Grants for Visiting Postdoc, Advanced Doctoral Students or Master’s Students to AIMS South Africa

As part of the Heidelberg-Cape Town Network for Applied Mathematics and Scientific Computing (heiAIMS) project, four grants (2xPostDoc/PhD & 2xMSc) is currently available for visiting young researchers from Heidelberg to spend two months at AIMS South Africa, Cape Town.

• Objective: Research stay at AIMS South Africa
• Period: 2025
• Duration: up to 2 months
• Costs funded: Travel & accommodation costs plus 1,000 EUR/month (grant)

• Eligible students: Master students in Scientific Computing, Mathematics, Computer Science or (Computational) Physics
• Recommended Period: September-November 2025 (other times are possible, please mention the desired period in the comments section of the online application form)
• Duration: up to 2 months
• Costs funded: Travel & accommodation costs plus 800 EUR/month (grant)
• Certificate: Proof of internship (up to 6 ECTS, e.g. for Fachübergreifende Kompetenzen)*

* Please contact the academic advisor for your program for crediting options.

Please use the online application form to apply for a research visit to AIMS South Africa.

The deadline for applications is March 10, 2025.

• Visa: For information about visa and passport requirements, visit the website of the Department of Home Affairs of the Republic of South Africa. If you need additional information please contact the Infocenter for Study and Internship Abroad of Heidelberg University.

Proposed project:

Anomaly Detection Algorithms for the ATLAS Trigger Systems

Description:

The ATLAS Experiment is one of the detectors of the Large Hadron Collider (LHC), an underground particle accelerator located at CERN, the European Centre for Nuclear and Particle Physics. A recent trendy approach to find New Physics, i.e. processes departing from the current, incomplete theoretical framework, is to search for proton-proton collisions that are not generic (most collisions at the LHC are known physics and define the 'normal', aka the physics we already know). The project would revolve into developing a compact, fast Variational AutoEncoder (VAE) that would extract most information about anomalous events, such as a possible directionality (from the latent space) or multi-dimensional anomaly score. Relevant metrics will be defined to assess the performance. There are available datasets open to the public. Signal samples can be used as a proxy for an initial benchmarking, yet the ultimate goal is to create a model-independent metric where events with high anomaly scores are the one most likely to contain interesting new physics.

The topic demands a short introduction about the physics context, yet it should be doable by a student without any background in particle physics.

Proposed project:

Interpolatory Subdivision and Wavelets on an Interval with General Integer Arity

Background information:

Wavelet decomposition and reconstruction algorithms, as widely applied in signal analysis applications, often have the drawback of being based on the assumption that the signal to be analyzed is known on the whole real line. Similarly, subdivision schemes are nearly always constructed based on the assumption that the initial control point sequence isbi-infinite. Nevertheless, various (often unsatisfactory) ad hoc methods are used in practice to overcome these difficulties. Hence there is a significant need for a systematic unified approach to construct wavelets on a bounded interval and subdivision schemes for finite initial control point sequences. Underlying the mathematical analysis of both wavelets and subdivision schemes is the concept of a refinable function, that is, a self-reproducing function that can be expressed as a linear combination of the integer translates of its own dilation by factor two.

A method of adapting the binary Dubuc-Deslauriers subdivision scheme defined for bi-infinite sequences to accommodate sequences of finite length has been studied in [1]. Based on this work thereof, this research project investigates a method of adapting the Dubuc-Deslauriers subdivision scheme with general integer arity to accommodate sequences of finite length. Two numerical examples of signature smoothing and two-dimensional feature extraction of the d-ary subdivision and wavelet algorithms will be explored.

Keywords:

Subdivision schemes, refinable function, wavelet decomposition, finite sequences, algorithms

References:

• Dubuc-Deslauriers subdivision for finite sequences and interpolation wavelets on an interval
• Geometric convergence rates for cardinal spline subdivision with general integer arity
• Wavelet Subdivision Methods: GEMS ­Geometry Editing and Manipulation Schemes

Proposed project:

Near-vector spaces

Background information:

Near-vector spaces are the less linear counterparts of vector spaces, where only one distributive law is satisfied. A natural question to ask in any branch of pure or applied mathematics is what the result is of replacing the vector space by a near-vector space.

We are open to working with a student who has an interest in exploring this topic in any area they are interested in.

