PRR Project

Summary

CAMGSD, established in 1991, is a research unit in pure mathematics whose main scientific pillars are the broad areas of (i) differential equations and dynamical systems and (ii) geometry and topology, including topics in mathematical physics such as mathematical relativity, quantum field theory and string theory, and it has consistently received Excellent in every FCT evaluation.In particular as regards (ii), topology is a fundamental and essential field that needs to have a strong presence in any R&D Unit whose scientific activities hinge crucially on pure mathematics. However, this area is currently under-represented in the center’s team of permanent members, and it needs to be reinforced by a strong researcher with expertise in geometric, algebraic and differential topology, in particular in specific important topics not covered by the permanent members. Such a reinforcement has both the benefit of complementing the existing expertise of the center, and of rejuvenating its team, and it is a crucial step towards ensuring its sustainable international standing in the long run.More concretely, in the last two decades, the field of algebraic topology has been revolutionized by the development of a mature theory of higher categories (at the hands of Joyal, Lurie, Street and many others). This new conceptual framework has taken a long time to be absorbed but is now, in the hands of a generation of topologists trained within the new paradigm, leading to the solution of many long standing conjectures (e.g., the recent resolution of the telescope and chromatic redshift conjectures) as well as a great expansion of the scope of feasible computations (cf. recent breakthroughs in the computation of stable homotopy groups of spheres, algebraic K-theory and related invariants).Together with this internal development has come increasing interaction of algebraic topology with other areas of pure mathematics, notably symplectic geometry (see for instance work of Dominic Joyce or Abouzaid–Blumberg), which is an area of particular strength at CAMGSD, as well as with certain topics of mathematical physics through the study of topological aspects of quantum field theories and condensed matter theory.This conceptual revolution took place after the graduate training of all the current topologists at CAMGSD who are permanent members. In order to have a team that can produce research in topology up to the highest international standards it is absolutely essential to recruit a member which has natively acquired the new conceptual package of algebraic topology during graduate training.The tasks that the hired researcher will perform will include: (1) to conduct research in the identified areas and to publish its results in high ranking journals; (2) to disseminate the results of the research in international scientific events; (3) to collaborate in the organization of seminars at CAMGSD that promote knowledge around the topics just described, in particular inviting researchers from other institutions, both national and foreign; (4) to organize or host local and international scientific events; (5) to apply for grants of various types, e.g., ERC grants, so as to attract additional funding that will promote the growth of the activities in this area, taking advantage of the Research & Innovation Funding support structure of IST-ID, in particular the ERC accelerator program; (6) to collaborate in the advanced training and supervision of students and postdoctoral fellows; (7) to collaborate in opportunities that may arise from the interaction with other R&D units of IST-ID, or from private companies, in connection with applications of topology to areas of increasing societal importance such as data science and machine learning.At CAMGSD we have identified excellent potential candidates amongst those that are eligible for the FCT Tenure program, in particular candidates that currently have temporary contracts with IST-ID as researchers of CAMGSD, and whom we know will be interested in applying for a research position at CAMGSD that fits the profile here described.