School of Science Department of Mathematics 48 Geometric Flows Supervisor: FONG Tsz Ho / MATH Student: WU Ruirui / MATH-PMA Course: UROP4100, Summer In this report we will present the proof of the theorem which says finite time existence occurs only if second fundamental form blows up by sorting, paraphrasing and completing the argument in Extrinsic Geometric Flows by Ben Andrews and Bennett Chow and Lecture Notes on Mean Curvature Flow by Mantegazza, together with a summary of chapters about basics of MCF in the former text, in which several propositions are used in the former proof. A Machine Learning Approach to Study the Relationship between Urban Morphology and Urban Heat Island Supervisor: FUNG Jimmy Chi Hung / MATH Student: MOK Wan Hin / SSCI Course: UROP1000, Summer Urban heat island effect is a common phenomenon in cities, with temperature in urban areas being higher than the rural counterparts. It is believed that there is a certain positive correlation between urban morphology and land surface temperature (LST). This project focuses on this phenomenon in the Greater Bay Area (GBA). Over this region, the data of land surface temperature, urban morphology factors, and geographical factors from satellite images were gathered. 2 types of machine learning models – deep neural network (DNN) and linear model - were built, aiming to predict the LST out of these factors. Results show that there is a moderate correlation between urban morphology factors and LST, and that DNN model has a better performance than a linear model in making such predictions. A Machine Learning Approach to Study the Relationship between Urban Morphology and Urban Heat Island Supervisor: FUNG Jimmy Chi Hung / MATH Student: SHREEHARSH Aastha / SSCI Course: UROP1000, Summer In today’s day and age, almost any problem civilization has, or any question humankind wants to answer that deals with a large amount of data can be solved using machine learning (ML) and computer vision. This project is a new attempt to utilize deep learning techniques in order to glean insights on building data and draw conclusions about the Urban Heat Island (UHI) effect based on the urban morphology without simplifying the data or narrowing it down to regional impact. This report focuses on the potential of obtaining this building data using a convolutional neural network (CNN), specifically the U-net Xception style of semantic segmentation. Multiple attempts to improve the accuracy of results produced by modifications to a pre-existing model architecture are outlined alongside recommendations for future work on the same.