Varesco, M Voisin, C
Published in
Milan journal of mathematics

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 manifold and its Kuga-Satake variety has been proved to be algebraic. We then turn to recent work of O'Grady and Markma...

Bottini, Alessio
Published in
Milan journal of mathematics

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 describe one irreducible component of the rational cohomology in the case of a compact hyperkähler manifold. © The ...

Beckmann, T
Published in
Milan journal of mathematics

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 invariant. Applications to the action of derived equivalences on cohomology and to the study of their Hodge structure...

Friedrich, Manuel Seitz, Manuel Stefanelli, Ulisse
Published in
Milan Journal of Mathematics

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 orientations of the squares and that these patterns are periodic and one-dimensional. In contrast to the flat case, the...

Huybrechts, D Mauri, M
Published in
Milan journal of mathematics

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 discussion by additional observations. © The Author(s) 2022.

Burger, M. Engl, H. W. Leitao, A. Markowich, P. A.
Published in
Milan Journal of Mathematics

This paper is devoted to the investigation of inverse problems related to stationary drift-diffusion equations modeling semiconductor devices. In this context we analyze several identification problems corresponding to different types of measurements, where the parameter to be reconstructed is an inhomogeneity in the PDE model (doping profile). For...

van Gennip, Yves
Published in
Milan Journal of Mathematics

The graph Merriman–Bence–Osher scheme produces, starting from an initial node subset, a sequence of node sets obtained by iteratively applying graph diffusion and thresholding to the characteristic (or indicator) function of the node subsets. One result in [14] gives sufficient conditions on the diffusion time to ensure that the set membership of a...

Leuyacc, Yony R. Santaria Soares, Sergio H. Monari
Published in
Milan Journal of Mathematics

We are interested in finding nontrivial solutions for a Hamiltonian elliptic system in dimension two involving a potential function which can be coercive and nonlinearities that have maximal growth with respect to the Trudinger–Moser inequality. To establish the existence of solutions, we use variational methods combined with Trudinger–Moser type i...

Da Prato, Giuseppe Lunardi, Alessandra Tubaro, Luciano
Published in
Milan Journal of Mathematics

We prove that the law of the minimum m:=mint∈[0,1]ξ(t)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${m := {\rm min}_{t\in[0,1]}\xi(t)}$$\end{document} of the solution...

Marino, Giuseppe Muglia, Luigi
Published in
Milan Journal of Mathematics

Let C be a closed, convex and nonempty subset of a Banach space X. Let T:C→X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${T : C \rightarrow X}$$\end{document} be a n...