Head of Department
Head of Department
The Department of Mathematics rolled out several new academic programmes under the College of Humanities and Sciences, offering students more choices to customise their learning and pursue breadth and depth in knowledge and skills. These include a Second Major in Quantitative Finance and a Specialisation in Pure Mathematics.
Together with the Faculty of Arts and Social Sciences, we also launched the Cross-Disciplinary Programme in Data Science and Economics to enable graduates to solve business challenges that require a tight integration of knowledge from these complementary disciplines.
The Master of Science (MSc) in Data Science and Machine Learning programme was launched last year and has been very well-received. Its first run drew close to 850 applicants and in 2021, the expected cohort size is over 100 students.
The Louis Chen Science Merit Scholarship was established in 2018 in honour of Emeritus Professor CHEN, in recognition of his achievements and contributions to the university. Former and present colleagues, and friends, notably Mr NG Kok Lip, gifted generously to support the scholarship. The first scholarship will be awarded in Academic Year 2021/2022.
Our scientists continue to push the boundaries in mathematical science research, contributing to the understanding of singular stochastic partial differential equations and geometry of Hitchin components, as well as developing machine learning algorithms.
The Stochastic Heat Equation (SHE) and Kardar-Parisi-Zhang equation (KPZ) are singular stochastic partial differential equations (SPDEs) that arise from the study of random interface growth models. Work by Prof M HAIRER and others have provided robust solution theories for such singular SPDEs. However, for SHE and KPZ, dimension 2 is critical and beyond the reach of these theories. Assoc Prof SUN Rongfeng, together with his coauthors, have made significant progress in understanding the SHE and KPZ in dimension 2, including identification of a phase transition as the noise strength varies, Gaussian fluctuations in the subcritical regime and identification of non-trivial limits in the critical regime. Part of this work was published in the Annals of Probability (May 2020).
To train contemporary machine learning models, optimisation algorithms need to explore the landscape and converge to good solutions quickly. Existing sampling algorithms such as the Langevin algorithm do well in the first task but are slow for the second. Greedy algorithms such as the gradient descent do well in the second task but cannot explore the landscape. Asst Prof TONG Xin showed that these two types of algorithms can “collaborate” through a simple mechanism called replica exchange. This work was published in the Journal of Machine Learning Research (August 2021).
Given a group and a geometry, one seeks to understand the space of geometrically well-behaved actions of the given group on the given geometry. One commonly studied example of this is the Hitchin component. Asst Prof ZHANG Tengren and his coauthors Prof Anna WIENHARD of Heidelberg University and Dr SUN Zhe of the Institut des Hautes Études Scientifiques give an explicit description of all deformations of such group actions, which in turn give rise to families of Hamiltonian flows on the Hitchin component. As an application, they found explicit global Darboux coordinates on the Hitchin component. The results were published in Geometric and Functional Analysis (May 2020).
The Centre was established in response to rapid developments in data science, machine learning and artificial intelligence. It will act as a focal point to organise and support research and educational activities in these areas. It also offers consulting services in data analytics and serves as an administration hub for the MSc in Data Science and Machine Learning programme.
Asst Prof LI Qianxiao was awarded the NRF Fellowship (2021), a competitive programme that seeks to recruit and root outstanding young scientists from around the world to conduct research in Singapore. He will work on the exciting area of dynamical systems approach to deep learning and its applications in science.
We consistently produce mathematically talented students with the potential to shape an increasingly complex future through creative problem-solving.
Our undergraduates won prizes for the fourth consecutive year in the international Simon Marais Mathematics Competition (2020). Year 2 student Bryan WANG beat some 600 participants to receive the Hofflin Prize which is awarded for the most creative solution to any problem in the competition. He tackled a difficult geometry challenge, showing that a three-dimensional (3D) pentagon with all sides and angles equal must in fact be a two-dimensional (2D) pentagon.
Fresh graduate YAP Jit Wu was one of four gold medallists in the international Alibaba Global Mathematics Competition (2020), which seeks to promote deeper understanding of mathematics in the global technology sector, facilitate mathematics research and encourage youths to pursue careers in this field.
“The project opened my eyes to how mathematical concepts and statistical tools can be used in the medical field.”
Mortality risk is a major concern for Intensive Care Unit (ICU) patients. Many machine learning models are hard to interpret and clinicians are typically unable to understand underlying risk factors. Eugene and his team used data from the Medical Information Mart for Intensive Care (MIMIC-III) clinical database and constructed risk calculators based on different machine learning techniques. Their benchmarking study compared the most salient features predicted by various methods and identified common features, to provide insights on patients’ health conditions.
Joel CHANG received the Outstanding Undergraduate Researcher Prize in 2021 for an efficient algorithm that identifies and maximises the reward of a “best” choice in decision-making through the design of a Thompson sampling-based algorithm called Conditional-Value-at-Risk (CVaR-TS). He also proved that it outperforms existing state-of-the-art algorithms.
“We have barely scratched the surface of Timor-Leste’s biodiversity. New discoveries can have profound impacts on conservation and policy-making.”
In August 2022, we led an expedition to Timor-Leste in collaboration with Conservation International and the government of Timor-Leste. The Museum’s herpetologist, Dr CHAN Kin Onn, discovered a new species of bent-toed gecko which was named Cyrtodactylus santana, in reference to the Nino Konis Santana National Park, in which the gecko was discovered.
