# Raziskovalni matematični seminar - Arhiv

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**Datum in ura**/ Date and time: 27.2.24

**Predavalnica**/ Location: FAMNIT-VP1

**Predavatelj**/ Lecturer: Joy Morris (University of Lethbridge, Canada)

**Naslov**/ Title: Detecting (Di)Graphical Regular Representations

**Vsebina**/ Abstract:

https://upr-si.zoom.us/j/85914318577

Meeting ID: 859 1431 8577

Don't miss out on this opportunity to delve into cutting-edge research and expand your mathematical horizons!

**Datum in ura**/ Date and time: 19.2.24

**Predavalnica**/ Location: FAMNIT-VP1

**Predavatelj**/ Lecturer: Marko Orel (University of Primorska)

**Naslov**/ Title: Marko Orel

**Vsebina**/ Abstract:

In this talk, a graph Γ = (V, E) is a finite simple graph, which means that V is a finite set and E is a family of its subsets that have two elements. Given two graphs Γ1 = (V1, E1) and Γ2 = (V2, E2), a map Φ : V1 → V2 is

a homomorphism if {Φ(u), Φ(v)} ∈ E2 whenever {u, v} ∈ E1. A bijective homomorphism is an isomorphism in the case {Φ(u), Φ(v)} ∈ E2 if and only if {u, v} ∈ E1. As usual, if Γ1 = Γ2, then a homomorphism/isomorphism is

an endomorphism/automorphism. A core of a graph Γ is any its subgraph Γ0 such that a) there exists some homomorphism from Γ to Γ0 and b) all endomorphisms of Γ0 are automorphisms.

In graph theory, Γ1 and Γ2 are usually treated as ‘equivalent’ if they are isomorphic, i.e. if there exists some isomorphism between them. Less frequent we meet the notion of homomorphically equivalent graphs Γ1, Γ2,

which means that there exists a graph homomorphism Φ : V1 → V2 and a graph homomorphism Ψ : V2 → V1. Here, the notion of a core appears very naturally because two graphs are homomorphically equivalent if and

only if they have isomorphic cores. Often, it is very difficult to decide if there exists a homomorphism between two graphs. In fact, this problem is related to many graph parameters that are hard to compute, such as the

chromatic/clique/independence number. As a result, the study of cores is challenging. In this talk, I will survey some properties of cores, with an emphasis on graphs that either admit a certain degree of ‘symmetry’ or have

‘nice’ combinatorial properties.

Everyone is welcome and encouraged to attend.

**Datum in ura**/ Date and time: 15.1.24

**Predavalnica**/ Location: FAMNIT-MP1

**Predavatelj**/ Lecturer: Hassan Cheraghpour (University of Primorska)

**Naslov**/ Title: Vanishing Immanants

**Vsebina**/ Abstract:

Let $ Q_{n}(\CC) $ be the space of all $ n\times n $ alternate matricesvover the complex field $ \CC $ and let $ d_{\chi}(A) $ denote the immanant of the matrix $ A \in Q_{n}(\CC) $ associated with the irreducible character $ \chi $ of the permutation group $ S_{n} $. The main goal in this paper is to find all the irreducible characters

such that the induced immanant function $ d_{\chi} $ vanishes identically on $ Q_{n}(\CC) $.

This is a joint work with Bojan Kuzma.

Everyone is welcome and encouraged to attend.

**Datum in ura**/ Date and time: 8.1.24

**Predavalnica**/ Location: FAMNIT-MP1

**Predavatelj**/ Lecturer: Franc Forstnerič (University of Ljubljana, Slovenia)

**Naslov**/ Title: Minimal surfaces with symmetries

**Vsebina**/ Abstract:

A minimal surface in a Euclidean space $\mathbb R^n$ for $n\ge 3$ is an immersed surface which locally minimizes the area. Every oriented minimal surface is parameterized by a conformal harmonic immersion from an open Riemann surface, and vice versa. In this talk, I shall present a recent result on the existence of minimal surfaces of a given conformal type having a given finite group of symmetries induced by orthogonal transformations on $\mathbb R^n$.

Everyone is welcome and encouraged to attend.