Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Thursday, July 12, 2012, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Vissarion Fisikopoulos (National and Kapodistrian University of Athens)

Constructing Polytopes via a Vertex Oracle

We develop a new paradigm to construct polytopes whose vertices can be obtained by an effective oracle in a unique fashion. Starting with the Newton polytope of the resultant, our method also efficiently computes secondary polytopes as well as the Newton polytope of the discriminant. We propose an output-sensitive algorithm that requires the minimum number of oracles, each reducing to the construction of a regular triangulation of the input pointset. The C++ implementation of this algorithm has allowed us to compute resultant polytopes in 7 or 8 dimensions. It has also yielded the most complex 3d and 4d resultant polytopes, the latter with f-vector (22,66,66,22,1), thus opening the study of this polytope family. Finally, we discuss open algorithmic problems regarding such polytopes.

Upcoming talks     |     All previous talks     |     Talks by speaker     |     Upcoming talks in iCal format (beta version!)

Previous talks by year:   2024  2023  2022  2021  2020  2019  2018  2017  2016  2015  2014  2013  2012  2011  2010  2009  2008  2007  2006  2005  2004  2003  2002  2001  2000  1999  1998  1997  1996  

Information for students and suggested topics for student talks

Automatic MiSe System Software Version 1.4803M   |   admin login