Concept

Ring (mathematics)

Related publications (120)

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Generic direct summands of tensor products for simple algebraic groups and quantum groups at roots of unity

Jonathan Gruber

Let G be either a simple linear algebraic group over an algebraically closed field of characteristic l>0 or a quantum group at an l-th root of unity. The category Rep(G) of finite-dimensional G-modules is non-semisimple. In this thesis, we develop new tech ...

EPFL2022

Quasi-Global Momentum: Accelerating Decentralized Deep Learning on Heterogeneous Data

Martin Jaggi, Sebastian Urban Stich, Tao Lin, Sai Praneeth Reddy Karimireddy

Decentralized training of deep learning models is a key element for enabling data privacy and on-device learning over networks. In realistic learning scenarios, the presence of heterogeneity across different clients' local datasets poses an optimization ch ...

JMLR-JOURNAL MACHINE LEARNING RESEARCH2021

Spherical birational sheets in reductive groups

Filippo Ambrosio

We classify the spherical birational sheets in a complex simple simply-connected algebraic group. We use the classification to show that, when G is a connected reductive complex algebraic group with simply-connected derived subgroup, two conjugacy classes ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2021

Realizing doubles: a conjugation zoo

Jérôme Scherer

Conjugation spaces are topological spaces equipped with an involution such that their fixed points have the same mod 2 cohomology (as a graded vector space, a ring and even an unstable algebra) but with all degrees divided by two, generalizing the classica ...

CAMBRIDGE UNIV PRESS2021

Variants of Homomorphism Polynomials Complete for Algebraic Complexity Classes

Aditya Vardhan Varre

We present polynomial families complete for the well-studied algebraic complexity classes VF, VBP, VP, and VNP. The polynomial families are based on the homomorphism polynomials studied in the recent works of Durand et al. (2014) and Mahajan et al. (2018). ...

ASSOC COMPUTING MACHINERY2021

On the stress tensor light-ray operator algebra

Grégoire Olivier Mathys, Matthew Thomas Walters, Alexandre Mathieu Frédéric Belin

We study correlation functions involving generalized ANEC operators of the form integral dx-x-n+2T--x -> in four dimensions. We compute two, three, and ...

2021

Ring a ring o' pulses

Quantum cascade lasers are bright and compact semiconductor lasers that emit light in the mid- to far-infrared spectral region. The use of a closed ring cavity has now set them on the path towards ultrafast pulses. ...

NATURE PUBLISHING GROUP2020

Synthetic Studies toward Amanita Phalloides Toxins

Philipp Georg Werner Seeberger

Amatoxins are ribosomally synthesized and post-translationally modified bicyclic octapeptides biosynthesized by the deadly basidiomycete fungus Amanita phalloides. Amongst this group, alpha-amanitin is the most widely known toxin and is currently under inv ...

EPFL2020

Restriction of 3D arithmetic Laplace eigenfunctions to a plane

We consider a random Gaussian ensemble of Laplace eigenfunctions on the 3D torus, and investigate the 1-dimensional Hausdorff measure ('length') of nodal intersections against a smooth 2-dimensional toral sub-manifold ('surface'). A prior result of ours pr ...

2020

Freestanding Silicon Photonic Ring and Disk Resonators

Niels Quack, Hamed Sattari, Alain Yuji Takabayashi, Yu Zhang

We report freestanding silicon photonic ring and disk resonators fabricated in a simplified silicon photonics process based on IMEC's iSiPP5OG standard platform that have been released by a custom MEMS post-processing step. Experimental results show high o ...

IEEE2019