University of Primorska Faculty of Mathematics, Natural Sciences and Information Technologies
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Mathematical Research Seminar - Archive

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Datum in ura / Date and time: 2.12.24
(15:00-16:00)
Predavalnica / Location: FAMNIT-MP1
Predavatelj / Lecturer: Russ Woodroofe (University of Primorska)
Naslov / Title: Some Hilton-Milner type theorems
Vsebina / Abstract:

The Erdős-Ko-Rado theorem describes the largest family of pairwise-intersecting k-element subsets of a fixed base set: for small k, this is the family of all sets containing some common element.  The Hilton-Milner theorem describes what happens if we disallow a common element.

I will present recent progress from joint work with Denys Bulavka and Francesca Gandini on the Hilton-Milner theorem and extensions.

Datum in ura / Date and time: 18.11.24
(15:00-16:00)
Predavalnica / Location: FAMNIT-MP1
Predavatelj / Lecturer: Tea Štrekelj (University of Primorska)
Naslov / Title: Exposed points of matrix convex sets
Vsebina / Abstract:
 
Matrix convex sets extend the classical notion of convexity to the noncommutative setting, where sets are closed under convex combinations with matrix-valued coefficients. In classical convexity, an exposed point can be weakly separated from the set, a concept central to convexity. 
In this talk we investigate an analogous notion for matrix convex sets, defining and studying matrix exposed points. We establish a connection between matrix exposed and matrix extreme points: a matrix extreme point is exposed in the classical sense if and only if it is matrix exposed. This result leads to a Krein-Milman type spanning theorem for matrix exposed points, akin to the classical results of Straszewicz and Klee. Specifically, any compact matrix convex set can be generated by its matrix exposed points via (limits of) matrix convex combinations. Moreover, with similar techniques, an even stronger result is obtained, namely that the matrix exposed points are dense in the matrix extreme points.
Datum in ura / Date and time: 13.11.24
(12:00-13:00)
Predavalnica / Location: FAMNIT-MP6
Predavatelj / Lecturer: Nour Alnajjarine (University of Rijeka)
Naslov / Title: Partially Symmetric Tensors: Connections and Classifications
Vsebina / Abstract:

In this talk, we present an interesting correspondence between partially symmetric  tensors over  (for ), linear systems of conics in , and subspaces of . We review the history of classifying these linear systems in  up to projective equivalence, an open problem dating back to 1908. We outline recent advances, showing how properties of the quadric Veronesean in  can be utilized to identify a set of complete invariants for projectively inequivalent pencils and webs of conics in .  These results contribute to the classification of partially symmetric 3x3xr tensors over Fq under the action of the group stabilising rank-1 tensors.