Concept
Derived algebraic geometry
Publications associées (45)
Unlabeled Principal Component Analysis and Matrix Completion
We introduce robust principal component analysis from a data matrix in which the entries of its columns have been corrupted by permutations, termed Unlabeled Principal Component Analysis (UPCA). Using algebraic geometry, we establish that UPCA is a well-de ...
Microtome Publ2024A Hopf algebra model for Dwyer's tame spaces
In this thesis, we give a modern treatment of Dwyer's tame homotopy theory using the language of -categories.We introduce the notion of tame spectra and show it has a concrete algebraic description.We then carry out a study of -operads and ...
EPFL2022Computational tools for twisted topological Hochschild homology of equivariant spectra
Kathryn Hess Bellwald, Inbar Klang
Twisted topological Hochschild homology of Cn-equivariant spectra was introduced by Angeltveit, Blumberg, Gerhardt, Hill, Lawson, and Mandell, building on the work of Hill, Hopkins, and Ravenel on norms in equivariant homotopy theory. In this paper we intr ...
ELSEVIER2022Algebraic Homotopy Interleaving Distance
The theory of persistence, which arises from topological data analysis, has been intensively studied in the one-parameter case both theoretically and in its applications. However, its extension to the multi-parameter case raises numerous difficulties, wher ...
SPRINGER INTERNATIONAL PUBLISHING AG2021MATHICSE Technical Report : Analytical and numerical study of a modified cell problem for the numerical homogenization of multiscale random fields
Assyr Abdulle, Doghonay Arjmand, Edoardo Paganoni
A central question in numerical homogenization of partial differential equations with multiscale coefficients is the accurate computation of effective quantities, such as the homogenized coefficients. Computing homogenized coefficients requires solving loc ...
EPFL2020Adaptive Gradient Descent without Descent
We present a strikingly simple proof that two rules are sufficient to automate gradient descent: 1) don’t increase the stepsize too fast and 2) don’t overstep the local curvature. No need for functional values, no line search, no information about the func ...
2020