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**Ateneo Aperiodic Systems Lab**

Primary interests include topology and dynamics of tilings and sequences arising from substitutions, as well as regularity properties of aperiodic sequences. Also interested in the application of symbolic dynamics in combinatorial game theory.

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**Ateneo Applied Mathematics Research Lab**

This research lab encompasses different areas of research that requires mathematical modeling, namely, disease modeling, financial mathematics and flood hazard modeling. The lab has a good track record in disease modeling, having been part of the FASSSTER project since the start of the COVID-19 pandemic, and having produced at least 5 Scopus-indexed publications on disease models over the last 2 years. Research on flood hazard models considers the concurrent crises of COVID-19 and flood in Marikina and neighboring areas. Lastly, a different field but requires mathematical modeling as well, financial mathematics research tackles issues in risk management among local banks.

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**Collaborative Analytics Group**

We are a mathematical modelling research group interested in applying machine learning techniques on data sets relating to health, disaster mitigation, and collective behaviour in humans and animals. Secondary interests include imitation and reinforcement learning applications.

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**Didactics of Mathematics Group**

The Didactics of Mathematics Research Group is primarily concerned about problems pertaining to the didactical triangle of Learner-Teacher-Subject Matter, with Mathematics as the subject matter. The group is interested in studies that revolve around the theories and practices of mathematics, curriculum, its implementation, assessment and language of mathematics, the everyday use of mathematics, technical and vocational mathematics education, and relevant perspectives that give light to issues in the teaching and learning of mathematics. The Didactics of Mathematics Group utilizes a diverse set of research methodologies and pursues interdisciplinary or multidisciplinary approaches for a deeper and broader understanding of the research problems.

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**Ateneo Graph Coloring Research Group**

The Ateneo Graph Coloring Research Group of the Mathematics Department is interested in pursuing various problems in the field of graph theory. The specific projects that the group has focused on include the following graph coloring schemes: sigma coloring, set coloring, twin edge coloring, rainbow mean coloring. Graph operations such as the join, corona, comb product of two or more graphs, and the middle graph of a graph have also been explored. Among the specific families of graphs that the group has worked on are the Hanoi graphs, Sierpinski graphs, zero divisor graphs and ideal-based zero divisor graphs.

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**Ateneo Mathematical Physics Lab**

Phase space methods in quantum mechanics, time-frequency and wavelet methods in signal analysis. Wigner-Weyl fomalism and Groenewold-Moyal formalism are implemented on Lie groups. Parallel methods apply to the analysis and recovery of signals, as well as filtering and denoising. The main tool is the construction of coherent states on Lie groups. Discrete quantum systems are also considered with a view towards quantum information and computing.

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**Ateneo Mathematics, Art, Culture and Creativity Laboratory**

The research group works on projects that link mathematics to the arts and sciences, design, and Philippine culture. It has been working on research in understanding the mathematics in the artworks of the Philippine indigenous communities such as mats, baskets, tattoos and textile.

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**Ateneo Mathplus Resources Laboratory**

The research group recognizes the advantages that technology can offer to mathematical learning, if only these can be designed well and made available easily. It envisions to design apps, databases and other software that can engage students through mathematical tasks and challenge them to investigate, make conjectures, and apply their reasoning. This group supports the implementation of the Philippine K to 12 mathematics framework, as it recognizes the affordances of technology, including manipulable objects, measuring devices, calculators, computers, smartphones, tablets, and the Internet. It is also involved in the creation of mathematical applications that support blended learning during the Covid 19 pandemic, making the applications accessible both through internet, community LTE networks and digital datacasting frameworks. The research group also conducts studies that determine the efficiency of the use of the technological tools in mathematical learning and reasoning.

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**Ateneo Symmetries in Algebra and Geometry Laboratory**

The research group focuses on the fields of group theory, mathematical crystallography, and discrete geometry. Current research topics include geometric and crystallographic groups, tilings and polytopes, and symmetries in nature and culture. We give an emphasis on the interplay between algebraic and geometric objects in our research.