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Homological methods, representation theory, and cluster algebras
CRM Short Courses, 2018 This text presents six mini-courses, all devoted to interactions between representation theory of algebras, homological algebra, and the new ever-expanding theory of cluster algebras.
Assem, Ibrahim, Trepode, Sonia
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Hodge theory-based biomolecular data analysis. [PDF]
Sci Rep, 2022 Hodge theory reveals the deep intrinsic relations of differential forms and provides a bridge between differential geometry, algebraic topology, and functional analysis.
Wei RKJ, Wee J, Laurent VE, Xia K.
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Geometric and homological methods in group theory: constructing small group resolutions [PDF]
, 2011 Given two groups K and H for which we have the free crossed resolutions, B* --> K and C* --> H respectively. Our aim is to construct a free crossed resolution, A* --> G, by way of induction on the degree n, for any semidirect product G = K x H.\ud First we show how to find a set Z1 of generators for the free group A1 and the corresponding unique ...
Gill, Olivia Jo
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Ergodic theoretic methods in group homology: a minicourse on l2-Betti numbers in group theory
, 2020 This book offers a concise introduction to ergodic methods in group homology, with a particular focus on the computation of L2-Betti numbers. Group homology integrates group actions into homological structure.
Löh, Clara
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Twisted Isospectrality, Homological Wideness, and Isometry [PDF]
, 2023 The question of reconstructing a geometric shape from spectra of operators (such as the Laplace operator) is decades old and an active area of research in mathematics and mathematical physics.
Peyerimhoff, Norbert +1 more
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Dieudonné theory for Faltings' strict ϭ-modules [PDF]
, 2005 The theory of group schemes and their liftings to mixed characteristic valuation rings is well-developed. In [Fal02], a new equi-characteristic analogue of group schemes, known as group schemes with strict ๕-action, or strict ๕-modules, was proposed and ...
Gibbons, William
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, 2007 We show that every fusion system (saturated or not) on a p-group S is equal to the fusion system associated to a discrete group G containing S as a subgroup and such that every finite subgroup of G is conjugate to a subgroup of ...
Stancu, Radu, Leary, Ian J.
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The homological functors of a bieberbach group of dimension four with dihedral point group of order eight [PDF]
, 2014 A Bieberbach group is a torsion free crystallographic group. It is an extension of a free abelian group of finite rank by a finite point group. The homological functors are originated in homotopy theory.
Mohammad, Siti Afiqah
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