Tuesday 23 April 2019 |

Events for day: Thursday 15 November 2018 |

11:00 - 13:00 LectureOn Codomains of Right almost Split Maps School MATHEMATICS In the talk, I would like to present the main ideas of the proof of the converse of the famous Auslander's theorem on the existence of (minimal) right almost split morphisms. In particular, we show that a module over an arbitrary ring is finitely presented whenever it appears as the codomain of a right almost split map. If time permits, I shall discuss the dual problem concerning domains of left almost split maps. ... 12:00 - 13:00 LectureTangles -vs- Trees School MATHEMATICS The topic of these talks is the structural theory of sparse graphs. More specifically, we study the interplay between highly cohesive substructures, which we figuratively refer to as `tangles', and decompositions over a (graph-theoretic) tree, which we simply call `trees'. At this point, we intentionally leave the meaning of these terms undefined and rely solely on the connotations they may carry. We are primarily interested in situations in which a certain pair of a tangle and a tree cannot coexist: the existence of the specified substructure makes a decomposition of the desired kind impossible and vice versa. For example, tree-dec ... 14:00 - 16:00 Mathtematical Logic Weekly SeminarHigher Aronszajn trees School MATHEMATICS Aronszajn trees are of fundamental importance in combinatorial set theory, and two of the most interesting problems about them, are the problem of their existence (the Tree Property), and the problem of their specialization (the Special Aronszajn Tree Property). In these talks, we review some known results about higher Aronszajn trees. The first talk is devoted to the tree property and the second one is devoted to the special Aronszajn Tree Property. We also mention some open problems. ... 14:30 - 15:30 LectureTowards Disproving the Pure Semisimplicity Conjecture School MATHEMATICS Based on the recent paper [1], we propose a way how to finally construct a minimal counterexample to the Pure Semisimplicity Conjecture suggested more than two decades ago by Daniel Simson. The construction can be carried out under the assumption of existence of certain (tight) embeddings of division rings into simple artinian rings. This problem seems to be more tractable than an explicit construction of a division ring embedding $G subseteq F$ with the prescribed dimension sequence $(infty,1,2,2,2,dots)$. [1] J. L. Garc�a, "Small potential counterexamples to the pure semisimplicity conjecture", about to appear in JAA. ... |