PhD position in Mathematics focusing on complex geometry and optimal transport
4 weeks ago
Project description
and tasksIn the 80’s and 90’s a surprising phenomenon was observed by physicists: It seemed like certain complicated geometric objects (Calabi-Yau manifolds) appeared in pairs, one taking the form of a mirror image of the other. The phenomenon was dubbed mirror symmetry and similarly as for other duality principles in mathematics, for example the duality of time and frequency in Fourier analysis, researchers quickly realized it could be very useful. An important branch of research with the aim of understanding mirror symmetry is the SYZ-conjecture, which gives a detailed description of a conjectural structure in Calabi-Yau manifolds. To show that this description is true has turned out to be very difficult. In essence, the problem consists of controlling the limit of solutions to certain (Monge-Ampère) partial differential equations when the dimension of their domain drops, which is a very challenging problem in general. However, due to a recent breakthrough the problem has been reduced to showing existence of solutions to a class of these equations in very singular settings. The purpose of this project is to show existence of these solutions and study their properties to learn more about mirror symmetry. The main new idea is to use optimal transport to achieve this. Optimal transport is a classical tool with roots in 18th century France, where it was studied in relation to engineering and geometry. Here, it will provide a link between the partial differential equations above and a very robust variational theory which, as indicated by preliminary results, might be very useful.
The doctoral student will carry out research in complex algebraic geometry and optimal transport as part of the project above, which is funded by the Swedish Research Council. As part of this, they will write articles (both as single author and in collaborations) and publish in international journals. The project will also present many opportunities to travel and take part in conferences and workshops with possibilities to initiate collaborations with researchers at other universities, both in Sweden and internationally. Upon completion of their doctoral degree, they will be in a good position to apply for national and international postdoc grants, for example the Mathematics Program by the Knut and Alice Wallenberg Foundation or the Marie Skłodowska-Curie Postodctoral Scholarships by the European Research Council.
Qualifications
The doctoral student will be admitted to the third-cycle programme in the subject Mathematics. To fulfil the general entry requirements, the applicant must have qualifications equivalent to a completed degree at second-cycle level or completed course requirements of at least 240 ECTS credits, including at least 60 ECTS credits at second-cycle level. To fulfil the specific entry requirements to be admitted for studies at third-cycle level in mathematics, the applicant is required to have completed at least 60 ECTS credits within the field of mathematics, of which at least 15 ECTS credits shall have been acquired at second-cycle level. Applicants who have acquired largely equivalent skills in some other system, either within Sweden or abroad, are also eligible.
The ability to communicate in written and spoken English is required. The doctoral student is expected to take on an active role in the research project and in institutional work. They should have a scientific mindset, and ability to work independently, and be structured, flexible and solution oriented. Above all, the doctoral student should be determined to continuously develop their skills and contribute to the research project. Prior experience with complex differential or algebraic geometry, partial differential equations or optimization is beneficial, but not a requirement.
The assessment of applicants is based on their qualifications and ability to benefit from the doctoral study they will receive.
About the employment
The position is intended to result in a doctoral degree. The main task of doctoral students is to pursue their third-cycle studies, including active participation in research and third-cycle courses. The duties may include teaching or other departmental work, although duties of this kind may not comprise more than 20 per cent of a full-time post. The employment is for a fixed term of four years full-time or up to five years when teaching part-time. Salary is set according to the salary ladder for PhD positions at Umeå University. Employment commences January 2025 or by agreement.
-
Umeå, Västerbotten, Sweden Euro Math Soc Full timeThe Department of Mathematics and Mathematical Statistics is opening a PhD position in mathematics, within the WASP AI program, focusing on geometric deep learning.The position covers four years of third-cycle studies, including participation in research and third-cycle courses. The last day to apply is 10 June 2024.This recruitment is part of a more...
-
Umeå, Sweden Umeå University Full timeProject description and tasks Deep learning has enjoyed tremendous success on an impressive number of complex problems. However, the fundamental mathematical understanding of deep learning models is still incomplete, presenting exciting research problems spanning areas such as differential geometry, numerical analysis, and dynamical systems. Neural...
-
Umeå, Sweden Umeå University Full timeProject description and tasks Deep learning has enjoyed tremendous success on an impressive number of complex problems. However, the fundamental mathematical understanding of deep learning models is still incomplete, presenting exciting research problems spanning areas such as differential geometry, numerical analysis, and dynamical systems. Neural...
-
Umeå, Sweden Umeå University Full timeProject description and tasks Machine learning (‘artificial intelligence’) is having an immense impact on both society at large and research especially, and this impact is expected to increase. This boom is driven by so-called deep neural networks, a class of machine learning models proven incredibly powerful, versatile, and capable of solving many...
-
Umeå, Västerbotten, Sweden Umeå University Full timeProject description and tasks Machine learning ('artificial intelligence') is having an immense impact on both society at large and research especially, and this impact is expected to increase. This boom is driven by so-called deep neural networks, a class of machine learning models proven incredibly powerful, versatile, and capable of solving many machine...
