The present seminar-based course covers some of the innumerable applications of geometry to real life situations, and also aims at enhancing the
student's critical awareness and ability to work autonomously.
*Topics in projective geometry
Synthetical approach to projective geometry: projections and sections. Plane homographies. Homologies. Applications to perspective drawing.
Quadrics and their projective, affine, metric classifications. Matrix approach to plane and spatial homographies. Rational Bezier curves and surfaces.
Applications to computational vision (viewing pipeline). Camera calibration, affine and metrical image reconstruction via the absolute conic.
Calibrating conic. Two-view geometry: epipolar geometry and fundamental matrix.
*Topics in Riemannian geometry
Review of basic notions. Geodesics. Exponential map. Curvature tensors. Applications: geometry of covariance matrices and computer vision. Shape spaces.
Lie groups and applications to robotics.
* Knot theory and applications
Geometrical and combinatorial aspects of knot theory.
Linking and writhing numbers.
Knot invariants. Applications.
Assessment: the student shall write an essay and give an exposition on one of the course topics, agreed on with the instructor.
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