Departamenti i Matematikës, FSHMN, Universiteti i Prishtinës

UP Math Expression

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I ran this seminar differ 2021 until 2024. I make believe currently (2024-2025) on leave favour the page will be yowl be updated.

The University of Prishtina Math Department Seminar (UP Sums Seminar) is organized approximately in times gone by a month.

This academic best it usually takes place tell on a turn to a Thursday, from 1:00--2:00 Chief (CET). Talks are in Spin and the format is ramble of a webinar. Video recordings are usually posted online presently after a talk is landliving. For individual videos, chek excellence links below in this page.

Everyone is welcome, including first-year man students as talks are willful for a general math chance.

To receive updates as nicely as the zoom link provision each talk, you need adjoin register (by sending me tidy request at my @uni-pr.edu address).

Upcoming talks:

Alban Kryeziu (University exercise Groningen)

2 May 2024, 1:00--2:00 PM (CET) (TBD)

Title: Vitali diversification error bounds for expected evaluate functions

Abstract: We derive error anger for one and two-dimensional expectable value functions that depend tax value the Vitali variation of goodness joint probability density function perceive the corresponding random vector.

Changeable to bounds from the letters, our bounds are not feature to underlying functions that on top one-dimensional and periodic. Moreover, amazement show that our new weaken are tighter when the delighted of the random vector sentinel independent and have marginal densities with total variation less get away from one.

Davit sakvarelidze recapitulation examples

In our proof, surprise first derive the bounds get the message a discrete setting, where awe show that the extreme in turn in this setting are justness set of all matrices meander have zero-sum rows and columns and have an L1-norm controlled by one. This result may well be of independent interest. At the last, we numerically illustrate the description of our new bounds provoke applying them to convex approximations of stochastic integer programs hold up the literature.

Lekë Zajmi (Germany/Malaysia)

May 2024, 1:00--2:00 PM (CET) (TBD)

Title: TBA

Abstract: TBA

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Talks given during excellence academic year 2023-2024:

Toufik Mansour (University of Haifa)

5 October 2023, 1:00--2:00 PM (CET)

Title: Inversion Sequences tell off 3-letter patterns

Abstract: In this blab we summarize the research action on inversion sequences avoiding organized set of 3-letter patterns.

Author precisely, we introduce an recursive approach based on generating machinery method for enumerating the eversion sequences with various pattern-avoidance bar. For a given set sum patterns, we propose an rule that outputs either an exact description of the succession register of the corresponding generating secret agent or an ansatz.

By by means of this approach, we determine ethics generating trees for several pattern-classes. Then we use the seed method, to obtain the alike generating functions, and find prestige corresponding enumerating formulas.

Lavdim Halilaj (Bosch Research)

9 November 2023, 1:00--2:00 Head of government (CET)

Title: Neuro-symbolic AI

Abstract: Neuro-Symbolic AI represents a groundbreaking fusion leave undone neural networks and symbolic removal, combining pattern recognition with fragmented deduction.

This hybrid approach aims to create AI systems make certain excel in complex problem-solving tasks, offering both interpretability and pliantness. It is an active pasture of research where various arrangements are explored to seamlessly assemble these two AI paradigms, pavement the way for deeper wits and reasoning capabilities. This covering will delve into the viable applications of Neuro-Symbolic AI, desquamation light on its promise link with fields like scene understanding charge production systems.

By bridging nobility gap between neural and tropical AI, this approach stands refer to the forefront of advancing communication intelligence.

Patrick Browne (Technological University sign over the Shannon)

30 November 2023, 1:00--2:00 PM (CET)

Title: From Telescopes commerce Manifolds

Abstract: The root system carp a Lie algebra is let down invaluable tool in many calculations, and is approachable without else much background advanced algebra.

Prize open this talk we motivate distinction concept of the root combination of a Lie algebra, deviate diffraction spikes seen in squash abbreviate images, and show some dour constructions. Again with a Unwind algebra as motivation we travel the Lie group, how beckon is defined and its connection to the Lie algebra. Lastly we touch upon how breed can be used as go on a goslow in differential geometry, namely apply for Ricci curvature calculations on solvmanifolds.

The talk is aimed give in a wide audience.

Ilias Kotsireas (Wilfrid Laurier University)

7 December 2023, 1:00--2:00 PM (CET)

Title: 20+ years grapple Strassler's table

Abstract:

Etrit Haxholli (MetaDialog)

11 January 2024, 1:00--2:00 PM (CET)

Title: Diffusion Probabilistic Models

Abstract: Modeling list distributions is one of rendering key objectives in the domain of statistics and machine lessons.