Proposed project 1:

Property testing in a Quantum World [Master’s level]

Background information:

“Your data is big, but is it blue?” - Clement Cannone

In some sense, the fundamental problem of machine learning is the following: Given some type of access to an unknown object, learn a description of that object. For example, given access to random input\output pairs of a function, learn how to implement the function. In many cases however, we are interested in a simpler problem, that of property testing: Given some type of access to an unknown object, decide whether or not it has a specific property. For example:

• Given input\output pairs from a function, decide whether or not the function is monotonic, or symmetric.
• Given examples of vertices and their neighbours from a graph, decide whether or not the graph is bipartite, or triangle-free.
• Given samples from a distribution, decide whether that distribution is close to, or far from, the uniform distribution.

The beautiful thing about property testing, is that often it can be done much more efficiently than learning. In fact, it can often be done with only sublinearly many examples. Because of this, property testing algorithms have a vast amount of applications across all of theoretical computer science and machine learning. Given these broad applications, a natural question is whether one can design quantum algorithms for property testing which are even more efficient than the best classical algorithms. Indeed, this turns out to be the case for a wide variety of settings, and the last few years has seen significant interest and progress in this question. In this project, we will focus on addressing one of a variety of open problems in the development of quantum algorithms for testing properties of functions, graphs, distributions and quantum states — from both classical and quantum data — with an emphasis on both the memory limited (i.e. streaming) setting, and the setting of distributed testing algorithms.

For some representative literature, have a look at:

• Your data is big, but is it blue? (https://theoryofcomputing.org/articles/gs009/)
• Testing classical properties from quantum data (arXiv:2411.12730v1)
• Distributional property testing in a quantum world (arXiv:1902.00814v1)

Proposed project 2:

Dequantizing Quantum Algorithms for Reinforcement Learning

Background information:

The last few years have witnessed an incredible number of proposals for variational quantum algorithms for machine learning. However, despite the volume of proposals, it is still completely unclear whether or not one can use any of the proposed methods to gain meaningful advantages over purely classical algorithms. One approach to answering this question is via dequantization. In this approach, one asks whether one can use an understanding of a proposed quantum method, to construct a purely classical method which performs in an analogous way, and can be proven to match the quantum method in performance. In the context of supervised learning, one approach to dequantization is via classical surrogate models [1], which share the inductive bias of variational quantum algorithms, and can indeed be proven to match the performance of such algorithms in a variety of settings [2]. Despite this progress, the notion or capability of surrogate models outside of the setting of supervised learning remains totally unexplored. In this project, we will explore the potential and limitations of classical surrogate models for dequantizing quantum reinforcement learning algorithms based on parameterised quantum circuits [3,4]. In particular, these are reinforcement learning algorithms in which a neural network parameterization (of a policy function for example) is replaced with a parameterised quantum circuit. The goal will be to gain a clear understanding of the regimes in which one may or may not expect previously proposed quantum algorithms to be advantageous for reinforcement learning.

1. Classical surrogates for quantum learning models (https://arxiv.org/abs/2206.11740)
2. Potential and limitations of random Fourier features for dequantization quantum machine learning (https://arxiv.org/abs/2309.11647)
3. Quantum policy gradient algorithms (https://arxiv.org/abs/2212.09328)
4. A quantum classical reinforcement learning model to play Atari games (https://arxiv.org/abs/2412.087)

Proposed project:

FRB Cosmology with HIRAX

Background information:

In this project, the student will study Fast Radio Bursts, their progenitor mechanisms and the ways they can be used to study cosmology. We will also look at the ways that HIRAX can be used to make these discoveries.

Proposed project:

Master’s exchanges to AIMSSEC South Africa (2025)

Background information:

AIMSSEC is a division of AIMS working in teacher training and the link between schools and university in the area of STEM.
The project is looking for an exchange student keen on working on projects that uplift historically marginalised teachers and school learners, someone who can be sensitive to working alongside socioeconomically challenged communities. Fluency in English would be great as most learners and some teachers have English as an additional language. The medium of instruction at their schools is English.

We require assistance from an Education Technology point of view, which includes:

• Working on data analysis and research related to computational thinking;
• Assisting in reviewing and refining EdTech modules for the January and June 2026 teacher training courses;
• Supporting the September computational thinking workshops as a student assistant;
• Contribute to expanding AIMSSEC’s online presence through engaging social media content and blog posts and
• Review the AIMSSEC website, suggest improvements, and prepare for a possible amalgamation with the AIMS site.