Giovanni Bellettini,Shokhrukh Yu Kholmatov
Giovanni Bellettini
Motivated by a conjecture of De Giorgi, we consider the Almgren-Taylor-Wang scheme for mean curvature flow, where the volume penalization is replaced by a term of the form ∫ E Δ F f d F τ d x for f ranging in...
Remarks on Regularization by Noise, Convex Integration and Spontaneous Stochasticity [0.03%]
关于噪声正则化、凸积分和自发随机性的注记
Franco Flandoli,Marco Rehmeier
Franco Flandoli
This note is devoted to a discussion of the potential links and differences between three topics: regularization by noise, convex integration, spontaneous stochasticity. All of them deal with the effect on large scales of a small-scale pert...
Stefano Almi,Claudio D&#x;Eramo,Marco Morandotti et al.
Stefano Almi et al.
The well-posedness of a multi-population dynamical system with an entropy regularization and its convergence to a suitable mean-field approximation are proved, under a general set of assumptions. Under further assumptions on the evolution o...
The Looijenga-Lunts-Verbitsky Algebra and Verbitsky's Theorem [0.03%]
Looijenga-Lunts-Verbitsky 代数和Verbitsky定理
Alessio Bottini
Alessio Bottini
In these notes we review some basic facts about the LLV Lie algebra. It is a rational Lie algebra, introduced by Looijenga-Lunts and Verbitsky, acting on the rational cohomology of a compact Kähler manifold. We study its structure and desc...
Lagrangian Fibrations [0.03%]
拉格朗日纤维化
D Huybrechts,M Mauri
D Huybrechts
We review the theory of Lagrangian fibrations of hyperkähler manifolds as initiated by Matsushita. We also discuss more recent work of Shen-Yin and Harder-Li-Shen-Yin. Occasionally, we give alternative arguments and complement the discussi...
Hyper-Kähler Manifolds of Generalized Kummer Type and the Kuga-Satake Correspondence [0.03%]
广义Kummer型超Kähler流形与Kuga-Satake对应关系
M Varesco,C Voisin
M Varesco
We first describe the construction of the Kuga-Satake variety associated to a (polarized) weight-two Hodge structure of hyper-Kähler type. We describe the classical cases where the Kuga-Satake correspondence between a hyper-Kähler manifol...
T Beckmann
T Beckmann
We mostly review work of Taelman (Derived equivalences of hyperkähler varieties, 2019, arXiv:1906.08081) on derived categories of hyper-Kähler manifolds. We study the LLV algebra using polyvector fields to prove that it is a derived invar...
Manuel Friedrich,Manuel Seitz,Ulisse Stefanelli
Manuel Friedrich
Inspired by the modelization of 2D materials systems, we characterize arrangements of identical nonflat squares in 3D. We prove that the fine geometry of such arrangements is completely characterized in terms of patterns of mutual orientati...