| Ref.No: | 61518900 |
| Start date: | 05.05.2025 |
| End date: | 04.05.2028 |
| Approval date: | 16.04.2025 |
| Department: | APPLIED MATHEMATICAL & PHYSICAL SCIENCES |
| Sector: | MATHEMATICS |
| Financier: | 3Η ΠΡΟΚΗΡΥΞΗ ΕΛΙΔΕΚ ΓΙΑ ΜΕΛΗ ΔΕΠ&ΕΡΕΥΝΗΤΕΣ, ELIDEK |
| Budget: | 240.001,00 € |
| Public key: | ΨΔΘ446ΨΖΣ4-7Ν8 |
| Scientific Responsible: | Assist. Prof. HRISTINA VASILAKOPOULOU |
| Email: | cvasilak@math.ntua.gr |
| Description: | AN OPERAD IS BROADLY A SYSTEM OF DATA THAT FORMALIZES PROPERTIES OF A COLLECTION OF MAPS WITH N INPUTS AND ONE OUTPUT, CLOSED UNDER PERMUTATIONS OF INPUTS. THIS CONCEPT OF AN OPERAD GREW TO BE OF FUNDAMENTAL SIGNIFICANCE FOR VARIOUS AREAS OF PURE MATHEMATICS AS WELL AS PHYSICS AND MORE APPLIED CONTEXTS. THE PRESENT PROPOSAL AIMS AT BUILDING AN ABSTRACT FRAMEWORK THAT BRINGS TOGETHER OPERADS AND THEIR DUAL STRUCTURE OF COOPERADS (ONE INPUT, N OUTPUTS), ALONG WITH OBJECTS ON WHICH THEY ACT, NAMELY MODULES AND COMODULES. MOREOVER, WE ARE INTERESTED IN CONNECTING THIS FRAMEWORK WITH THE SO-CALLED GROTHENDIECK CONSTRUCTION, NOW EXTENDED TO AN ENRICHED VERSION - NAMELY ONE WHERE THE SETS OF SPACES OF MORPHISMS OBTAIN EXTRA STRUCTURE, USUALLY ALGEBRAIC. FINALLY, WE SHALL FURTHER EXPLORE HOW OPERADS CAN BE CONCRETELY USED AS TOOLS TO MODEL, ANALYZE AND INTERCONNECT CYBER-PHYSICAL SYSTEMS IN A WELL-ESTABLISHED WAY, AND WORK OUT SPECIFIC EXAMPLES OF SYSTEM BEHAVIORS THAT EVOLVE OVER TIME. OUR APPROACH STEMS FROM ALGEBRA AND CATEGORY THEORY – A MATHEMATICAL AREA WHERE CONCEPTS AND CONSTRUCTIONS ARE ABSTRACTED AND FORMALIZED IN A HIGHER CONCEPTUAL LEVEL WHERE THEY CAN BE BETTER UNDERSTOOD AND THOROUGHLY STUDIED – AND AIMS TO OPEN NEW HORIZONS FOR THE STUDY AND USE OF OPERADS. |
