Grothendieck–Serre Conjecture: A conjecture concerning the triviality of principal G–bundles over regular local rings, significant for its implications in algebraic geometry and cohomology.

Combinatorial algebraic geometry sits at the intersection of discrete mathematics and algebraic geometry, exploring the deep interplay between algebraic structures and combinatorial methodologies.

We prove that Grothendieck's Hodge standard conjecture holds for abelian varieties in arbitrary characteristic if the Hodge conjecture holds for complex abelian varieties of CM-type. For abelian ...

David I. Lieberman, Numerical and Homological Equivalence of Algebraic Cycles on Hodge Manifolds, American Journal of Mathematics, Vol. 90, No. 2 (Apr., 1968), pp ...

The knapsack problem is a classic NP-hard optimization challenge with wide-ranging applications in computer science, such as resource allocation. While several variants have been developed, including ...

The geometry and topology group at UB is traditionally strong in research and mentoring. Our faculty work in the areas of algebraic topology, complex geometry, differential geometry, geometric group ...

In time-varying software-defined wireless sensor networks (SDWSNs) for Internet of Things (IoT) applications, the topology may change due to the interference or abnormal events, thus leading to ...