Combinatorial Algebraic Geometry

01/02/2016-07/02/2016

• Dates: 1 February – 7 February 2016 (Arrival to the village: 31 January 2016)
• Aims
  This 6 day long camp is designed for advanced undergraduate and graduate students. There will be five (45-60 minutes) lectures each day. Each lecture series will be on a certain topic related to combinatorial methods and problems in algebraic geometry. After the lectures, the students will be expected to work on individual and group assignments. The lectures will be in English. For any questions, please write to gunturkunhakan@gmail.com
• Fees: Camp fee is 500 TL (Around €160). This fee includes accomodation, four meals a day, tea, water, all the basic requirements.. Nesin Mathematics Village is a non-profit organization.
• Information: Registation: Click here for the registration. You will receive an approval message. If you cannot get a message, please submit the form again.

• Courses:

  Feza Arslan: Computational Commutative Algebra and Grobner Basis
  Monomial orderings, division algorithm, Gröbner basis, basic concepts of algebraic geometry and elimination theory

  Alperen Ergür: Polynomial method in combinatorial algebraic geometry. In recent years many outstanding problems in combinatorial geometry is solved by means of algebraic and topological tools. We are planning to present Finite Field Kakeya Conjecture, Joints Conjecture, Combinatorial Nullstellesatz and Polynomial Ham Sandwich Theorem in this direction. If time permits further topics will be discussed.

  Hakan Güntürkün: Enumerative tropical geometry
  Introduction to tropical geometry, tropical lines, tropical curves, classical enumeration of curves, tropical enumeration of curves.

  Özgür Kişisel: Sylvester-Gallai type problems, Dirac-Motzkin conjecture
  Suppose we have a line arrangement in real projective space. A point is called ordinary if it lies in the intersection of exactly two lines of the arrangement. If there are at least three lines and not all lines are concurrent, then there exist at least three ordinary points. If the number of lines n tends to infinity then asymptotically, the number of ordinary points is at least n/2. The last statement is a recently resolved conjecture. The aim of these lectures will be to describe these problems and similar variants.

  Özer Öztürk: Examples of polyhedral methods in algebraic geometry
  With a focus on toric varieties we shall discuss several applications of polyhedral methods in algebraic geometry. Poster: