Καλωσόρισμα και ευχαριστίες.

Περίληψη: Traditional Neural Networks often ignore the underlying geometry of data, treating inputs like images or graphs as simple lists of numbers. In this presentation, we explore how Geometric Deep Learning (GDL) solves this by building mathematical symmetries directly into the network’s architecture. This approach allows models to learn much more efficiently, as they don’t need to see every possible orientation of an object to recognize it. Starting [...]

Περίληψη: Θα συζητήσουμε το paper των V.A. Mironov, A.I. Smirnov και L.A. Smirnov με τίτλο "Dynamics of Vortex Structure Formation during the evolution of Modulation Instability of Dark Solitons". Στόχος είναι πρώτα η κατανόηση του φυσικού μας προβλήματος και έπειτα η εξαγωγή εξισώσεων που περιγράφουν την συμπεριφορά του. Μην σας τρομάζει ο τίτλος, όλες οι άγνωστες λέξεις θα εξηγηθούν (ελπίζω) επαρκώς.

Περίληψη: The Combinatorial Nullstellensatz is a powerful tool developed by Noga Alon which has found many applications in a variety of problems with an algebraic flavour in number theory, combinatorics and elsewhere. It is also connected to several modern algebraic techniques such as the polynomial method and related algebraic results, for example the Schwartz-Zippel lemma. Our goal will be to introduce the main result and discuss some interesting and unexpected applications in a variety of problems.

Περίληψη: In classical Galois theory over ℚ (char. 0), there is the Galois correspondence matching subfields of an extension with subgroups of the automorphism group. We want to explore the behavior of field extensions in fields of char. p>0, beginning with finite fields 𝔽_p and moving on to infinite ones, like 𝔽_p(t). We will focus on when and why does the Galois correspondence fail and showcase some solutions to this problem.

Περίληψη: Κύριες ταξινομήσεις Θεωριών Μάθησης στην Διδασκαλία (σύντομα), σχολιασμός και παραδείγματα στην Διδακτική των Μαθηματικών, ανέκδοτες παρατηρήσεις σε σχέση με την προέλευση και ανάπτυξη τους.

Περίληψη: In 1977 Joachim Cuntz's paper about the C*-algebra generated by n isometries was published. Along with other relevant works, its influence can be seen in various results concerning universal C*-algebras and more. The language used has since changed in various ways. The aim of this talk is to glance at the more modern graph algebraic landscape, in which Cuntz's construction can be interpreted, using it as a specific example.

Ευχαριστίες και λήξη.