# Computational geometry seminars: J. Pfeifle

• Computational geometry seminars: J. Pfeifle
• 2016-06-07T12:30:00+02:00
• 2016-06-10T13:30:00+02:00
• The simplexity of a convex d-polytope P with n vertices is the minimum number of simplices necessary to triangulate P without using new vertices. In dimension 3 and above, bounds for the simplexity are scarce, even in such well-studied cases as the d-dimensional cube. One general method for obtaining bounds on the simplexity is doing linear optimization over the universal polytope U(P). However, since U(P) lives in (d+1)-dimensional space, these linear programs quickly become infeasible computationally. On the other hand, if P is symmetric, we can use techniques from the representation theory of finite groups to simplify the computations. In the Tuesday session, we'll give a crash course on the basics of representation theory, and apply these tools to the problem at hand on Friday.

The simplexity of a convex d-polytope P with n vertices is the minimum number of simplices necessary to triangulate P without using new vertices. In dimension 3 and above, bounds for the simplexity are scarce, even in such well-studied cases as the d-dimensional cube. One general method for obtaining bounds on the simplexity is doing linear optimization over the universal polytope U(P). However, since U(P) lives in (d+1)-dimensional space, these linear programs quickly become infeasible computationally. On the other hand, if P is symmetric, we can use techniques from the representation theory of finite groups to simplify the computations. In the Tuesday session, we'll give a crash course on the basics of representation theory, and apply these tools to the problem at hand on Friday.

Quan
07/06/2016 12:30 a 10/06/2016 13:30
On
Room S215 Omega Building, Campus Nord UPC (equiv.: Room 215 Floor -2)
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Tuesday, June 7, 2016, 12:30-13:30 and Friday, June 10, 2016, 12:30-13:30