On April 6, 2021, Rutger Campbell from the IBS Discrete Mathematics Group gave a talk at the Discrete Math Seminar on the difficulty of deciding whether a matroid given by the independence oracle is representable over the reals even if the matroid is representable over the complex field and is orientable. The title of his talk was “Matroid orientability and representability“.
In this talk we will have a brief introduction to oriented matroids and their relation to real-representability.
On September 8, 2020, Rutger Campbell from the IBS Discrete Mathematics Group presented a talk on various results on the real representability of matroids at the Discrete Math Seminar. The title of his talk was “Disasters in abstracting combinatorial properties of linear dependence“.
Let E be a finite set and I be a collection of subsets of E. When is there a set of real vectors indexed by E such that I correspond to its linearly independent subsets? In 1935, Whitney introduced matroids using some necessary conditions for this. However, complete characterizations with various techniques are intractable. This remains the case even if it is already known that there is a set of complex vectors indexed by E whose collection of linearly independent subsets corresponds to I.
The IBS discrete mathematics group welcomes Dr. Rutger Campbell and Dr. Debsoumya Chakraborti, new research fellows at the IBS discrete mathematics group from August 16, 2020.
Rutger Campbell received his Ph.D. from the Department of Combinatorics and Optimization at the University of Waterloo in 2020 under the supervision of Prof. Jim Geelen. He is interested in matroid theory and structural graph theory.