A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Formally proves machine learning for simple classifiers.
GPT-f uses language models to find new proofs in formal math.
Formalizes synthetic differential geometry in Lean.
Transformed geometry into algebra to prove Pick's theorem efficiently.
Formally verifies fairness and uniformity in financial market trades.
Formalizes vNM utility theorem using Lean 4, proving existence and uniqueness.
Survey on finite dimensional Lie groups over real numbers.
Proof of boundedness of quasimorphisms for certain Lie groups.
Direct proof of Alexander polynomial scaling for L-shaped representations.
New IRL algorithm for continuous state spaces with formal guarantees.
We formalize and verify double auctions for multiple-quantity trades.
We give a proof of Kontsevich's formality theorem for a general manifold using Fedosov resolutions of algebras of polydifferential operators and polyvector fields. The main advantage of our construction of the formality quasi-isomorphism is that it is based on the use of covariant tensors unlike Kontsevich's original p…
The isotropy action on certain symmetric spaces is shown to be equivariantly formal.
We introduce a formal framework for analyzing trades in financial markets. An exchange is where multiple buyers and sellers participate to trade. These days, all big exchanges use computer algorithms that implement double sided auctions to match buy and sell requests and these algorithms must abide by certain regulator…
Algebraic treatment of connection reduction over a special disc.
In this paper we pursue the study of formal geometric quantization of non-compact Hamiltonian manifolds. Our main result is the proof that two quantization process coincide. This fact was obtained by Ma and Zhang in the preprint arXiv:0812.3989 by completely different means.
Simple proof shows forecasts can be calibrated in a few periods.
We present an original theorem in auction theory: it specifies general conditions under which the sum of the payments of all bidders is necessarily not identically zero, and more generally not constant. Moreover, it explicitly supplies a construction for a finite minimal set of possible bids on which such a sum is not …
Formal methods verify continuous auctions at exchanges.
We prove the formality and the evenness of odd-degree Betti numbers for compact Kähler orbifolds, by adapting the classical proofs for Kähler manifolds. As a consequence, we obtain examples of symplectic orbifolds not admitting any Kähler orbifold structure. We also review the known examples of non-formal simply connec…
This paper explores formal verification for autonomous systems, identifying limitations and proposing improvements.
In this work we analyze the behavior of Massey products of closed manifolds under the blow-up construction. The results obtained in the article are applied to the problem of constructing closed symplectic non-formal manifolds. The proofs use Thom spaces as an important technical tool. This application of Thom spaces is…
This expository paper contains a detailed introduction to some important works concerning the Gauss-Bonnet-Chern theorem. The study of this theorem has a long history dating back to Gauss's Theorema Egregium (Latin: Remarkable Theorem) and culminated in Chern's groundbreaking work [14] in 1944, which is a deep and wond…
This paper autoformalizes Euclidean geometry using LLMs and theorem provers.
Symplectic forms from two phase spaces are proven equivalent.
We formalize in the proof assistant Isabelle essential basic notions and results in financial mathematics. We provide generic formal definitions of concepts such as markets, portfolios, derivative products, arbitrages or fair prices, and we show that, under the usual no-arbitrage condition, the existence of a replicati…
Technical proofs for Radon-Nikodym derivative identities.
We recall the notions of Frölicher and diffeological spaces and we build regular Frölicher Lie groups and Lie algebras of formal pseudo-differential operators in one independent variable. Combining these constructions with a smooth version of the Mulase factorization of infinite dimensional groups based on formal pseud…
This research simplifies verification of machine learning systems using reparameterization.
A conjecture about rational curves' formal principle and convergence proved for Goursat type families.
Paper formalizes multi-dimensional FSD using geometric methods.
In this short note we prove an equivariant version of the formality of multidiffirential operators for a proper Lie group action. More precisely, we show that the equivariant Hochschild-Kostant-Rosenberg quasi-isomorphism between the cohomology of the equivariant multidifferential operators and the complex of equivaria…
Develops calculus on Wasserstein spaces for Riemannian manifolds.
In this paper, we introduce a system called GamePad that can be used to explore the application of machine learning methods to theorem proving in the Coq proof assistant. Interactive theorem provers such as Coq enable users to construct machine-checkable proofs in a step-by-step manner. Hence, they provide an opportuni…
Obstruction theory for complex bigraded differential algebras.
Humans prove theorems by relying on substantial high-level reasoning and problem-specific insights. Proof assistants offer a formalism that resembles human mathematical reasoning, representing theorems in higher-order logic and proofs as high-level tactics. However, human experts have to construct proofs manually by en…
Lean 4 library formalizes mathematical finance, verifying over 200 theorems.
In this article, we first describe a normal form of real-analytic, Levi-nondegenerate submanifolds of of codimension d 1 under the action of formal biholomorphisms, that is, of perturbations of Levi-nondegenerate hyperquadrics. We give a sufficient condition on the formal normal form that ensures that the n…
Lean 4 library formalizes mathematical finance, verifying over 200 theorems.
Deep neural networks are proven universally powerful using Koopman operator.
For an oriented 2-dimensional manifold of genus with boundary components the space carries the Goldman-Turaev Lie bialgebra structure defined in terms of intersections and self-intersections of curves. Its associated graded (under the natural filtratio…
In this paper, we describe a canopolis (i.e. categorified planar algebra) formalism for Khovanov and Rozansky's link homology theory. We show how this allows us to organize simplifications in the matrix factorizations appearing in their theory. In particular, it will put the equivalence of the original definition of Kh…
New method selects facts in proofs using stateful recurrent neural networks.
We construct a lagrangian geometric formulation for first-order field theories using the canonical structures of first-order jet bundles, which are taken as the phase spaces of the systems in consideration. First of all, we construct all the geometric structures associated with a first-order jet bundle and, using them,…
Self-supervised skip-tree training improves mathematical reasoning in language models.
We establish that Hitchin's connection exist for any rigid holomorphic family of Kahler structures on any compact pre-quantizable symplectic manifold which satisfies certain simple topological constraints. Using Toeplitz operators we prove that Hitchin's connection induces a unique formal connection on smooth functions…
Paper formalizes Simon's satisficing through FFSD, proving its equivalence to expected utility theory.
Using Quillen's superconnection formalism we give a new "twisted" approach to the rational Gromov-Lawson-Rosenberg (GLR) conjecture on topological obstructions to the existence of Riemannian metrics of positive scalar curvature on compact spin manifolds. In particular, we present a short proof of the rational GLR conje…