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Aaron Chan

Aaron Chan appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

ResearcherUnclaimed source record
math.RTmath.COArtificial IntelligenceComputation and LanguageCryptography and Securitymath.RA

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Published work

8 published item(s)

preprint2026arXiv

LATTICE: Evaluating Decision Support Utility of Crypto Agents

We introduce LATTICE, a benchmark for evaluating the decision support utility of crypto agents in realistic user-facing scenarios. Prior crypto agent benchmarks mainly focus on reasoning-based or outcome-based evaluation, but do not assess agents' ability to assist user decision-making. LATTICE addresses this gap by: (1) defining six evaluation dimensions that capture key decision support properties; (2) proposing 16 task types that span the end-to-end crypto copilot workflow; and (3) using LLM judges to automatically score agent outputs based on these dimensions and tasks. Crucially, the dimensions and tasks are designed to be evaluable at scale using LLM judges, without relying on ground truth from expert annotators or external data sources. In lieu of these dependencies, LATTICE's LLM judge rubrics can be continually audited and updated given new dimensions, tasks, criteria, and human feedback, thus promoting reliable and extensible evaluation. While other benchmarks often compare foundation models sharing a generic agent framework, we use LATTICE to assess production-level agents used in actual crypto copilot products, reflecting the importance of orchestration and UI/UX design in determining agent quality. In this paper, we evaluate six real-world crypto copilots on 1,200 diverse queries and report breakdowns across dimensions, tasks, and query categories. Our experiments show that most of the tested copilots achieve comparable aggregate scores, but differ more significantly on dimension-level and task-level performance. This pattern suggests meaningful trade-offs in decision support quality: users with different priorities may be better served by different copilots than the aggregate rankings alone would indicate. To support reproducible research, we open-source all LATTICE code and data used in this paper.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Classifying torsion classes of gentle algebras

For a finite-dimensional gentle algebra, it is already known that the functorially finite torsion classes of its category of finite-dimensional modules can be classified using a combinatorial interpretation, called maximal non-crossing sets of strings, of the corresponding support $τ$-tilting module (or equivalently, two-term silting complexes). In the topological interpretation of gentle algebras via marked surfaces, such a set can be interpreted as a dissection (or partial triangulation), or equivalently, a lamination that does not contain a closed curve. We will refine this combinatorics, which gives us a classification of torsion classes in the category of finite length modules over a (possibly infinite-dimensional) gentle algebra. As a consequence, our result also unifies the functorially finite torsion class classification of finite-dimensional gentle algebras with certain classes of special biserial algebras - such as Brauer graph algebras.

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preprint2020arXiv

Irreducible representations of the symmetric groups from slash homologies of p-complexes

In the 40s, Mayer introduced a construction of (simplicial) $p$-complex by using the unsigned boundary map and taking coefficients of chains modulo $p$. We look at such a $p$-complex associated to an $(n-1)$-simplex; in which case, this is also a $p$-complex of representations of the symmetric group of rank $n$ - specifically, of permutation modules associated to two-row compositions. In this article, we calculate the so-called slash homology - a homology theory introduced by Khovanov and Qi - of such a $p$-complex. We show that every non-trivial slash homology group appears as an irreducible representation associated to two-row partitions, and how this calculation leads to a basis of these irreducible representations given by the so-called $p$-standard tableaux.

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preprint2020arXiv

On representation-finite gendo-symmetric algebras with only one non-injective projective module

Motivated by the relation between Schur algebra and the group algebra of a symmetric group, along with other similar examples in algebraic Lie theory, Min Fang and Steffen Koenig addressed some behaviour of the endomorphism algebra of a generator over a symmetric algebra, which they called gendo-symmetric algebra. Continuing this line of works, we classify in this article the representation-finite gendo-symmetric algebras that have at most one isomorphism class of indecomposable non-injective projective module. We also determine their almost ν-stable derived equivalence classes in the sense of Wei Hu and Changchang Xi. It turns out that a representative can be chosen as the quotient of a representation-finite symmetric algebra by the socle of a certain indecomposable projective module.

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preprint2016arXiv

On representation-finite gendo-symmetric biserial algebras

Gendo-symmetric algebras were introduced by Fang and Koenig as a generalisation of symmetric algebras. Namely, they are endomorphism rings of generators over a symmetric algebra. This article studies various algebraic and homological properties of representation-finite gendo-symmetric biserial algebras. We show that the associated symmetric algebras for these gendo-symmetric algebras are Brauer tree algebras, and classify the generators involved using Brauer tree combinatorics. We also study almost $ν$-stable derived equivalences, introduced by Hu and Xi, between representation-finite gendo-symmetric biserial algebras. We classify these algebras up to almost $ν$-stable derived equivalence by showing that the representative of each equivalence class can be chosen as a Brauer star with some additional combinatorics. We also calculate the dominant, global, and Gorenstein dimensions of these algebras. In particular, we found that representation-finite gendo-symmetric biserial algebras are always Iwanaga-Gorenstein algebras.

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preprint2014arXiv

Two-term tilting complexes and simple-minded systems of self-injective Nakayama algebras

We study the relation between simple-minded systems and two-term tilting complexes for self-injective Nakayama algebras. More precisely, we show that any simple-minded system of a self-injective Nakayama algebra is the image of the set of simple modules under a stable equivalence, which is given by the restriction of a standard derived equivalence induced by a two-term tilting complex. We achieve this by exploiting and connecting the mutation theories from the combinatorics of Brauer tree, configurations of stable translations quivers of type A, and triangulations of a punctured convex regular polygon.

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preprint2013arXiv

Simple-minded systems, configurations and mutations for representation-finite self-injective algebras

Simple-minded systems of objects in a stable module category are defined by common properties with the set of simple modules, whose images under stable equivalences do form simple-minded systems. Over a representation-finite self-injective algebra, it is shown that all simple-minded systems are images of simple modules under stable equivalences of Morita type, and that all simple-minded systems can be lifted to Nakayama-stable simple-minded collections in the derived category. In particular, all simple-minded systems can be obtained algorithmically using mutations.

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