Conveners
Algebra and Number Theory
- Rosswitha Rissner
Cluster algebras are built by repeated “mutation,” but their basic arithmetic is still mysterious: do elements factor uniquely? I’ll describe algorithms that, for a large class of cluster algebras (including many from surfaces and Grassmannians), compute the divisor class group, decide when unique factorization holds, and even list all factorizations of a given element. This is a joint work...
In this talk, we recall some challenging problems in algebra, such as the characterization problem of polynomial rings, the automorphism groups of certain algebras, and the Dixmier property of algebras. We then explain how the concept of Aut-stable subspaces can be used as a tool to approach these problems, [1, 2, 3, 4, 5].
[1] H. Huang, Z. Nazemian, X. Tang, X.-T. Wang, Y. Wang, and J. J....
In his 10th problem, Hilbert asked for an algorithm to determine whether
a given Diophantine equation has integer solutions.
While it has been proven that such an algorithm does not exist, several
important classes of Diophantine equations can still be solved effectively.\
In this talk, we will study one such class, the class of Thue equations, with a
particular focus on the family of...