176 citations · 512 across the 54 of their papers we have counts for
57 papers
Hierarchical Reinforcement Learning for Sparse-Reward Search in Commutative Algebra
Giorgi Butbaia, Paul Orland, Coco Huang +7
Applying machine learning techniques to solving long-standing mathematical conjectures can be particularly challenging due to their extreme reward sparsity. As an illustrative exam…
Syzygies of the residue field over Golod rings
Doan Trung Cuong, Hailong Dao, David Eisenbud +3
Let be a Golod ring. We show a recurrent formula for high syzygies of interms of previous ones. In the case of embedding dimension at most , we provided complete d…
Hyperelliptic curves and Ulrich sheaves on the complete intersection of two quadrics
David Eisenbud, Frank-Olaf Schreyer
Using the connection between hyperelliptic curves, Clifford algebras, and complete intersections of two quadrics, we describe Ulrich bundles on and construct some of minima…
Burch index, summands of syzygies and linearity in resolutions
Hailong Dao, David Eisenbud
The Burch index is a new invariant of a local ring whose positivity implies a kind of linearity in resolutions of -modules. For example, if has depth zero and Burch inde…
Residual Intersections of Determinantal Ideals
David Eisenbud, Bernd Ulrich
Schemes defined by residual intersections have been extensively studied in the case when they are Cohen-Macaulay, but this is a very restrictive condition. In this paper we make th…
Linearity of Free Resolutions of Monomial Ideals
Hailong Dao, David Eisenbud
We study monomial ideals with linear presentation or partially linear resolution. We give combinatorial characterizations of linear presentation for square-free ideals of degree 3,…