Publications (32)
Prompting open-source and commercial language models for grammatical error correction of English learner text
Christopher Davis, Andrew Caines, Ãistein Andersen +6
Thanks to recent advances in generative AI, we are able to prompt large language models (LLMs) to produce texts which are fluent and grammatical. In addition, it has been shown tha…
Explicit points on and related character sums
Christopher Davis, Tommy Occhipinti
Let denote a finite field of characteristic and let . Let denote the elliptic curve over the function field defined b…
Almost purity and overconvergent Witt vectors
Christopher Davis, Kiran S. Kedlaya
In a previous paper, we stated a general almost purity theorem in the style of Faltings: if R is a ring for which the Frobenius maps on finite p-typical Witt vectors over R are sur…
On the de Rham-Witt complex over perfectoid rings
Christopher Davis, Irakli Patchkoria
Fix an odd prime . The results in this paper are modeled after work of Hesselholt and Hesselholt-Madsen on the -typical absolute de Rham-Witt complex in mixed characteristic.…
Astrometry and Occultation predictions to Trans-Neptunian and Centaur Objects observed within the Dark Energy Survey
Martin Banda-Huarca, Julio Camargo, Josselin Desmars +59
Transneptunian objects (TNOs) are a source of invaluable information to access the history and evolution of the outer solar system. However, observing these faint objects is a diff…
Probing for targeted syntactic knowledge through grammatical error detection
Christopher Davis, Christopher Bryant, Andrew Caines +2
Targeted studies testing knowledge of subject-verb agreement (SVA) indicate that pre-trained language models encode syntactic information. We assert that if models robustly encode…
On the cyclic homology of certain universal differential graded algebras
Christopher Davis, Julius Frank, Irakli Patchkoria
Let be an odd prime and a -torsion-free commutative -algebra. We compute the periodic cyclic homology over of the universal differential graded alg…
On the Witt vector Frobenius
Christopher Davis, Kiran S. Kedlaya
We study the kernel and cokernel of the Frobenius map on the -typical Witt vectors of a commutative ring, not necessarily of characteristic . We give some equivalent conditio…
Benchmarking Deflection and Hallucination in Large Vision-Language Models
Nicholas Moratelli, Christopher Davis, Leonardo F. R. Ribeiro +2
Large Vision-Language Models (LVLMs) increasingly rely on retrieval to answer knowledge-intensive multimodal questions. Existing benchmarks overlook conflicts between visual and te…
On the application of Large Language Models for language teaching and assessment technology
Andrew Caines, Luca Benedetto, Shiva Taslimipoor +12
The recent release of very large language models such as PaLM and GPT-4 has made an unprecedented impact in the popular media and public consciousness, giving rise to a mixture of…
Reflective Groupwork for Introductory Proof-Writing Courses
Jennifer Pi, Christopher Davis, Yasmeen Baki +1
We discuss two proof evaluation activities meant to promote the acquisition of learning behaviors of professional mathematics within an introductory undergraduate proof-writing cou…
CLIMB: Curriculum Learning for Infant-inspired Model Building
Richard Diehl Martinez, Zebulon Goriely, Hope McGovern +4
We describe our team's contribution to the STRICT-SMALL track of the BabyLM Challenge. The challenge requires training a language model from scratch using only a relatively small t…
Which finite simple groups are unit groups?
Christopher Davis, Tommy Occhipinti
We prove that if is a finite simple group which is the unit group of a ring, then is isomorphic to either (a) a cyclic group of order 2; (b) a cyclic group of prime order $…
Which alternating and symmetric groups are unit groups?
