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“.
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.
Debsoumya Chakraborti received his Ph.D. from the Program of Algorithms, Combinatorics, and Optimization at the Carnegie Mellon University in 2020 under the supervision of Prof. Po-Shen Loh. He is interested in extremal combinatorics, probabilistic combinatorics, and random graphs.
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.