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Обычная версия сайта
2016/2017

## Научно-исследовательский семинар "Выпуклая и алгебраическая геометрия 1"

Статус: Дисциплина общефакультетского пула
Когда читается: 1, 2 модуль
Язык: английский
Кредиты: 3

### 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

• Final exam
Midterm

#### 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

#### 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