We present selected results from the work in the topology group at KAG FMFI UK supported by the grant VEGA 1/0425/25. The main focus is on the results of the PhD student Ajay Raj, who defended his thesis in August 2025. His work is located in surgery theory which is a specific way of approaching classification problems of topological and smooth manifolds. His aim was to calculate the...
We present a bottom-up approach to an effective theory that simultaneously explains the matter–antimatter asymmetry via leptogenesis, the dark matter relic abundance via freeze-in or freeze-out mechanisms, and neutrino masses via the Weinberg operator. We show that, in the minimal scenario, only two new particles and a single portal operator coupling the visible and dark sectors are sufficient...
In this paper, we present innovative approaches to teaching probability that were developed as part of the KEGA 037UK-4/2024 project Innovative learning technologies in the preparation of future mathematics teachers and the project Digital Transformation of Education and Schools (DiTEdu, code ITMS2014+: 401402DVR6). These approaches aim to foster a deep conceptual understanding of...
Binary quantization approaches, which replace weight matrices with binary matrices and substitute costly multiplications with cheaper additions, offer a computationally efficient approach to address the increasing computational and storage requirements of Large Language Models (LLMs). However, the severe quantization constraint ($\pm1$) can lead to significant accuracy degradation.
In this...