-
Umeå, Sweden Umeå University Full timeProject description and tasks Machine learning (‘artificial intelligence’) is having an immense impact on both society at large and research especially, and this impact is expected to increase. This boom is driven by so-called deep neural networks, a class of machine learning models proven incredibly powerful, versatile, and capable of solving many...
-
Umeå, Västerbotten, Sweden Euro Math Soc Full timeThe Department of Mathematics and Mathematical Statistics is opening a PhD position in mathematics focusing on discrete mathematics and combinatorics. The position covers four years of third-cycle studies, including participation in research and third-cycle courses. The last day to apply is the 30th of April 2024.Project description and tasks:The candidate...
-
Umeå, Sweden Umeå University Full timeProject description The project will develop privacy-aware machine learning (ML) models. We are interested in building models that are explainable and are extracted from complex and heterogeneous data. Within explainable ML, we are interested in topics as provenance, interpretable and transparent models. Within privacy, we are interested in different...
-
Umeå, Sweden Umeå University Full timeProject description The project will develop privacy-aware machine learning (ML) models. We are interested in building models that are explainable and are extracted from complex and heterogeneous data. Within explainable ML, we are interested in topics as provenance, interpretable and transparent models. Within privacy, we are interested in different...
-
Umeå, Västerbotten, Sweden Umeå University Full timeProject focus:Develop privacy-aware machine learning (ML) modelsBuild explainable models from complex dataInterest in provenance, interpretable and transparent modelsFocus on various privacy measures and modelsConsider centralized and decentralized data scenariosTopics include federated learning, aggregation, game theory, and graph theory Research group:...
-
PhD position in Medical Science
2 weeks ago
Umeå, Västerbotten, Sweden Umeå University Full timePhD position in Medical Science We are looking for a qualified candidate to embark on a PhD in Medical Science with an orientation towards Neurophysiology (sensorimotor neurophysiology). The position is at the Department of Medical and Translational Biology at Umeå University and is temporary for four years, to start during October 1st 2024 or as...
-
Umeå, Sweden Umeå University Full timeProject description and tasks This project addresses a fundamental topic in evolution concerning how and why microbes interact in the ways they do. We know that microbes have many possible options, or strategies, regarding what resources they consume to grow. Depending on these choices, pairs of microbes may either compete or cooperate. What actually...
-
Umeå, Sweden Umeå University Full timeProject description and tasks This project addresses a fundamental topic in evolution concerning how and why microbes interact in the ways they do. We know that microbes have many possible options, or strategies, regarding what resources they consume to grow. Depending on these choices, pairs of microbes may either compete or cooperate. What actually...
-
Umeå, Västerbotten, Sweden Umeå University Full timeProject description and tasks This project addresses a fundamental topic in evolution concerning how and why microbes interact in the ways they do. We know that microbes have many possible options, or strategies, regarding what resources they consume to grow. Depending on these choices, pairs of microbes may either compete or cooperate. What actually...
-
Umeå, Västerbotten, Sweden Umeå University Full timeProject description : "High-Performance Parallel Tensor Network Algorithms" A tensor network is a flexible mathematical framework for efficiently approximating and computing with high-dimensional tensors. Tensor networks appear in a broad variety of scientific applications, ranging from the study of quantum many-body systems to autonomous driving and to...
-
Umeå, Sweden Umeå University Full timeProject description : “High-Performance Parallel Tensor Network Algorithms” A tensor network is a flexible mathematical framework for efficiently approximating and computing with high-dimensional tensors. Tensor networks appear in a broad variety of scientific applications, ranging from the study of quantum many-body systems to autonomous driving and...
-
PhD position in Medical Science
3 weeks ago
Umeå, Sweden Umeå University Full timePhD position in Medical Science We are looking for a qualified candidate to embark on a PhD in Medical Science with an orientation towards Neurophysiology (sensorimotor neurophysiology). The position is at the Department of Medical and Translational Biology at Umeå University and is temporary for four years, to start during October 1st 2024 or as...
-
Umeå, Sweden Umeå University Full timeProject description and tasks Viruses belonging to the Pneumoviridae family are the predominant cause of acute lower respiratory infections (ALRIs) in young children. A thorough comprehension of viral structure is crucial to understand the molecular basis of viral replicative cycles and to inform on the rational development of therapeutics. In your PhD...
-
Umeå, Västerbotten, Sweden Umeå University Full timeProject Description and TasksOur research group at the Nordic Membrane Laboratory, Umeå University, is dedicated to designing and synthesizing innovative materials and methods to advance the field of separation science. In collaboration with Toyota Motor Europe (TME), we are pleased to offer a PhD position focused on developing a novel approach to recycling...
-
Umeå, Västerbotten, Sweden Umeå University Full timeProject description and tasks Our research group at the Nordic Membrane Laboratory, Umeå University, is dedicated to designing and synthesizing innovative materials and methods to advance the field of separation science. In collaboration with Toyota Motor Europe (TME), we are pleased to offer a PhD position focused on developing a novel approach to...