Christopher Davis, Tommy Occhipinti
We prove there is no ring with unit group isomorphic to S_n for n \geq 5 and that there is no ring with unit group isomorphic to A_n for n \geq 5, n \neq 8. We give examples of rin…
Discovery of a Candidate Binary Supermassive Black Hole in a Periodic Quasar from Circumbinary Accretion Variability
Wei-Ting Liao, Yu-Ching Chen, Xin Liu +68
Binary supermassive black holes (BSBHs) are expected to be a generic byproduct from hierarchical galaxy formation. The final coalescence of BSBHs is thought to be the loudest gravi…
A characterization of strictly APF extensions
Bryden Cais, Christopher Davis, Jonathan Lubin
Let K denote a finite extension of Qp. We give necessary and sufficient conditions for an infinite totally wildly ramified extension L/K to be strictly APF in the sense of Fontaine…
Overconvergent Witt Vectors
Christopher Davis, Andreas Langer, Thomas Zink
Let A be a finitely generated algebra over a field K of characteristic p >0. We introduce a subring of the ring of Witt vectors W(A). We call it the ring of overconvergent Witt vec…
GaRAGe: A Benchmark with Grounding Annotations for RAG Evaluation
Ionut-Teodor Sorodoc, Leonardo F. R. Ribeiro, Rexhina Blloshmi +2
We present GaRAGe, a large RAG benchmark with human-curated long-form answers and annotations of each grounding passage, allowing a fine-grained evaluation of whether LLMs can iden…
Integral Monsky-Washnitzer cohomology and the overconvergent de Rham-Witt complex
Christopher Davis, David Zureick-Brown
In their paper which introduced Monsky-Washnitzer cohomology, Monsky and Washnitzer described conditions under which the definition can be adapted to give integral cohomology group…
The Amazon Nova Family of Models: Technical Report and Model Card
Amazon AGI, Aaron Langford, Aayush Shah +783
We present Amazon Nova, a new generation of state-of-the-art foundation models that deliver frontier intelligence and industry-leading price performance. Amazon Nova Pro is a highl…
On the p-typical de Rham-Witt complex over W(k)
Christopher Davis
Hesselholt and Madsen in [7] define and study the (absolute, p-typical) de Rham-Witt complex in mixed characteristic, where p is an odd prime. They give as an example an elementary…
Kinematics of SiO J=8-7 Emission towards the HH 212 Jet
Michihiro Takami, Shigehisa Takamuwa, Munetake Momose +5
We present SiO J=8-7 (347.3 GHz) observations towards HH 212 using the ASTE telescope. Our observations with a 22''-diameter beam show that the SiO emission is highly concentrated…
A Micro Molecular Bipolar Outflow From HL Tau
Michihiro Takami, Tracy L. Beck, Tae-Soo Pyo +2
We present detailed geometry and kinematics of the inner outflow toward HL Tau observed using Near Infrared Integral Field Spectograph (NIFS) at the Gemini-North 8-m Observatory. W…
Newton slopes for Artin-Schreier-Witt towers
Christopher Davis, Daqing Wan, Liang Xiao
We fix a monic polynomial over a finite field and consider the Artin-Schreier-Witt tower defined by ; this is a tower of curves $\cdots \to C_m \to…
VISTA Variables in the VÃa Láctea (VVV): Halfway Status and Results
Maren Hempel, Dante Minniti, István Dékány +89
The VISTA Variables in the VÃa Láctea (VVV) survey is one of six public ESO surveys, and is now in its 4th year of observing. Although far from being complete, the VVV survey has…
Survey of Gravitationally-lensed Objects in HSC Imaging (SuGOHI). VI. Crowdsourced lens finding with Space Warps
Alessandro Sonnenfeld, Aprajita Verma, Anupreeta More +19
Strong lenses are extremely useful probes of the distribution of matter on galaxy and cluster scales at cosmological distances, but are rare and difficult to find. The number of cu…
Totally Geodesic Seifert Surfaces in Hyperbolic Knot and Link Complements II
Colin Adams, Hanna Bennett, Christopher Davis +4
We generalize the results of [AS], finding large classes of totally geodesic Seifert surfaces in hyperbolic knot and link complements, each the lift of a rigid 2-orbifold embedded…
AutoOR: Scalably Post-training LLMs to Autoformalize Operations Research Problems
Sumeet Ramesh Motwani, Chuan Du, Aleksander Petrov +4
Optimization problems are central to decision-making in manufacturing, logistics, scheduling, and other industrial settings. Translating complicated descriptions of these problems…
Canonical Cohen rings for norm fields
Bryden Cais, Christopher Davis
Fix a finite extension and let be an infinite, strictly APF extension in the sense of Fontaine--Wintenberger. Let denote its associated norm field.…
SceneDiffuser: Efficient and Controllable Driving Simulation Initialization and Rollout
Chiyu Max Jiang, Yijing Bai, Andre Cornman +12
Realistic and interactive scene simulation is a key prerequisite for autonomous vehicle (AV) development. In this work, we present SceneDiffuser, a scene-level diffusion prior desi…
L-functions of p-adic characters
Christopher Davis, Daqing Wan
We define a p-adic character to be a continuous homomorphism from 1 + t\Fq[[t]] to \Zp^*. We use the ring of big Witt vectors over Fq to exhibit a bijection between p-adic characte…
The Buzzard Flock: Dark Energy Survey Synthetic Sky Catalogs
Joseph DeRose, Risa H. Wechsler, Matthew R. Becker +52
We present a suite of 18 synthetic sky catalogs designed to support science analysis of galaxies in the Dark Energy Survey Year 1 (DES Y1) data. For each catalog, we use a computat…