Sven, who joined Teesside University in 2018, will be focusing on the 'hearts of karoubian categories', a project covering the areas of
homological algebra and functional analysis.
The lectures cover randomized numerical linear algebra, optimization algorithms for data analysis, introductory stochastic optimization, randomized methods for matrix computations, probabilistic methods for data science, and
homological algebra and data.
An Introduction to
Homological Algebra. Second Edition.
Stammbach, A Course in
Homological Algebra, Springer, Berlin, Germany, 1971.
Some notions of
homological algebra should be recalled from [3, 13], in order to formulate the next result.
He assumes students are familiar with
homological algebra, algebraic topology based on different forms, and de Rham cohomology.
We present here a synopsis of the results together with applications of this beautiful interplay between combinatorial topology and
homological algebra.
Singer, "The transfer in
homological algebra," Mathematische Zeitschrift, vol.
This two-volume research monograph on the general Lagrangian Floer theory and the accompanying
homological algebra of filtered $A_\infty$-algebras provides the most important step towards a rigorous foundation of the Fukaya category in general context.
For example, set theory was invented in order to help in analysing the convergence behaviour of Fourier series;
homological algebra was invented in order to serve algebraic topology, and category theory was first developed with the view of applying it in
homological algebra (as well as algebraic topology and algebraic geometry).