This proceedings volume presents selected, peer-reviewed contributions from the 26th National School on Algebra, which was held in Constan a, 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).
Nearly normally torsionfree ideals (Andrei-Ciobanu).- Gröbner-nice pairs
of ideals (Stamate).- Veneroni maps (Tutaj-Gasi“nska et al.).- On the
symbolic powers of binomial edge ideals (Herzog et al.).- Multigraded Betti
numbers of some path ideals (Erey).- Depth of an initial ideal (Tsuchiya et
al.).- Asymptotic behavior of symmetric ideals: A brief survey (Römer et
al.).- On piecewise-linear homeomorphisms between distributive and
anti-blocking polyhedra (Sanyal et al.).- The Bass-Quillen Conjecture and
Swans question (Popescu).- Licci level Stanley-Reisner ideals with height
three and with type two (Yoshida et al.).- Homological and combinatorial
properties of powers of cover ideals of graphs (Fakhari).- Fermat-type
arrangements (Szpond).
Dumitru I. Stamate holds a PhD in Mathematics (2009) from the University of Bucharest, Romania and two MSc degrees in Mathematics (2004), one from the coala Normal Superioar Bucureti, Romania, and the other from the University of Iai. He is currently an Assistant Professor at the University of Bucharest, Romania. His research focuses on commutative algebra, particularly problems related to free resolutions, computational algebra and combinatorics. Tomasz Szemberg is a Professor at the Pedagogical University National Education Committee in Krakow, Poland. He completed his PhD in Mathematics (1994) at the Friedrich-Alexander-Universität, Erlangen-Nürnberg, Germany, and his MSc (1990) at the Jagiellonian University, Poland. In 2002, he received his postdoctoral qualification in Mathematical Sciences and in 2014, the academic title of Professor of Mathematical Sciences. His research interests encompass the fields of commutative algebra, algebraic geometry and discrete mathematics.
