SSMI2023
20. Prof. dr Mihai Bărbosu, de la School of Mathematics and Statistics Rochester Institute of Technology, SUA
Data: 3 decembrie 2023, la ora 13:00, in sala PI9
Titlul prezentării: Riemannian Geometry Concepts in the Qualitative Study of a Dynamical System
ABSTRACT. In this presentation, Riemannian geometry concepts will be used in the qualitative study of the stability and instability of a conservative dynamical system. With appropriate metrics in the configuration space and in the phase space, criteria for stability and instability will be established for specific examples. Moreover, we will discuss the potential use of Riemannian metrics for clustering in Machine Learning.
19. Prof. Dr. Peter Singer, Technische Hochschule Ingolstadt, Germany
Data: Luni, 7 august 2023, ora 13:00, sala PP6
Titlul prezentării: Snakes in Computer Vision - existence and computation
ABSTRACT. In this talk existence and uniqueness questions for a class of variational models in computer vision, better known as "active contours" or "snakes", are investigated. Hammerstein integral equations are used to analyze the associated Euler equations. For computation multiple shooting methods are suggested. Results are sketched for a toy example and real images.
18. Prof. P.K. Sahoo, Department of Mathematics, Birla Institute of Technology Science-Pilani, Hyderabad Campus, Hyderabad 500078, India and Dep. of Mathematics and Computer Science, Transilvania University of Brasov, Romania
Data: Miercuri, 5 iulie 2023, ora 12:00, sala PI9
Titlul prezentării: Wormhole geometry: Is it Science or Science fiction?
Abstract. A wormhole is a special solution to the equations describing Einstein’s theory of general relativity, connecting two distant points in space or time via a tunnel. Ideally, the length of this tunnel is shorter than the distance between those two points, making the wormhole a kind of shortcut. Though they make for good science fiction as ways for faster-than light-speed travel between two extremely distant points in the universe. They are legitimate solutions to general relativity, but scientists have never figured out a way to maintain a stable wormhole in the real universe. Nowadays, one of the biggest arguments is whether “Wormholes are real Science or Science fiction". Here, we discuss the geometrical developments to present the wormhole structures and scientific measurements to test these types of theories.
17. R. Pasupathi, Post-doctoral researcher, Transilvania University of Brasov, Department of Mathematics and Computer Science
Data: Miercuri, 5 iulie 2023, ora 13:00, sala PI9
Titlul prezentării: A general framework for fractal interpolation functions
Abstract. Fractal geometry effectively captures various types of complexities present in natural phenomena and scientific experiments. Iterated Function System constitutes the most primitive framework to generate many fascinating and irregular fractal sets (called attractors). On the other hand, fractal interpolation function is an alternative method for construction of interpolation functions. Such a function is the attractor of an iterated function system comprising Banach contractions (on the product of two real compact intervals) with respect to the second variable. In this talk, we will discuss a much more flexible framework for the construction of fractal interpolation functions by using weaker contractions called Edelstein contraction. We will also discuss the estimation of lower and upper box dimensions of the graph of a fractal interpolation function constructed via this general method.
16. Prof. dr. Ion Chițescu, Universitatea Politehnică din Bucureşti
Data: Joi, 29 iunie 2023, ora 14:00, sala PI9
Titlul prezentării: Măsuri non-aditive şi integrale non-liniare.
Abstract. În prima parte se prezintă măsurile care nu sunt aditive. Se pun în evidenţă proprietăţi de bază şi se prezintă câteva consideraţii şi exemple specifice acestor măsuri. În a doua parte se prezintă două integrale care nu sunt liniare. Pe lângă anumite proprietăţi de bază se prezintă mai multe exemple.
În incheiere se prezintă calculul aproximativ al acestor integrale, exemplificat numeric.
15. Prof. dr. Florin Avram, Université de Pau, France
Data: Miercuri, 31 mai 2023, ora 13:00, sala PI9
Titlul prezentării: On the role of Scientific Computing in Mathematical epidemiology
Abstract. This mainly expository paper reviews some key concepts in mathematical epidemiology. Our purpose is to make the case that currently this field is focusing too much on simple particular cases, and deemphasizes more complex models, whose challenges would require cooperation with scientific computing experts (as an example, even the SIR model is not yet sufficiently understood). Our paper attempts also to invitate researchers working in the applied "sister sciences" which involve essentially nonnegative kinetic systems (like mathematical epidemiology, virology, chemical reaction networks, population dynamics, etc), to unite their efforts under the banner of "algebraic biology".
14. Ludovic DUCOBU, PhD student & Teaching assistant at the Faculty of Sciences of the University of Mons (Belgium) CV
Data: Marti, 25 aprilie 2023, ora 14:00, sala PI9
Titlul prezentării: The mathematical structure of spacetime : From Geometry of Physics to Physics of Geometry
ABSTRACT. In a rather general sense, one of the main aims of Physics as a scientific discipline is to identify the laws ruling the evolution of natural processes trough space and time. But doesn't this require a precise definition of those two concepts beforehand?
In this talk, I will provide an overview of the mathematical structures underlying the physical description of spacetime in the three main cases of Newtonian Mechanics, Special Relativity and General Relativity. Apart from the discussion of the structures themselves, this presentation will serve a double-purpose : First, emphasizing the evolution in our conceptions of space and time and how this was of key importance in the development of some of the most important discoveries of the twentieth century.
Second, commenting on the central place taken by geometry in the formulation of modern physical theories.
One take-home message is that, if a precise definition of spacetime is not enough to fully determine the laws of evolution ruling physical systems, it sets constraints on how one can consistently formulate those laws. If time permits, I will then talk a bit more on how the choice of a particular mathematical description of spacetime influences the formulation of the dynamics of a physical theory in the three discussed cases and comment on some ongoing research related to that idea.
13. Prof. emerit Constantin P. NICULESCU de la Universitatea din Craiova
Data: Miercuri, 18 ianuarie 2023, ora 12:00, sala PI9 Pagina personala: http://math.ucv.ro/~niculescu/
Titlul prezentării: Funcțiile avand diferente iterate pozitive si legătura lor cu functiile convexe de ordin superior
Abstract. Funcții convexe de ordin superior au fost introduse de Hopf si de Popoviciu, dar studiul lor a fost aprofundat doar in cazul funcțiilor de o variabila. In cazul funcțiilor de mai multe variabile formalismul utilizării diferențelor divizate multiple este foarte greoi si asta împiedica orice progres. In prezentarea noastra arătăm de ce varianta utilizării diferențelor iterate este realmente mult mai avantajoasa. Rezultatele obtinute au legatura cu inegalitatea Hornich-Hlawka si au fost obtinute in colaborare cu profesorul Suvrit Sra de la MIT.
