Research project title: Geometric combinatorics and its applications to algebra (Ref: PID2022-137283NB-C21) Principal Investigator: Francisco Santos (co-PI Arnau Padrol Sureda) Doctorate Program: Science and Technology Deadline for applications: November 20, 2023
The contract will be for four years and is formalized with the University of Cantabria. The expected beginning date is February 1st, 2024. Gross salary will range from 17 222 euro the first year to 23 065 the fourth. In addition to this, there is additional money to cover the candidate's expenses to register in the doctoral school and to cover accommodation, travel and per diem for research stays during the contract.
The successful candidate will also be a member of the research grant referenced above, which will cover additional expenses such as attendance to workshops, advanced courses, etc. Although the contract and doctorate program are based in Cantabria, depending on the particular interests and research project the doctoral thesis might be any of the researchers in the project: Mónica Blanco (UC), Francisco Criado (CUNEF), Arnau Padrol (UB), Julian Pfeifle (UPC), Vincent Pilaud (UB), Francisco Santos (UC).
The candidate will have a certain freedom to choose research topics, within the research lines of the project. In it several problems related to the combinatorics and complexity of certain research objects are studied. The choice of topics is made with a view towards applications, algorithms and connections to other areas, particularly methods and applications in algebra. Our goals are structured in three research lines, not totally disjoint.
Combinatorics of simplicial and polytopal complexes. Tha main goal here is to understand better the combinatorics of polytopes and polyhedra. We study in particular, face numbers, diameter, number of combinatorially different polytopes, or of polytopes with certain properties, and the theory of fiber polytopes.
Geometric realizability. Most simplicial spheres, (simplicial complexes homeomorphic to a sphere) are not polytopal (cannot be realized as the face poset of a polytope). It is important in many applications to decide whether concrete examples are realizable, and to devise efficient methods to prove or disprove realizability for certain classes of them.
Combinatorial methods in algebraic geometry. Some parts of algebraic geometry are closely related to polytope theory. This includes Gröbner bases, toric geometry, and tropical geometry. Of particular importance for these connections are the study of numerical semigroups and lattice polytopes (polytopes with integer vertices).
According to the official call candidates must, at the moment they apply be admitted in a doctoral program or fulfill the requiremeents to be admitted in one.
In practice this means the candidate must have completed a bachelors and a master (or equivalent degrees) comprising together at least 300 ECTS of university education.
The most adequate profile is that of a mathematician, but candidates in related fields can be considered.
Applications should be filed via the Sede Electrónica de la Universidad de Cantabria. As part of the application the project and PI data listed above will be asked for. To file the application electronically you will need to have an electronic certificate issued by one of the''Trusted Certificate Authorities'' (TSL) admitted by the Spanish administration. Together with the application form you must attach:
We recommend interested candidates to get in contact with the PI at francisco.santos@unican.es, including a CV and transcript of records, in addition to filing the official application.