Unit information: Topics in Modern Geometry 34 in 2019/20

Unit name	Topics in Modern Geometry 34
Unit code	MATHM0008
Credit points	10
Level of study	M/7
Teaching block(s)	Teaching Block 1A (weeks 1 - 6)
Unit director	Dr. Jordan
Open unit status	Not open
Pre-requisites	MATH20006 Metric Spaces and MATH21800 Algebra 2. MATH20004 Introduction to Geometry and MATH33300 Group Theory are helpful but not essential.
Co-requisites	None
School/department	School of Mathematics
Faculty	Faculty of Science

Description including Unit Aims

Unit Aims

The aim of the unit is to introduce students to types of geometry which are instrumental in current research. In particular the unit will look at the use fo notion from abstract algebra and analysis in geometry.

Unit Description

The unit will look at two topics in modern geometry. This topic will be one of topological groups, hyperbolic geometry, Lie groups or the geometry of group actions. It will also develop the topology and algebra needed to studey these topics.

Relation to Other Units

The course expands ideas introduced in MATH21800 Algebra 2, and has relations to MATH20200 Metric Spaces, MATH33300 Group Theory, MATHM1200 Algebraic Topology and the proposed new level M unit Algebraic Geometry. Students may not take this unit if they have taken the corresponding Level H/6 unit MATH30001 Topics in Modern Geometry 3.

Intended Learning Outcomes

Students who successfully complete the unit should:

• be able to clearly define topological groups, discrete groups and manifolds
• be familiar with examples of all three;
• be able to use techniques from abstract algebra and mathematical analysis to solve problems in geometry;
• be familiar with aspects of one of differentiable manifolds, projective space and algebraic curves or hyperbolic geometry.
• have developed an awareness of a broader literature,
• have gained an appreciation of how the basic ideas may be further developed,
• be able to assimilate material from several sources into a coherent document.

Teaching Information

Lectures, including examples and revision classes, supported by lecture notes with problem sets and model solutions. Self-study with directed reading based on recommended material.

Assessment Information

80% Examination and 20% Coursework.

Coursework will be 4 homework sheets during the lectures weeks 1-6 each worth 2.5% and then a sheet with questions from the whole unit set in weeks 7-10 worth 10%.

Reading and References

Recommended

• Joseph Harris, Algebraic Geometry: A First Course, Springer, 1992
• Miles Reid, Undergraduate Algebraic Geometry, Cambridge University Press, 1988
• Karen E. Smith et al., An Invitation to Algebraic Geometry, Springer, 2000