相关论文: Exercises on derived categories, resolutions, and …

As suggested by the title, this paper is a survey of recent results and questions on the collection of computably enumerable sets under inclusion. This is not a broad survey but one focused on the author's and a few others' current…

We study the problem of learning permutation invariant representations that can capture "flexible" notions of containment. We formalize this problem via a measure theoretic definition of multisets, and obtain a theoretically-motivated…

The aim of this note is to clarify the relationship between Green's formula and the associativity of multiplication for derived Hall algebra in the sense of To\"{e}n (Duke Math J 135(3):587-615, 2006), Xiao and Xu (Duke Math J…

We give a statement on extension with estimates of convex functions defined on a linear subspace, inspired by similar extension results concerning metrics on positive line bundles

We investigate notions of support and cosupport for differential graded (DG) modules over DG algebras. We apply these notions to identify certain classes of derived functors that are able to detect triviality and isomorphisms in derived…

Primarily this paper presents an expository report on alternatives to the traditional methods of classifying representations of finite dimensional algebras. Some new results illustrating such alternatives for algebras with only finitely…

The main content of this paper is Lectures 5 and 6 that continue lecture notes [20]. Content of Lectures 1-4 of [20] is reviewed for the reader's convenience in sections 1-4, respectively. It is shown in Lecture 5 how residual parts of the…

Reinforcement learning (RL) agents make decisions using nothing but observations from the environment, and consequently, heavily rely on the representations of those observations. Though some recent breakthroughs have used vector-based…

We construct a fundamental theory of the derived category of non-finite bi-filtered complexes.

This is an overview of higher structural constructions in physics. The main motivations of our current attempt are as follows: (i) to provide a brief introduction to derived algebraic geometry, (ii) to understand how derived objects…

We consider recollements of derived categories of dg-algebras induced by self orthogonal compact objects obtaining a generalization of Rickard's Theorem. Specializing to the case of partial tilting modules over a ring, we extend the results…

We define quasi--locally presentable categories as big unions of coreflective subcategories which are locally presentable. Under appropriate hypotheses we prove a representability theorem for exact contravariant functors defined on a…

We propose a solution to the "curvature problem" from arXiv:1505.03698 and arXiv:0905.3845 for infinitesimal deformations. Let $k$ be a field, $A$ a dg algebra over $k$ and $A_n = A[t]/(t^{n+1})$ a cdg algebra over $R_n = k[t]/(t^{n+1})$,…

We define a fragment of monadic infinitary second-order logic corresponding to an abstract separation property. We use this to define the concept of a separation subclass. We use model theoretic techniques and games to show that separation…

We introduce a generalization of the Stirling numbers via symmetric functions involving two weight functions. The resulting extension unifies previously known Stirling-type sequences with known symmetric function forms, as well as other…

We show how one can do algebraic geometry with respect to the category of simplicial objects in an exact category. As a biproduct, we get a theory of derived analytic geometry.

This is a supplement to the article "Markov Chain Monte Carlo Based on Deterministic Transformations" available at http://arxiv.org/abs/1106.5850

We obtain similar types of conclusions as that of Br\"{u}ck [1] for two differential polynomials which in turn radically improve and generalize several existing results. Moreover, a number of examples have been exhibited to justify the…

We prove some general recursions for the numbers of representations of positive integers as a sum x+y, x in X, y in Y, where X,Y are increasing sequences. In particular, we obtain recursions for the number of the Goldbach, Lemoine-Levy,…

These are notes of a graduate course on representations of non-compact semisimple Lie groups given by the author at MIT.