2016/2017
Research Seminar "Convex and Algebraic Geometry 1"
Type:
Optional course (faculty)
Delivered by:
Faculty of Mathematics
Where:
Faculty of Mathematics
When:
1, 2 module
Language:
English
ECTS credits:
3
Contact hours:
32
Course Syllabus
Abstract
This course is aimed as an introduction to a variety of mathematical fields, which all have a common theme – convex geometry. The classes consist of either a lecture or a talk by one of the students. The students are encourage to take one of the topics from the course as a research project.
Learning Objectives
- Acquaintance with the basic notions, methods, and problems of convex geometry.
- Acquiring an idea of the role of convex geometry in other areas of mathematics (algebra, geometry, analysis, etc.)
- Acquiring the skills of applying methods and constructions of convex geometry to scientific research in various areas of mathematics.
- Acquiring the ability for independent study of topical mathematical literature.
Expected Learning Outcomes
- Knowledge of the basic notions, methods and problems of convex geometry.
- Skills of applying methods and construction of convex geometry in other areas of mathematics.
- Experience in independent study of topical mathematical literature
Course Contents
- Convexity and lattices
- Smooth convex bodies
- Convex polyhedra
- Mixed volumes
- Convex inequalities
- Ehrhart polynomials
Interim Assessment
- Interim assessment (2 module)O_{current} = O_{homework}*0.8 + O_{independent works}*0.2 O_{midterm/final} = O_{current}*0.2 + O_{final exam}*0.8
Bibliography
Recommended Core Bibliography
- Günter M. Ziegler. (2007). Lectures on Polytopes: Updates, Corrections, and More. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.2D793EFE
- John R. Harper, & Richard Mandelbaum. (2011). Combinatorial Methods in Topology and Algebraic Geometry. [N.p.]: AMS. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=776570
- Tao, T. (2013). Algebraic combinatorial geometry: the polynomial method in arithmetic combinatorics, incidence combinatorics, and number theory. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsarx&AN=edsarx.1310.6482
Recommended Additional Bibliography
- Dolgachev, I. (2012). Classical Algebraic Geometry : A Modern View. Cambridge: Cambridge University Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=473170