2016/2017
Научно-исследовательский семинар "Выпуклая и алгебраическая геометрия 2"
Статус:
Дисциплина общефакультетского пула
Кто читает:
Факультет математики
Где читается:
Факультет математики
Когда читается:
3, 4 модуль
Язык:
английский
Кредиты:
3
Контактные часы:
42
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.
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
- Patchworking
- Bernstein-Kushnirenko Theorem
- Fiber polytopes and polyhedral subdivisions
- Tropical Geometry
- Coxter groups and polytopes
- Number of faces of a convex polytope
Interim Assessment
- Interim assessment (4 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
- Erwan Brugallé, Mariá Angélica Cueto, Alicia Dickenstein, Eva-Maria Feichtner, & Ilia Itenberg. (2013). Algebraic and Combinatorial Aspects of Tropical Geometry. [N.p.]: AMS. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=974654
Recommended Additional Bibliography
- 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=edsbas&AN=edsbas.53754841