SEMINARI I DEPARTAMENTIT TË MATEMATIKËS


Ky seminar do të mbahet përafërsisht një herë në muaj, zakonisht ditën e hënë, në orarin 12:30--13:30.

Fillimisht seminari do të organizohet online.

Seminari është i hapur për të gjithë stafin dhe studentët (përfshirë vitin e parë).

Për të marrë njoftime në lidhje me Seminarin, ju duhet të jeni i regjistruar në listën e Seminarit, gjë që bëhet thjesht duke ma dërguar një email në adresën @uni-pr.edu (por nuk keni nevojë të regjistroheni për të marrë pjesë në Seminar).

Seminaret e radhës:

Travis Schedler 23 maj 2022

Titulli: Symplectic representation theory

Abstrakti: Recently, a unifying theme has emerged in representation theory---the mathematical study of linear symmetries---wherein these symmetries can be seen as coming from a rich geometric object, a symplectic resolution of singularities. These objects have their origin in physics---Hamiltonian classical mechanics---and representation theory emerges from the passage to quantum mechanics. I will explain these ideas in the elementary context of representations of two-by-two matrices. I will then outline a program to classify symplectic resolutions, which is a vast extension of the celebrated Cartan--Killing--Dynkin classification of simple complex Lie algebras via Dynkin diagrams. No familiarity with these ideas (or with physics) will be assumed.



Seminaret e mbajtura:

Qamil Haxhibeqiri 11 prill 2022

11 prill 2022, 12:30--13:30

Titulli: To Shape theory via procategories

Abstrakti: Shape theory is a new branch of topology. Like homotopy theory, shape theory is devoted to study of global properties of topological spaces. However, the tools of homotopy theory are of a such nature that they yield interesting results only for spaces behave well locally (e.g.Absolute Neighborhood retracts (ANR spaces) or CW-complexes). On the other hand the tools of shape theory are so disegned that they also yield interesting results in the case of bad local behavior. Moreover shape theory agrees with homotopy theory on class of ANR's and CW-complexes i.e. on spaces with good local properties.

There are two approaches to define shape theory: one is Borsuk's which use the notion of fundamental sequences and the other is Mardesic-Segal's approach which use the notion of inverse systems of ANR's. K. Borsuk introduced the shape theory for compact metric spaces. After that S. Mardesic and J.Segal developed shape theory for compact Hausdorff spaces and S. Mardesic generalized shape theory for arbitrary topological spaces. The aim of this talk is to define shape category by Mardesic's approach. The shape category is defined by an arbitrary pair of categories and then are given special cases of shape category for compact Hausdorff spaces and some other spaces.

Alban Rrustemi

14 mars 2022, 12:30--13:30

Titulli: Emergence of large language models

Abstrakti: Language models (LMs) are becoming pervasive across a wide range of applications including search, machine translation, and speech recognition. Over the past two years, modern LMs have produced some of the most impressive demonstrations of artificial intelligence (AI) -- e.g. they can write newspaper articles, summarise books, take part in coding competitions, etc. In this talk, I'll provide a brief overview of LMs and aspects of machine learning that power these models. I'll focus on the scaling properties that unlock some of these advancements. I'll also comment on the overall role that LMs play in the field of AI.

Bahtijar Vogel

7 shkurt 2022, 12:30--13:30

Titulli: Sustainable Design Principles for Internet of Things (IoT): Towards open and secure IoT systems

Abstrakti: The Internet of Things (IoT) market is predicted to grow from an installed base of 30.7 billion devices in 2020, to 75.4 billion in 2025. There are different types of platforms available that often are referred to as IoT platforms, such as device-to-device, cloud-based and device-to-cloud platforms (which are often also referred to as enterprise platforms that face a vendor lockdown). The diversity of IoT platforms and their complex offerings creates confusion among developers and researchers, as well as end users. As such, today the IoT is mainly associated with vertically integrated systems that often are closed and fragmented in their applicability. With such closed nature and fragmentation in the market, developers usually struggle to reach critical mass, and even end users need to navigate through different brands and understand which devices are compatible in relation to which IoT platforms. Commercial or proprietary IoT platforms carry a pricing model and often promote vendor lock-in. Thus, often IoT platform providers lack support of new protocols, tools and data formats in time due to a constantly changing IoT landscape. Openness in IoT systems offer a multitude of benefits, even though security is never assured. While security is often recognized as a top priority for organizations and a push for competitive advantage, repeatedly, IoT products have become a target of diverse security attacks. Thus, orchestrating smart services and devices in a more open, standardized and secure way in IoT environments is yet a desire as much as it is a challenge. In order to address some of the above mentioned challenges, in this presentation, Dr. Vogel will be talking about his research related to the need for open and secure design principles for Internet of Things (IoT).

Uran Meha

20 dhjetor 2021, 12:30--13:30

Titulli: Plactic monoids via rewriting theory

Abstrakti: Two powerful approaches to the study of algebraic objects are homological algebra and representation theory. Recently the field of rewriting theory has supplied an algorithmic viewpoint for the homological study of monoids given via adequate presentations by generators and relations. In this talk we show how rewriting theory applies to certain monoids arising from the representation theory of Lie algebras (plactic monoids), and we obtain explicit 3-dimensional homological information for two classes of plactic monoids.

Vlerë Mehmeti

22 nëntor 2021, 12:30--13:30

Titulli: Local--global principle and non--Archimedean geometry

Abstrakti: We know since the 19th century, by the works of Galois, that we can't always explicitly determine the solutions of polynomial equations, we can at most approximate them. Ever since, the following question has been given a central place in Number Theory: when do solutions exist? I will be speaking of one (of the numerous) approaches to study this problem, called the local--global principle. Among other things, I will introduce for this purpose a geometry (called non-Archimedean), which satisfies surprising properties that are often incompatible with our Euclidean intuition.

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