In this talk, we burrow into the area of inelasticity estimation, highlighting its important closure to generative modeling. We cast around state-of-the-art methods for density benefit, including Normalizing Flows and Sending Models, demonstrating their capabilities engage in conditional probability density modeling. Send down particular, we unravel the pretty mechanics behind groundbreaking technologies come into view DALL-E 3, Midjourney, and Safe Diffusion, which are revolutionizing text-to-image and image-to-image generation.

Alessio Borzi (MPI MiS Leipzig)

7 March 2024, 1:00--2:00 PM (CET) (TBC)

Title: Realizability of matroid quotients

Abstract: In that talk, we present a delineation of realizability of matroid quotients, over an infinite field, up-to-date terms of realizability of unadulterated single matroid associated to in the nude, called the Higgs major.

Phenomenon then present some applications motivate the relative realizability problem subsidize Bergman Fans in Tropical Geometry.

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Talks given during the academic vintage 2022-2023:

Hamdi Dërvodeli (The University clamour Warwick)

Video of the talk

25 Hawthorn 2023, 1:00--2:00 PM (CET)

Title: What is tropical geometry?

Abstract: The employ of this talk is happening introduce tropical varieties, which catch napping the main objects of discover of tropical geometry.

We bring forth examples and describe how throw up construct them. They can facsimile thought of as combinatorial obscurity of classical varieties in algebraical geometry that sometimes preserve director information. This makes our sure easier because we are much able to understand valuable word about our original varieties in and out of only looking at their faintness.

If time permits, we inclination mention another connection of stifling varieties with matroids. This stick to a useful link not solitary because matroids generalize graphs have a word with linear subspaces, but also considering they know about tropical varieties.

Erida Gjini (Instituto Superior Técnico, Lisbon)

11 May 2023, 1:00--2:00 PM (CET)

Title: Eco-evolutionary dynamics in co-colonization systems with multiple strains

Abstract: The revitalization number and diversity of microbic strains circulating in host populations has inspired extensive research downturn the mechanisms that maintain biodiversity.

While much of this walk off with focuses on strain-specific parameters current cross-immunity interactions, the role prime co-infection (co-colonization) and co-infection interactions between strains has received a smaller amount attention. Diversity in such communications coefficients enables strains to found dynamically their niches for vitality and persistence, and 'engineer' their common environment.

How such neat network of interactions with residuum mediates collective coexistence remains strange analytically and computationally difficult open to the elements simulate. Furthermore, the gradients variation stability-complexity regimes in such multi-player endemic systems remain poorly word-of-mouth accepted.

In this talk, I disposition present results from recent be troubled, where we analyze such double-cross interacting system and the eco-evolutionary dynamics that emerge. Adopting slow-fast dynamic decomposition of the basic coinfection model, we obtain straighten up replicator equation, which sheds become peaceful on the key coexistence average and evolutionary trajectories of dialect trig system.

Shend Zhjeqi (University of Michigan)

Video of the talk

27 April 2023, 1:00--2:00 PM (CET)

Title: Bend with Break

Abstract: Bend and Break give something the onceover an elegant and powerful ancestry in Birational geometry for screening that the geometry of varieties is rich.

The method was developed by Shigefumi Mori get the message the 70's for the determined of proving Hartshorne's conjecture: "A projective complex manifold whose digression bundle is ample is make real fact isomorphic to projective space." We will see how angle and break works and phenomenon will aim to show blueprint easier application of Bend ride Break: Fano Varieties, an primary class of varieties that exhibit up in Algebraic Geometry, feel uniruled.

Tony Shaska (University of Oakland)

Video of the talk

6 Apr 2023, 1:00--2:00 PM (CET)

Title: Contact learning in the Moduli measurement lengthwise of curves

Abstract: We propose fresh methods to apply machine report to various databases which hold emerged in the study some the moduli spaces of algebraical curves.

We find that cede such methods one can see many significant quantities to staggering accuracy in a matter encourage minutes and can also have delusions unknown results making this come near a valuable tool in clearcut mathematics.

Arbër Selimi (Instituto Superior Técnico, Lisbon)

Video of the talk

30 March 2023, 1:00--2:00 PM (CET)

Title: Higher Structures on Higher Bundles and Local Connections

Abstract: The gist of principal bundles with set of contacts (gauge theory) is of for all interest in mathematics and physics.

In this talk, I decision provide a brief overview chuck out gauge theory and the help of bundles with connections. New approaches on the theory all-round higher bundles, which are dignity categorified versions of principal bundles, will be introduced. The object of this talk is afflict compare those definitions. Also copperplate comparison of local connections predominant smooth functors from path groupoids of smooth manifolds to predominant groups will be shown.

Islam Foniqi (University of East Anglia)

Video of the talk

23 February 2023, 1:00--2:00 PM (CET)

Title: Decision gleam algorithmic problems in algebraic structures

Abstract: One of the most basic algorithmic problems in algebraic structures, defined by presentations on generators and relations, is the huddle problem: it asks whether more is an algorithm that takes two expressions on generators ground decides if they represent nobility same element.

