their papers we have counts for
10 papers
Humanity's Last Exam
Long Phan, Alice Gatti, Ziwen Han +1168
Benchmarks are important tools for tracking the rapid advancements in large language model (LLM) capabilities. However, benchmarks are not keeping pace in difficulty: LLMs now achi…
A construction of -manifolds from K3 surfaces with a -action
Frank Reidegeld
A product of a K3 surface and a flat 3-dimensional torus is a manifold with holonomy . Since is a subgroup of , carries a torsion-free $…
K3 surfaces with a pair of commuting non-symplectic involutions
Frank Reidegeld
We study K3 surfaces with a pair of commuting involutions that are non-symplectic with respect to two anti-commuting complex structures that are determined by a hyper-Kähler metric…
-orbifolds from K3 surfaces with ADE-singularities
Frank Reidegeld
We construct compact -orbifolds with ADE-singularities that carry exactly one parallel spinor. Our examples are related to certain quotients of that h…
K3 surfaces with non-symplectic automorphisms of order three and Calabi-Yau orbifolds
Frank Reidegeld
Let S be a K3 surface that admits a non-symplectic automorphism of order 3. We divide by where is an automorphism of order 3 of $\mathbb{P…
G2-manifolds from K3 surfaces with non-symplectic automorphisms
Max Pumperla, Frank Reidegeld
We show that K3 surfaces with non-symplectic automorphisms of prime order can be used to construct new compact irreducible G2-manifolds. This technique was carried out in detail by…
Exceptional holonomy on vector bundles with two-dimensional fibers
Frank Reidegeld
An SU(3)- or SU(1,2)-structure on a 6-dimensional manifold N^6 can be defined as a pair of a 2-form omega and a 3-form rho. We prove that any analytic SU(3)- or SU(1,2)-structure o…
Exceptional holonomy and Einstein metrics constructed from Aloff-Wallach spaces
Frank Reidegeld
We investigate cohomogeneity-one metrics whose principal orbit is an Aloff-Wallach space SU(3)/U(1). In particular, we are interested in metrics whose holonomy is contained in Spin…
Special cohomogeneity one metrics with Q^111 or M^110 as principal orbit
Frank Reidegeld
We classify all cohomogeneity one manifolds with principal orbit Q^111=SU(2)^3/U(1)^2 or M^110=(SU(3) x SU(2))/(SU(2) x U(1)) whose holonomy is contained in Spin(7). Various metric…
Spaces admitting homogeneous G2-structures
Frank Reidegeld
We classify all seven-dimensional spaces which admit a homogeneous cosymplectic G2-structure. The motivation for this classification is that each of these spaces is a possible prin…