Mathematics Days in Sofia – 2026
Section “Mathematical Foundations of Computer Science and Artificial Intelligence”
Participants
Invited Speakers
- Giuseppe Amato, Istituto di Scienza e Tecnologie dell’Informazione “Alessandro Faedo”, Consiglio Nazionale delle Ricerche, Italy
- Maria Nisheva-Pavlova, Sofia University “St. Kliment Ohridski” and Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria
Contributors
Aleksandar Aytov, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria
Antoaneta Tsvetanova, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria
- Dimiter Dobrev, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria
- Galina Momcheva, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria
Ivan Kavaldzhiev, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria
- Maria Pashinska-Gadzheva, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria
- Maya Lekova-Armyanova, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria
Neli Zhekova, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria
Petar Krastev, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria
Preslava Datsova, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria
- Soowhan Yoon, American University in Bulgaria, Bulgaria
- Stela Zhelezova, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria
Svetoslava Minkova, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria
- Teodora Todorova, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria
- Tsonka Baicheva, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria
- Tsvetyana Yoveva, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria
Ventsislav Polimenov, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria
Wonwoo Kang, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria
Program and Abstracts
Extended Reality (XR) builds on Augmented Reality (AR) and Mixed Reality (MR), which themselves extend the foundations of Virtual Reality (VR). VR immerses users in fully digital environments through headsets, smart devices, or computer screens, but it isolates them from the physical world. AR and MR, instead, overlay digital content onto the real environment. Virtual objects are aligned, fused, and synchronized with physical surroundings, and in MR users can interact with both physical and virtual elements in a unified space.
XR goes even further. It is not limited to visual augmentation; it enhances the realism of interactions across multiple sensory dimensions. With XR, users can feel virtual objects—their weight, their temperature, even their texture and consistency—bringing the physical and digital worlds into deeper, more natural continuity.
Artificial Intelligence plays a crucial role in enabling this integration. AI can enrich virtual scenes with semantic information, reconstruct and interpret 3D environments, correct and enhance data during 3D digitization, support the creation of virtual worlds from physical ones, and facilitate seamless interaction across both realms.
In this keynote, we will explore how these challenges have been addressed within the SUN project (Social and hUman ceNtered XR – https://www.sun-xr-project.eu/) and discuss the current limitations and emerging opportunities in this rapidly evolving field.
Knowledge graphs have emerged as a pivotal model that serves as an essential bridge between classical symbolic artificial intelligence and modern data-driven machine learning approaches. By representing knowledge in a structured, interconnected format, they enable AI systems to reason, infer new facts, and integrate heterogeneous sources of information more effectively than traditional methods. We discuss the role of knowledge graphs in advancing the capabilities and the usability of AI systems, from enhancing explainability and interoperability to powering recommendation engines and decision support systems. We analyze key challenges such as graph construction, entity resolution, graph completion, reasoning scalability, and integration with neural networks, while highlighting recent approaches that address these issues. Based on relevant examples, we demonstrate that knowledge graphs are essential for building robust, explainable, and reliable AI systems capable of handling a variety of complex problems.
Modern organisations increasingly depend on information systems that are fragmented, heterogeneous, and difficult to integrate with through conventional programmatic interfaces. This research investigates how autonomous AI agents can effectively interact with such systems by grounding their actions in structured, domain-specific knowledge rather than relying solely on large language model reasoning. The proposed architecture combines a semantic Knowledge Graph, a Retrieval-Augmented Generation pipeline, and an autonomous web browsing agent under a unifying design principle: knowledge before action — the agent consults relevant structured knowledge before initiating any interaction with an external system. This approach aims to address known failure modes of current AI agents, such as poor performance on domain-specific tasks and low form-filling accuracy, by providing richer contextual grounding at inference time. A proof-of-concept implementation in a real-world service delivery context is used to evaluate the framework and explore what each knowledge component contributes to overall agent performance
Quantum machine learning combines quantum computing and machine learning to develop algorithms that gives some computational advantages through quantum principles mainly to optimize learning, prediction, classification, optimization, and data analysis. Started from current challenges in the area we address both Quantum Machine Learning and Machine Learning with Quantum Computers and provide some viewpoints and perspectives. We demonstrate the role of
algorithms and metaheuristics in quantum computing and some ideas for their visualization. A new multidisciplinary research open group in the field of quantum computing has already been established and will be unveiled.
Cyclic difference families (CDFs) are of particular interest because they are closely related to several other combinatorial structures and have therefore numerous applications. Most closely related to the difference families are the cyclic Steiner systems and the perfect (v,k,1) optical orthogonal codes (OOCs). The latter are equivalent to (v,k,1) cyclically permutable constant weight (CPCW) codes. Thus, the results obtained for one of these objects are valid for the rest of them.
CDFs are widely studied during the years and there are obtained many existence and classification results about a variety of parameters. In this work we construct all nonequivalent (v, k, 1) CDFs for 18 sets of parameters v and k for which classification results were not known. We also present the multipliers of all previously classified CDFs with small parameters. Most of the results are double-checked by two different backtrack search algorithms. The usage of an interesting property of the considered objects makes one of these algorithms faster than the other.
All classification results obtained in this work can be freely downloaded from https://www.moi.math.bas.bg/~tsonka/MainCDF.htm.
We think that the availability online of files with all nonequivalent CDFs with definite small parameters and their multipliers might be of particular interest for some possible applications, as well as for future theoretical research on the topic.
This talk will discuss Markov Decision Process (MDP) as the mathematical framework for reinforcement learning, a field in artificial intelligence which played an instrumental role in the development of general purpose agentic models such as AlphaZero or MuZero. We may survey a few algorithms used as “good” stochastic policies for an MDP. This presentation is intended for the mathematical audience who wish to familiarize themselves with mathematical results (especially in probability theory) that went into the development of modern AI models.
Persistence images vectorize persistence diagrams into stable, finite-dimensional features. Inspired by this approach, we developed a vectorization framework for the spectral information encoded by the persistent Laplacian (PL). Given a scalar signature of a PL, we form a Persistent Laplacian Diagram (PLD) and smooth it into a Persistent Laplacian Image (PLI).
We prove stability bounds for PLIs with respect to Wasserstein perturbations of the underlying persistence diagrams under an admissibility condition on the signature. Through experiments on datasets such as MNIST and QM7, we show that PLIs with suitable signatures, especially the trace, provide an effective way to extract predictive topological and geometric information from the PL, outperforming existing PL-based representations in these settings.
This is joint work with Inkee Jung and Heehyun Park.
