SSMI2025

34. Prof. Ovidiu Bagdasar, University of Derby, Derby, UK

Link prezentare: AICI

Data: 10 iulie 2025, la ora 13:00, în sala PI9, Corpul P

Titlul prezentării: Nonlinear Aspects in Dynamic Geometry

ABSTRACT: Starting with a fixed triangle A0B0C0 in the complex plane, one can construct recursively a dynamic geometry by applying a sequence of transformations (Tn)n>=0, to obtain a sequence of triangles (AnBnCn)n>=0. Some general questions arise:

1) Can we find the explicit coordinates of the triangle AnBnCn?

2) Does the sequence (AnBnCn)n>=0 converge? If so, describe the limit.

3) Does the sequence (AnBnCn)n>=0 converge in shape? If so, describe the limit.

In this talk we present some recent results related to Kasner triangles with complex parameter, whose dynamics can be described by linear transformations, and where exact analytical formulae determine the asymptotic behaviour. We then examine nonlinear dynamic geometries determined by various configurations associated to the triangles in the sequence. In certain cases, the convergence to a point, or in shape can be proved, but other resulting iterations are chaotic and difficult to describe.

33. Prof. Dorin Andrica, Babeș-Bolyai University, Cluj-Napoca

Link prezentare: AICI

Data: 10 iulie 2025, la ora 12:00, în sala PI9, Corpul P

Titlul prezentării: Some new results on the coefficients of cyclotomic and of inverse cyclotomic polynomials

ABSTRACT: Cyclotomic and inverse cyclotomic polynomials have many interesting properties, playing a fundamental role in various areas of mathematics, bridging classical and modern theory. In this talk we will present some recently obtained results regarding the coefficients of these polynomials, including exact integral formulas, recursive formulas, and numerical simulations for binary and ternary polynomials.

 
32. Prof. Subhash Chandra, School of Mathematics, Harish-Chandra Research Institute,India

Data: 26 iunie 2025, la ora 13:00, în sala PI9, Corpul P

Titlul prezentării: On the dimension of graph of continuous functions

ABSTRACT: In this talk, first, we discuss the notions of the box dimension and the Hausdorff dimension along with some fundamental properties. Then we discuss the concept of fractal functions and we estimate some bounds of the Hausdorff dimension and box dimension of fractal functions on function spaces such as Convex-Lipschitz space and Holder space. We also give the estimates of the Hausdorff dimension and the box dimension of the graph of the mixed Riemann-Liouville fractional integral for various choices of continuous functions on a rectangular region
31. Ovidiu CĂLIN, Prof., Eastern Michigan University, SUA
Data: 3 martie 2025, la ora 13:00, în sala PI9, Corpul P
Titlul prezentării: Deep Learning in Geometric Analysis
ABSTRACT: Mechanics, rooted in Riemannian geometry, is traditionally described using conservation laws and differential equations.Deep Learning now offers a powerful tool  to solve systems dynamics directly using neural networks. This fact bridges the geometric theory and computational solutions. I shall describe a few examples of this type of applications.
Scurtă biografie. Ovidiu Călin este profesor de matematică și statistică la Eastern Michigan University. Și-a obținut doctoratul la University of Toronto în anul 2000. A fost profesor invitat la Princeton University (2016-2017) și la University Notre Dame (2000-2002). Interesele sale matematice variate includ învățarea profundă, finanțele matematice, calculul stocastic, teoria informației, analiza geometrică și calculul variațiilor.