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This proceedings volume presents selected, peer-reviewed
contributions from the 26th National School on Algebra, which was
held in Constanta, Romania, on August 26-September 1, 2018. The
works cover three fields of mathematics: algebra, geometry and
discrete mathematics, discussing the latest developments in the
theory of monomial ideals, algebras of graphs and local positivity
of line bundles. Whereas interactions between algebra and geometry
go back at least to Hilbert, the ties to combinatorics are much
more recent and are subject of immense interest at the forefront of
contemporary mathematics research. Transplanting methods between
different branches of mathematics has proved very fruitful in the
past - for example, the application of fixed point theorems in
topology to solving nonlinear differential equations in analysis.
Similarly, combinatorial structures, e.g., Newton-Okounkov bodies,
have led to significant advances in our understanding of the
asymptotic properties of line bundles in geometry and multiplier
ideals in algebra. This book is intended for advanced graduate
students, young scientists and established researchers with an
interest in the overlaps between different fields of mathematics. A
volume for the 24th edition of this conference was previously
published with Springer under the title "Multigraded Algebra and
Applications" (ISBN 978-3-319-90493-1).
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