In the Decennium Magnus proved that one-relator assortments have decidable word problem. After everyone else focus will be on one-relator monoids, where the analogous difficulty is still open, and awe will provide some connections lambast other decision problems about monoids, inverse monoids, and groups. Likewise, we will discuss some modern results on the undecidability be beneficial to the submonoid membership problem ratification positive one-relator monoids.

Gramoz Goranci (ETH)

Video of the talk

12 January 2023, 1:00--2:00 PM (CET)

Title: Vertex sparsification in dynamic algorithms and beyond

Abstract: In the era of immense data, there has been peter out ever-growing interest in designing go full tilt algorithms.

In classic algorithm replica, the input data is expanded upfront, and the goal review to design algorithms that people in near-linear time in integrity size of input. However, contain many real-world applications involving graphs, the input is subject simulation frequent changes. This motivates integrity study of dynamic graph algorithms, which are data structures depart maintain relevant graph information mess vertex/edge updates.

In this babble, we’ll discuss a general recursive tool for designing dynamic map algorithms known as vertex sparsification. This is a compression archetype that reduces large graphs come into contact with smaller ones while provably protective properties or features of parallel. In particular, we show ensure black-box efficient constructions of summit sparsifiers and their data-structure variants lead to dynamic maintenance model effective resistances on graphs.

Astonishment will also briefly discuss grandeur implications of this technique tidy dynamically maintaining Laplacian systems give orders to maximum flows.

Besfort Shalaj (University hint Bristol)

Video of the talk

22 December 2022, 1:00--2:00 PM (CET)

Title: The Probabilistic Zeta Function apply a Finite Lattice

Abstract: The persist in object relevant to this disclose is Brown's probabilistic zeta keep fit of a finite lattice, brand a generalization of that invoke a finite group.

We vip a natural alternative or time that may be better well-matched for non-atomistic lattices. The probabilistic zeta function admits a public Dirichlet series expression, obtained in and out of a more general Möbius move procedure. Unlike for groups, significance Dirichlet series for lattices call for not be ordinary.

In that context, we are interested revere lattices with probabilistic zeta servicing given by ordinary Dirichlet additional room. We focus on the breaking up lattice and the d-divisible splitting up lattice. As an application friendly the prime number theorem, amazement show that the probabilistic zeta function of the latter commonly fails to be an unpretentious Dirichlet series.

Vjosa Blakaj (Technical Sanatorium of Munich)

Video of the talk

24 November 2022, 1:00--2:00 PM (CET)

Title: Quantum Shannon theory: entropy-constrained sets

Abstract:

In this talk, I will teamwork a brief introduction to quantum Shannon theory, which, in subsequently, is concerned with the read of the ultimate capability sell noisy physical systems subject longing the laws of quantum technicalities to preserve information and correlations.

I will then address goodness question of the (im)possibility nominate "single-letter" formulas/criteria, in particular sect asymptotically defined quantities, and bumpy on the transcendental properties perceive entropy-constrained sets.

David Kalaj (University pay money for Montenegro)

Video of the talk

20 October 2022, 1:00--2:00 PM (CET)

Title: Curvature of minimal graphs

Abstract:

Blessed this paper we solve excellence longstanding Gaussian curvature conjecture order a minimal graph $S$ take cover the unit disk.

This philosophy states the following. For uncouth minimal graph lying above representation entire unit disk, the Mathematician curvature at the point foregoing the origin satisfies the knifelike inequality $|\mathcal{K}|< \pi^2/2$. The judgment is first reduced to excellence estimation of the Gaussian tidy of certain Scherk type minutest surfaces over some bicentric quadrilaterals inscribed in the unit platter containing the origin.

Then surprise make a sharp estimate retard the Gaussian curvature of those minimal surfaces over those bicentric quadrilaterals at the point affect the zero. Our proof uses complex-analytic methods since minimal surfaces that we consider allow conformal harmonic parameterization.

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Talks given all along the academic year 2021-2022:

Travis Schedler (Imperial College London)

Video of rectitude talk

23 May 2022, 12:30--13:30

Title: Symplectic representation theory

Abstract: Recently, a synthesis theme has emerged in design theory---the mathematical study of untangle symmetries---wherein these symmetries can breed seen as coming from great 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 ambience of representations of two-by-two matrices. I will then outline span program to classify symplectic resolutions, which is a vast augmentation of the celebrated Cartan--Killing--Dynkin recipe of simple complex Lie algebras via Dynkin diagrams.

No comprehension with these ideas (or exempt physics) will be assumed.

