# Raziskovalni matematični seminar - Arhiv

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**Datum in ura**/ Date and time: 1.6.20

**Predavalnica**/ Location: ZOOM (See link below)

**Predavatelj**/ Lecturer: Tomaž Pisanski (UP FAMNIT and UL FMF)

**Naslov**/ Title: Flexible configurations

**Vsebina**/ Abstract:

In a flexible (n_k) configuration at least one configuration line has the property that its k configuration points may be placed on it in k predetermined positions, while rearranging the rest of configuration in such a way that the point-line incidences are preserved.

We will show some useful applications of this concept in connection with Grünbaum incidence calculus. In particular, we will give a proof that for any k and for each sufficiently large number n, there exists an (n_k) configuration of points and lines.

This is joint work in progress with Leah Berman and Gábor Gévay.

Everyone is welcome and encouraged to join the video-lecture through the following link:

https://us02web.zoom.us/j/

**Datum in ura**/ Date and time: 25.5.20

**Predavalnica**/ Location: ZOOM (See link below)

**Predavatelj**/ Lecturer: Andrés David Santamaría-Galvis (UP FAMNIT)

**Naslov**/ Title: PARTITIONING THE PROJECTIVE PLANE AND THE DUNCE HAT

**Vsebina**/ Abstract:

**Datum in ura**/ Date and time: 18.5.20

**Predavalnica**/ Location: ZOOM (See link below)

**Predavatelj**/ Lecturer: Žiga Velkavrh (UP FAMNIT and UP IAM)

**Naslov**/ Title: Market makers, information, and bid-ask spread

**Vsebina**/ Abstract:

The talk starts with the brief introduction of Mechanism Design theory, with particular focus on dominant strategy incentive compatible mechanisms. Next, the joint work with Prof. Dr. J. Čopič and Dr. M. Castellani is presented. We study the bilateral trade problem under no subsidies constraint which has not been explored much due to its complexity. In our setting, there are two traders, i.e., a seller and a buyer, one indivisible good, and a market maker. The traders have private valuations over one indivisible good and have a scarce information. A market maker is in full command of the choice of market platform and has no private information. We consider market equilibrium mechanisms, among which a special attention is devoted to stochastic bid-ask mechanisms. We conclude with an example that shows that in general a mechanism that maximizes a social welfare function may lie outside the set of simple posted prices mechanisms.

Link Zoom: https://us02web.zoom.us/j/86227923652

**Datum in ura**/ Date and time: 11.5.20

**Predavalnica**/ Location: ZOOM

**Predavatelj**/ Lecturer: Blas Fernandez (UP FAMNIT - UP IAM)

**Naslov**/ Title: On the Terwilliger algebra of distance-regularised graphs

**Vsebina**/ Abstract:

Terwilliger algebra of a commutative association scheme was successfully used for studying distance-regular graphs. However, this notion can be easily generalized to an arbitrary finite, simple and connected graph. In many instances, this algebra can be better studied via its irreducible modules. In this talk, we show how to relate the module structure of the Terwilliger algebra of a graph with the concept of local distance-regularity. Finally, we investigate how this algebra can be used as an effective tool for studying some combinatorial properties in the graph.

This is joint work with Stefko Miklavic.

Nut graphs are singular graphs of nullity one with full corresponding eigenvector. Recently, the existence problem of regular nut graphs was successfully addressed. In this talk, we present a generalisation of nut graphs to signed nut graphs and give some preliminary results of their existence. In particular, Fowler construction, switching equivalence and connection to double covers will be presented.

This is work in progress with Patrick W. Fowler, Irene Sciricha and Nino Bašić.

Link for the Conference: https://us02web.zoom.us/j/87925579576