​Program na zimný semester 2022/2023

14.9.2022 (netradične v stredu o 10:30)
Prednášajúci: Dr. Andrew Craig
Department of mathematics and applied mathematics, University of Johannesburg, South Africa
Názov prednášky: "The finite lattice representation problem"
Abstrakt: "One of the most intriguing open problems in universal algebra asks the following question: Is every finite lattice isomorphic to the congruence lattice of a finite algebra? After nearly 60 years of study, the problem remains unsolved. However, important progress has been made which linked this problem to the study of subgroup lattices of groups. After surveying the problem, we will report on some ongoing joint work with Miroslav Haviar (UMB), and how these results could be applied to provide congruence representations of lattices."


8.11.2022
Prednášajúci: Mgr. Matúš Maciak, PhD.
Katedra pravděpodobnosti a matematické statistiky, Matematicko-fyzikální fakulta, Univerzita Karlova v Praze
Názov prednášky: "Changepoint detection and estimation using self-normalization and regularization"

Abstrakt: Atomic pursuit estimation techniques and self-normalized testing procedures are proposed and stochas- tically developed for dealing with a detection and estimation of significant changepoints in complex data structures—various regression type models. The overall complexity of the data may involve sophisti- cated and nontrivial structures (nonlinearity, lack of smoothness, irregularities, etc.), heteroscedasticity, dependency, non-stationarity, or extreme data—all represented within the given data structure itself (for instance, multivariate surfaces and time series, panel data, or run-off triangles common for actuaries).The main focus is given on the overall methodological framework: important statistical properties are derived and some cons&prons are discussed from the mathematical and empirical perspective. Finite sample properties are investigated via simulation study and real data examples.



22.11.2022
Prednášajúci: doc. Mgr. Ján Karabáš, PhD.
Katedra Informatiky Fakulty prírodných vied Univerzity Mateja Bela
Názov prednášky: "6-cycles and perfect matchings in snarks"

Abstrakt: The lecture is based on the results of the joint work with Edita Máčajová, Roman Nedela, and Martin Škoviera.
Cubic graphs not possesing any regular 3-edge-colourings are called snarks. Any collection of three perfect matchings of a cubic graph G misses some edges, if G is snark. Certainly, some edges are doubly- or triply-covered in this case. The minimum number of edges of a cubic graph G left uncovered by any three perfect matchings is called the colouring defect (shortly defect) of G, denoted as df(G). This invariant has been introduced by E. Steffen in 2015 [3] and it is an invariant of snarks worth to study.
Clearly, a cubic graph has defect zero if and only if it is 3-edge-colourable and this number is greater or equal to three for snarks. Far the most of the snarks have defect equal to three, which implies a strong structural constraint – the existence of a six-cycle. We will show the small snarks with defect greater than 3 and discuss the consequences of this observation. We will set the colouring defect for several families of snarks or, at least, we will present the working hypotheses on them.
We will discuss relationships of the defect of a snark to other invariants such as (colouring) resistance, oddness, girth, criticality, irreducibility [2] and others. We will also exhibit the close relationship of the study of snarks with small defect and well-known hypotheses e.g. Berge-Fulkerson Conjecture and 6-decomposition theorem [1, 2] (Jaeger Conjecture).
[1] J. Karabáš, E. Máčajová, R. Nedela, 6-decomposition of snarks, Euro- pean J. Combin. 34 (2013), 111–122.
[2] R. Nedela and M. Škoviera, Decompositions and reductions of snarks, J. Graph Theory 22 (1996), 253–279
[3] E. Steffen, 1-Factor and cycle covers of cubic graphs, J. Graph Theory 78 (2015), 195–206



6.12.2022
Prednášajúci: Mgr. Samuel Rosa, PhD.
Katedra aplikovanej matematiky a štatistiky Fakulty matematiky, fyziky a informatiky Univerzity Komenského
Názov prednášky: "Pohľad do viac dimenzií - vykreslenie veľarozmerných dát"
Abstrakt: "Jedným zo základných stavebných kameňov práce s dátami je schopnosť sa na ne pozrieť. Dáta pozostávajúce z dvoch, či troch premenných (napr. príjem, vek a majetok ľudí) dokážeme pekne vykresliť do dvoj- alebo trojrozmeru. Problém nastáva pri väčšom počte premenných - vtedy sa nám minú rozmery, a nevhodnou 2/3-rozmernou vizualizáciou môžeme stratiť veľké množstvo informácie.
V prednáške predstavíme niektoré známe pokusy štatistiky a strojového učenia vyriešiť tento problém, od tradičnej metódy hlavných komponentov, až po moderné metódy, ako je t-SNE."

Program v uplynulých rokoch:​_