The EMS Summer School on Multigraded Algebra and Applications will take place in the period August 17-24, 2016, in Moieciu de Sus, Romania, in the frame of the National School of Algebra, an event with a long tradition in Romania which is organized by the Ovidius University of Constanta, the Simion Stoilow Institute of Mathematics of the Romanian Academy, Bucharest, and the University of Bucharest.
The organizers gratefully acknowledge the financial support awarded by the European Mathematical Society and Foundation Compositio Mathematica .
The goal of this school is to present the main research directions of combinatorial commutative algebra with a strong focus on its applicability in various fields, like combinatorics, statistics, and biology. For this purpose we plan to offer integrated courses where the theoretical developments are directly motivated by topics from the above mentioned fields. This activity will be complemented by informal tutorial sessions, computer demos, and problem sessions lead by senior participants, where the audience has the chance to ask questions and discuss aspects of the material.
There will be the following two main courses:
Monomial and binomial ideals, by Juergen Herzog and Apostolos Thoma.
Contents: Toric rings and toric ideals; Groeobner bases; Convex polytopes; Edge rings of finite graphs; Toric rings and ideals arising from finite distributive lattices; Lattice and lattice basis ideals; The cotangent functors T^i and deformation theory; The cotangent functor T^1 for Stanley-Reisner rings and separability; Bi-Cohen-Macaulay graphs; T^1 for toric rings and separation.
Applicable combinatorial commutative algebra, by Ezra Miller and Thomas Kahle.
Contents: Multigradings, multigraded Hilbert series, affine semigroups; Multigraded free and injective resolutions; Irreducible resolutions and Alexander duality; Review of homology and persistent homology; Computing with Macaulay2; Solving polynomial equations with Groebner bases; Primary decomposition in applications; Random walks on discrete objects: Markov bases; Binomials, monoid algebras, congruences, and decompositions.
Venue of the school: Mistral Resort-Moieciu, Romania, located in a superb part of Moieciu de Sus, at 1100 meters altitude. The resort is situated in a very beautiful mountain area, providing an atmosphere comparable to other places that combine peaceful natural ambiance with stimulating meetings. The participants have access to various recreational activities like walking and hiking trails in the surrounding mountains, excursions to historical sites in the neighborhood (Bran Castle, Risnov fortress), biking tours, etc.
Funds for covering the local expenses to a limited number of selected participants will be available. Preference will be given to graduate students and early career mathematicians. The interested participants are invited to send an e-mail to Viviana Ene (firstname.lastname@example.org or email@example.com).
REGISTRATIONS ARE NOW CLOSED. WE REACHED THE MAXIMUM CAPACITY FOR THE SCHOOL.