Abstract
Differential geometry is a mathematical framework that uses algebra and calculus to study geometric structures. It provided the foundation for Einstein&rsquos general theory of relativity and has since influenced many areas of mathematical physics, from particle theory to cosmology. More recently, differential geometry has gained traction in computer science, particularly in computer graphics and computer vision.
In the past decade, its applications have expanded into computational medicine, where mathematical models help analyze large-scale biomedical data and quantify disease-related anatomical changes. By modeling healthy anatomical structures and measuring deviations from them, differential geometry aids in diagnosis, disease progression analysis, and computer-assisted surgical planning.
This talk will explore the role of differential geometry in computational medicine, highlighting its impact on statistical shape analysis and medical imaging. It will conclude with insights into the future of AI-driven healthcare and its potential to transform diagnostics and treatment planning.
Learning Objectives
By the end of this talk, participants will be able to:
1. Understand how mathematical concepts from differential geometry are used to study shapes and structures in medicine.
2. Recognize the role of computational techniques in analyzing medical images and anatomical changes.
3. Identify real-world applications of differential geometry in diagnosing diseases and planning surgeries.
4. Appreciate how technology and mathematics come together to improve healthcare outcomes.
5. Discuss the future potential of advanced computing and artificial intelligence in medical research and treatment.