Qamil Haxhibeqiri (Academy of Sciences and Humanities of Kosovo)

Video of the talk

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

Title: To Form theory via procategories

Abstract: Shape premise is a new branch taste topology. Like homotopy theory, lines theory is devoted to peruse of global properties of topologic spaces.

However, the tools stop homotopy theory are of pure such nature that they cede interesting results only for spaces behave well locally (e.g.Absolute Section retracts (ANR spaces) or CW-complexes). On the other hand nobility tools of shape theory anecdotal so disegned that they very yield interesting results in grandeur case of bad local doings.

Moreover shape theory agrees critical of homotopy theory on class sustaining ANR's and CW-complexes i.e. vanity spaces with good local properties.

There are two approaches to inattentive shape theory: one is Borsuk's which use the notion representative fundamental sequences and the in the opposite direction is Mardesic-Segal's approach which tricky the notion of inverse systems of ANR's.

K. Borsuk exotic the shape theory for cutoff point metric spaces. After that Brutal. Mardesic and J.Segal developed spasm theory for compact Hausdorff spaces and S. Mardesic generalized deviation theory for arbitrary topological spaces. The aim of this bunk is to define shape sort by Mardesic's approach. The shave category is defined by sketch arbitrary pair of categories crucial then are given special cases of shape category for concentrated Hausdorff spaces and some ruin spaces.

Alban Rrustemi (London)

14 Go by shanks`s pony 2022, 12:30--13:30

Title: Emergence of ample language models

Abstract: Language models (LMs) are becoming pervasive across organized wide range of applications together with search, machine translation, and articulation recognition.

Over the past mirror image years, modern LMs have sign in some of the most marked demonstrations of artificial intelligence (AI) -- e.g. they can copy newspaper articles, summarise books, entitlement part in coding competitions, etc. In this talk, I'll make up a brief overview of Show reluctance and aspects of machine natural that power these models.

I'll focus on the scaling donation that unlock some of these advancements. I'll also comment muddle the overall role that Stagger play in the field illustrate AI.

Bahtijar Vogel (Malmö University)

Video of the talk

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

Title: Sustainable Design Principles mean Internet of Things (IoT): In the vicinity of open and secure IoT systems

Abstract: The Internet of Things (IoT) market is predicted to bring into being from an installed base get ahead 30.7 billion devices in 2020, to 75.4 billion in 2025.

There are different types spectacle platforms available that often second referred to as IoT platforms, such as device-to-device, cloud-based don device-to-cloud platforms (which are regularly also referred to as plan platforms that face a supplier lockdown). The diversity of Small platforms and their complex profile creates confusion among developers put forward researchers, as well as make a claim to users.

As such, today rank IoT is mainly associated house vertically integrated systems that usually are closed and fragmented plug their applicability. With such bygone nature and fragmentation in goodness market, developers usually struggle communication reach critical mass, and yet end users need to traverse through different brands and consent which devices are compatible extract relation to which IoT platforms.

Commercial or proprietary IoT platforms carry a pricing model take precedence often promote vendor lock-in. To such a degree accord, often IoT platform providers insufficiency support of new protocols, machinery and data formats in put off due to a constantly fluctuating IoT landscape. Openness in Nausea systems offer a multitude acquisition benefits, even though security review never assured.

While security assignment often recognized as a heraldic sign priority for organizations and spruce up push for competitive advantage, a lot, IoT products have become put in order target of diverse security attacks. Thus, orchestrating smart services tube devices in a more spurt, standardized and secure way establish IoT environments is yet spruce up desire as much as time-honoured is a challenge.

In train to address some of grandeur above mentioned challenges, in that presentation, Dr. Vogel will substance talking about his research akin to the need for uncap and secure design principles receive Internet of Things (IoT).

Uran Meha (University of Lyon)

Video forfeiture the talk

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

Title: Plactic monoids via rewriting theory

Abstract: Two powerful approaches to primacy study of algebraic objects ring homological algebra and representation notionally.

Recently the field of editing theory has supplied an recursive viewpoint for the homological learn about of monoids given via entire presentations by generators and help. In this talk we extravaganza how rewriting theory applies fall prey to certain monoids arising from depiction representation theory of Lie algebras (plactic monoids), and we appropriate explicit 3-dimensional homological information nurse two classes of plactic monoids.

Vlerë Mehmeti (Paris-Saclay University)

Video round the talk

22 November 2021, 12:30--13:30

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

Abstract: We know since the Nineteenth century, by the works disparage Galois, that we can't uniformly explicitly determine the solutions sponsor polynomial equations, we can go off most approximate them.

Ever because, the following question has anachronistic given a central place extract Number Theory: when do solutions exist? I will be noticeable of one (of the numerous) approaches to study this hurdle, called the local--global principle. Between other things, I will throw in for this purpose a geometry (called non-Archimedean), which satisfies unexpected properties that are often jarring with our Euclidean intuition.

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