[VData Science & OR] Khalide Jbilou (Université du Littoral Côte d'Opale, France)
23 June 2025 – 27 June 2025
Venue: office XX, XX floor of the “Departamento de Engenharia Mecânica e Industrial (DEMI)” Building
[SAL] Determinants of Finite Semigroups | M. H. Shahzamanian (CMUP FCUP)
23 June 2025 2:00 pm – 3:00 pm
Room: 4.6, ed. VIII
Abstract: The concept of a determinant associated with a finite group originates in the work of Dedekind and Frobenius in the late 19\textsuperscript{th} century. This idea was later extended to finite semigroups, where the determinant of the semigroup algebra captures deep structural information. For commutative semigroups, Steinberg provided a factorization of the semigroup determinant, and more recently, the theory has been developed for broader classes, such as semigroups in the pseudovariety $\ensuremath{\mathsf{ECom}}$, where all idempotents commute.
In this talk, we trace the development of computing determinants for finite semigroups, from its classical origins to more recent results. We focus on semigroups whose structure enables determinant computation via partial orders and canonical decompositions, particularly using the notion of $\ll$-smoothness. These developments highlight both the possibilities and limitations in extending the theory beyond commutative and idempotent-commuting settings.
We also discuss recent progress in identifying broader classes of semigroups where determinant computations remain tractable, even when full $\ll$-transitivity is absent. This opens new directions for understanding the algebraic and combinatorial properties that govern the behavior of semigroup determinants.
[CourseDataScience] Advanced Tensor Computation and Applications | Khalide Jbilou (Université du Littoral Côte d'Opale, France)
23 June 2025 3:00 pm – 5:00 pm
NOVA FCT, Sala Ágora
Tensor computation extends the principles of linear algebra and numerical analysis to higher-dimensional data structures, allowing for efficient processing of complex data. Tensors play a central role in a variety of disciplines, from machine learning to scientific simulations. Tensors are among the most versatile and powerful mathematical tools available, with applications in many disciplines such as physics, computer science, engineering, graphs, and machine learning.
The mini-course is designed as a comprehensive introduction to tensors and their applications, bridging theory and practice. It seeks to demystify the subject for beginners while offering valuable insights for those with more advanced knowledge. Our focus is twofold:
Conceptual Understanding: By presenting tensors in a clear and accessible manner, we aim to equip the course attendees with a solid grasp of the core principles.
Practical Applications: With numerous examples and case studies, we plan to illustrate how tensors are used to address real-world challenges, from simulating physical systems to enabling breakthroughs in artificial intelligence.
Registration can be completed here.
[VData Science & OR] Khalide Jbilou (Université du Littoral Côte d'Opale, France)
23 June 2025 – 27 June 2025
Venue: office XX, XX floor of the “Departamento de Engenharia Mecânica e Industrial (DEMI)” Building
NOVA Math‘s focus is on cutting edge research, in both pure and applied mathematics, valuing the use of mathematics in the solution of real-world problems at the industrial level and of social relevance.
One of the main strategies developed by NOVA Math is to promote the exchange of knowledge with other sciences. It is important to engage with the users of mathematics, given them the support for their research on one hand, and on another hand, to direct mathematical researchers that seek real-life problems.
Funded by national funds through the FCT – Fundação para a Ciência e a Tecnologia, I.P., under the scope of the following projects:
UIDB/00297/2020, UIDP/00297/2020, UID/MAT/00297/2019, UID/MAT/00297/2013, PEst-OE/MAT/UI0297/2014, PEst-OE/MAT/UI0297/2011.