# Raziskovalni matematični seminar - Arhiv

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**Datum in ura**/ Date and time: 30.5.22

**Predavalnica**/ Location: FAMNIT-MP1

**Predavatelj**/ Lecturer: Žiga Velkavrh (UP FAMNIT, Slovenia)

**Naslov**/ Title: Indicators of human sociality in Slovenia and the Netherlands: Evidence from experiments with students

**Vsebina**/ Abstract:

In this talk we present the results of a cross-national research designed to detect differences/similarities in behavioral characteristics between Slovenian, Dutch and international students. Using eight standard tasks (games) from experimental economics we investigate the differences along the experimental measures of solidarity, trust, cooperation, positive and negative reciprocity, competition, honesty and risk attitudes. We find no significant cohort effects when we compare Slovenian and international cohorts, in any of the eight decisions. On the other hand, comparing the Dutch and Slovenian cohorts we do find that Dutch students exhibit lower solidarity, generosity and honesty.

Hope to see you there!

Everyone is welcome and encouraged to attend.

**Datum in ura**/ Date and time: 25.5.22

**Predavalnica**/ Location: FAMNIT-MP1

**Predavatelj**/ Lecturer: Wilfreid Meidl

**Naslov**/ Title: Z_p^k -bent functions

**Vsebina**/ Abstract:

To be announced.

Everyone is welcome and encouraged to attend.

**Datum in ura**/ Date and time: 16.5.22

**Predavalnica**/ Location: ZOOM

**Predavatelj**/ Lecturer: Ratko Darda (University of Osaka, Japan)

**Naslov**/ Title: On the number of rational points of varieties and stacks

**Vsebina**/ Abstract:

Manin-Peyre conjecture predicts the number of integral solutions of polynomial equations, i.e. the number of rational points on varieties. The predicted number is expressed by arithmetic and geometric invariants of the variety. Malle conjecture, predicts the number of field extensions of the field Q. Two predictions, despite the fact they are concerned with different questions, coming from different areas of number theory, appear very similar.

Stacks are geometrical objects, which are more general than varieties. They arise as solutions of classifying questions. Field extensions of Q are classified by rational points of certain stack. We try to motivate that there may exist a theory of Manin-Peyre conjecture for stacks which could have Malle conjecture for its consequence, and hence explain the above phenomenon.

**O**ur Math Research Seminar will ONLY be broadcasted via Zoom this time.

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Everyone is welcome and encouraged to attend.

**Datum in ura**/ Date and time: 19.5.22

**Predavalnica**/ Location: FAMNIT-MP4 & ZOOM

**Predavatelj**/ Lecturer: Vladimir Muller (Czech Academy of Sciences, Czech Republic)

**Naslov**/ Title: Matrices of operators

**Vsebina**/ Abstract:

Let $T$ be a linear operator on a separable infinite-dimensional Hilbert space $H$. Then $T$ allows for a variety of matrix representations $(\langle Tu_j,u_n\rangle)_{n,j=1}^\infty$ induced by the set of all orthonormal bases $(u_n)$ in $H$. We discuss the following problem:

Problem: Let $B\subset{\bf N}\times{\bf N}$ be a subset and $a_{nj}\quad(j,n)\in B$ given complex numbers. What are natural assumptions on $B$ and $a_{nj}$ to ensure that there exists an orthonormal basis $(u_n)$ such that

$$

\langle Tu_j,u_n\rangle=a_{nj}\qquad(n,j)\in B?

$$

This is a joint work with Yu. Tomilov.

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Everyone is welcome and encouraged to attend.

**Datum in ura**/ Date and time: 9.5.22

**Predavalnica**/ Location: FAMNIT-MP1

**Predavatelj**/ Lecturer: Safet Penjić (UP IAM, Slovenia)

**Naslov**/ Title: A unified view of inequalities for distance-regular graphs

**Vsebina**/ Abstract:

In this talk, we introduce the language of a configuration and of t-point counts for distance-regular graphs (DRGs). Every t-point count can be written as a sum of (t-1)-point counts. This leads to a system of linear equations and inequalities for the t-point counts in terms of the intersection numbers, i.e., a linear constraint satisfaction problem (CSP). This language is a very useful tool for a better understanding of the combinatorial structure of distance-regular graphs. Among others we prove a new diameter bound for DRGs that is tight for the Biggs--Smith graph. We also obtain various old and new inequalities for the parameters of DRGs, including the diameter bounds by Terwilliger.

This is joint work with prof Arnold Neumaier. The results are published in Journal of Combinatorial Theory, Series B, and the paper is available at https://doi.org/10.1016/j.

Everyone is welcome and encouraged to attend.

Hope to see you there!

**Datum in ura**/ Date and time: 4.5.22

**Predavalnica**/ Location: ZOOM

**Predavatelj**/ Lecturer: Jelena Radović (University of Novi Sad, Serbia)

**Naslov**/ Title: Higher commutators in semigroups with zero

**Vsebina**/ Abstract:

A group is nilpotent if it has a finite central series. In universal algebra we have two generalizations of the notion of nilpotency for arbitrary algebras: nilpotency and supernilpotency. We obtain these definitions by using the term condition commutator, as introduced by Freese and McKenzie. The definition of supernilpotency uses a higher order commutator which was introduced by Bulatov.

We develop the notion of the higher commutator of ideals in semigroups with zero. Further on, we show that the higher order commutator of Rees congruences is equal to the Rees congruence of the commutator of the corresponding ideals. We obtain that, for Rees congruences, higher order commutator is a composition of binary commutators. As a consequence, we prove that in semigroups with zero all three conditions of supernilpotency, nilpotency and nilpotency in the sense of semigroup theory, are equivalent. We also give a sufficient and necessary condition for solvability of semigroups with zero.

Join the Zoom Meeting Here!

See you there!

Everyone is welcome and encouraged to attend.