Related papers: $\tau$-tilting theory: a self-contained introducti…
Assume that $\D$ is a Krull-Schmidt, Hom-finite triangulated category with a Serre functor and a cluster-tilting object $T$. We introduce the notion of relative cluster tilting objects, and $T[1]$-cluster tilting objects in $\D$, which are…
In this paper, we develop differential twisted K-theory and define a twisted Chern character on twisted K-theory which depends on a choice of connection and curving on the twisting gerbe. We also establish the general Riemann-Roch theorem…
In this paper we describe some of the constructions of FJRW theory. We also briefly describe its relation to Saito-Givental theory via Landau-Ginzburg mirror symmetry and its relation to Gromov-Witten theory via the…
Let $B$ be the one-point extension algebra of $A$ by an $A$-module $X$. We proved that every support $\tau$-tilting $A$-module can be extended to be a support $\tau$-tilting $B$-module by two different ways. As a consequence, it is shown…
This paper provides a conceptual study of the twisting procedure, which amounts to create functorially new differential graded Lie algebras, associative algebras or operads (as well as their homotopy versions) from a Maurer--Cartan element.…
These notes provide a self-contained introduction to Lie algebroids, Lie-Rinehart algebras and their universal envelopes. This review is motivated by the speculation that higher-spin gauge symmetries should admit a natural formulation as…
The link between Tauberian theorems and large deviations is surveyed, with particular reference to regular variation.
In this paper, we extend the work of Pimentel et al. (2015) and propose an adjusted estimator of Kendall's $\tau$ for bivariate zero-inflated count data. We provide achievable lower and upper bounds of our proposed estimator and show its…
The higher APR tilting modules and higher BB tilting modules were introduced and studied in higher Auslander-Reiten theory. Our objective is to consider these tilting modules by the corresponding simple modules, and show that the tensor…
We give a generalization of the classical tilting theorem. We show that for a 2-term silting complex $\mathbf{P}$ in the bounded homotopy category $K^b(\mathop{\rm proj}\nolimits A)$ of finitely generated projective modules of a finite…
We prove an existence result for twisted K\"ahler-Einstein metrics, assuming an appropriate twisted K-stability condition. An improvement over earlier results is that certain non-negative twisting forms are allowed.
This paper has been withdrawn by the authors because it has been combined with "Higher Auslander Algebras Admitting Trivial Maximal Orthogonal Subcategories" (arXiv:0903.0761) together. Please see the new version of the latter paper for the…
This is an introduction to some recent developments in string theory and M theory. We try to concentrate on the main physical aspects, and often leave more technical details to the original literature.
We present a self-contained development of the Weierstrass theory of those analytic functions (single-valued or multiform) which admit an algebraic addition theorem. We review the history of the theory and present detailed proofs of the…
The author has recognized an error in the section of the text regarding induced Compton scattering. The paper has been withdrawn pending a revision to this section.
We consider the topological theory of Witten type for gauge differential p-forms. It is shown that some topological invariants such as linking numbers appear under quantization of this theory. The non-abelian generalization of the model is…
This book is an introduction to the nascent field of Fourier analysis on polytopes, and cones. There is a rapidly growing number of applications of these methods, so it is appropriate to invite students, as well as professionals, to the…
We simplify Hitchin's description of SU(2)-invariant self-dual Einstein metrics, making use of the tau-function of related four-pole Schlesinger system.
This an expository article on Givental's axiomatic Gromov--Witten theory and some of its applications.
We provide a proof of the Alpern multi-tower theorem for Z^d actions. We reformulate the theorem as a problem of measurably tiling orbits of a Z^d action by a collection of rectangles whose corresponding sides have no non-trivial common…