Events

Abstract:  Discretizable Distance Geometry Problems (DDGP) consist in a subclass of Distance Geometry Problems (DGP) where the search space can be discretized and reduced to a binary tree. Such problems can be tackled by applying a Branch-and- Prune algorithm (BP), which is able to perform an exhaustive enumeration of the solution set. 

Abstract:  Exceptional collections are a powerful tool for understanding the derived category of coherent sheaves on algebraic varieties, with applications in commutative algebra, birational geometry, and mirror symmetry. While the existence of exceptional collections is known for classical varieties such as Grassmannians and flag varieties, constructing explicit collections for toric varieties presents challenges in combinatorial algebraic geometry. In this talk I will describe a computational approach to constructing full strong exceptional collections consisting of complexes of line bundles for toric varieties. No background in derived categories is assumed.

There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1:30pm.

Abstract:  The study of matroid tensor products dates back to the 1970s, extending the tensor operation from linear algebra to the combinatorial setting. While any two matroids representable over the same field admit a tensor product via the Kronecker product of matrices, Las Vergnas showed that such products do not exist for matroids in general, leaving the area underexplored. In this work, we utilize this operation to study skew-representability — representation over division rings that need not be commutative — by proving that a matroid is skew-representable if and only if it admits iterated tensor products with specific test matroids. A key consequence is the existence of algorithmic certificates for non-representability. We further show that every rank-3 matroid admits a tensor product with any uniform matroid, constructing the unique freest such product. Finally, we demonstrate the power of this framework by deriving the first known linear rank inequality for (folded skew-)representable matroids that is independent of the common information property.