**Reference Number:** 2018-MAX-01

**Reference Number:** ACM

**Reference Number:** 2018-HW-AMS-14

**Reference Number:** 2018-HW-AMS-02

**Reference Number:** ACM

**Reference Number:** 2018-HW-Maths-42

**Reference Number:** 2018-HW-Maths-41

**Reference Number:** ACM

**Reference Number:** 2018-HW-Maths-17

**Reference Number:** ACM

**Reference Number:** ACM

**Reference Number:** ACM

**Reference Number:** 2018-HW-Maths-07

**Reference Number:** ACM

**Reference Number:** 2018-HW-Maths-19

**Reference Number:** ACM

**Reference Number:** ACM

**Reference Number:** ACM

**Reference Number:** 2018-HW-Maths-09

Some directions: At high frequencies naive numerical methods require a very fine mesh to capture the rapidly oscillating sound pressure. Tools from harmonic analysis and PDE give rise to new regularity estimates and efficient adaptive mesh refinements. Detailed models of instruments (or other sound sources like tires or high-speed trains) give rise to realistic simulations of sound, based on mathematically challenging multi-physics problems.

**Reference Number:** 2018-HW-Maths-27

**Reference Number:** 2018-HW-Maths-10

**Reference Number:** 2018-HW-Maths-30

Equipped with these tools, we will look into a quantum-like description for photosynthesis. Here, quantum-like means that the mathematical structure is different from conventional quantum mechanics. We will investigate a quantum network formulation for electron transport in organic molecules and describe the photosynthesis by a quantum channel representation. A question of general interest then is whether and how we can transfer these ideas to solar cells to ultimately improve the performance.

**Reference Number:** 2018-HW-Maths-26

**Reference Number:** 2018-HW-Maths-40

**Reference Number:** 2018-HW-Maths-01

**Reference Number:** 2018-HW-Maths-33

**Reference Number:** ACM

Edinburgh Earth and Environment Doctoral Training Partnership

**Reference Number:** ACM

**Reference Number:** ACM

**Reference Number:** ACM

**Reference Number:** 2018-HW-Maths-54

**Reference Number:** 2018-HW-Maths-29

**Reference Number:** 2018-HW-Maths-11

**Reference Number:** 2018-HW-Maths-24

**Reference Number:** 2018-HW-Maths-23

**Reference Number:** 2018-HW-Maths-53

**Reference Number:** 2018-HW-Maths-39

**Reference Number:** ACM

**Reference Number:** 2018-HW-Maths-31

**Reference Number:** ACM

**Reference Number:** 2018-HW-Maths-12

**Reference Number:** 2018-HW-Maths-18

At the other end of the scale, with colleagues in biology we have the opportunity to take a large amount of cell movement data and to develop models for molecular movement and interactions. The project would apply new techniques for estimating parameters and could be used to inform new biological theories and experiments.

**Reference Number:** ACM

**Reference Number:** ACM

**Reference Number:** ACM

**Reference Number:** ACM

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**Reference Number:** 2018-HW-Maths-25

**Reference Number:** 2018-HW-Maths-06

**Reference Number:** ACM

**Reference Number:** 2018-HW-AMS-15

Various stakeholders in finance and insurance—such as regulators, investors and managers—rely on quantitative analysis in their decision-making processes. This research project employs quantitative models and methods from probability theory and statistics to tackle problems that are of practical relevance in these fields. Three topics are mainly concerned. The first topic studies numerical techniques that are useful in financial and actuarial valuation such as option pricing, capital allocation and risk aggregation etc. We aim to propose new efficient computational methods and techniques. The second topic studies investment strategies and behaviors under general risk preference with emphasis on portfolio selection, skewness preference and performance measure etc. The third topic delves into dependence modeling of risks and its applications in finance and insurance. It covers popular research questions such as model uncertainty, systemic risk, high-dimensional risk measure and worst-scenario analysis etc.

**Reference Number:** 2018-HW-Maths-28

**Reference Number:** ACM

**Reference Number:** 2018-HW-Maths-22

**Reference Number:** ACM

**Reference Number:** ACM

**Reference Number:** ACM

**Reference Number:** ACM

**Reference Number:** ACM

**Reference Number:** ACM

**Reference Number:** ACM

**Reference Number:** ACM

**Reference Number:** ACM