During the talk, we give a short introduction to some basic definitions and notions regarding (vectorial) bent functions, which have been extensively studied in the past four decades. We present two new superclasses of bent functions obtained from the Maiorana-McFarland class (M) and Carlet's C and D classes. This is the first time bent functions are obtained from the M class by modifying the values on a set rather than some linear/affine subspace of GF(2^m). We also present a new generic construction method for vectorial bent functions using the so-called (P_U) property, which was introduced by Tang et al. in 2017. By combining these results, we obtain new families of vectorial bent functions weakly/strongly outside the completed M class. Some results obtained jointly with Enes Pasalic, Fengrong Zhang and Samir Hodžić are presented.

We are looking forward to meeting you at FAMNIT-MP1.

This Monday, April 4, 2022, from 10 am to 11 am.

Our Math Research Seminar will not be broadcasted via Zoom this time.

Everyone is welcome and encouraged to attend.

Datum in ura / Date and time: 28.3.22

(10:00 -- 11:00)

Predavalnica / Location: FAMNIT-MP1

Predavatelj / Lecturer: Nicolas Trotignon (CNRS, Lyon, France)

Naslov / Title: Minors vs induced subgraphs

Vsebina / Abstract:

During the talk, we give a short introduction to the graph minor project of Robertson and Seymour, that is a series of twenty papers that runs along more than 500 pages published from 1983 to 2004. The main result is the proof of conjecture of Wagner : in any infinite set of graphs, there must be a pair of graphs one of which is a minor of the other. This seemingly simple statement is in fact very deep and has algorithmic consequences of stunning generality. We will explain the statement and its consequences in a gentle way for computer scientists and mathematicians who are not specialists in graph theory (including all basic definitions). We will also present recent developments on analogs of some of the results of Robertson and Seymour when the « minor » containment relation is replaced by the « induced subgraph » containment relation.

Some results obtained jointly with Pierre Aboulker, Isolde Adler, Eunjung Kim and Ni Luh Dewi Sintiari will be presented.

Our Math Research Seminar will not be broadcasted via Zoom this time.

Everyone is welcome and encouraged to attend.

Datum in ura / Date and time: 21.3.22

(10:00 -- 11:00)

Predavalnica / Location: FAMNIT-MP1

Predavatelj / Lecturer: Ademir Hujdurović (UP FAMNIT, Slovenia)

Naslov / Title: Erdős-Ko-Rado type theorems for permutation groups

Vsebina / Abstract:

The Erdős-Ko-Rado theorem is one of the central results in extremal combinatorics. It gives a bound on the size of a family of intersecting k-subsets of a set and classifies the families satisfying the bound.

In this presentation I will talk about the extension of the Erdős-Ko-Rado theorem to permutation groups. Given a permutation group G acting on a set V, a subset S of G is called intersecting if any two permutations in S coincide on at least one point.

I will present some known and some new results on the maximum sizes of intersecting sets in certain permutation groups, and present several open problems.

Based on joint work with Istvan Kovacs, Klavdija Kutnar, Bojan Kuzma, Dragan Marušič, Štefko Miklavič and Marko Orel.

Our Math Research Seminar will not be broadcasted via Zoom this time.

Everyone is welcome and encouraged to attend.

Datum in ura / Date and time: 7.3.22

(10:00 -- 11:00)

Predavalnica / Location: ZOOM

Predavatelj / Lecturer: Nina Klobas (Durham University)

Naslov / Title: Temporal Graphs

Vsebina / Abstract:

Temporal graphs are graphs with a fixed vertex set and a set of edges that changes over time. This paradigm reflects the structure and operation of a great variety of modern networks, such as social networks, wired or wireless networks whose links change dynamically, transportation networks, etc.

Mainly motivated by the fact that, due to causality, information can be transferred in a temporal graph along sequences of edges whose time-labels are increasing, the most traditional research on temporal graphs has focused on temporal paths and other "path-related" notions, such as e.g. temporal analogues of distance, reachability, and exploration. To complement this direction, several attempts have been recently made to define meaningful "non-path" temporal graph problems, which appropriately model specific applications, such as e.g. temporal analogs of matching, colouring, and vertex covert.

In this talk we will introduce two different problems on temporal graphs (one path-related and one non-path related), and study their complexity.

Join the Zoom Meeting Here.

Everyone is welcome and encouraged to attend.

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