Schedule of talks and abstracts, 12 May 2026
All lectures will be in Innorenew CoE, Livade 6a, Izola..
A simple version of the program is here.
The conference luch will take place at Innorenew CoE, Livade 6a, Izola.
10:00 - 10:25, Marston Conder
| Title: | Recent discoveries about finite quotients of triangle groups |
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Abstract: |
For integers k, l, m > 1, the ordinary triangle group Δ+(k, l, m) is the group with presentation ⟨ x, y | xk = yl = (xy)m = 1 ⟩, or equivalently ⟨ x, y, z | xk = yl = zm = xyz = 1 ⟩. Such groups play an important role in the study of large automorphism groups of algebraic curves and compact Riemann surfaces, and of regular maps on orientable and non-orientable surfaces. In this talk I will describe some recent developments concerning their finite quotients: (a) a surprising discovery that despite decades of attention being paid to non-abelian simple quotients, such quotients are relatively rare; (b) some work with my PhD student Darius Young why non-perfect hyperbolic ordinary triangle groups have vast numbers of finite soluble quotients; (c) a new theorem by Darius Young showing that the natural density (in the positive integers) of the set of orders of finite quotients of every given triangle group is zero, proved without resorting to the classification of finite simple groups; and (d) some unexpected consequences for the densities of orders of finite edge-transitive graphs, and the density of orders of finite quotients of any given finitely-generated infinite group. |
| PDF: | Abstract (PDF) |
10:30 - 10:55, Sabrina Melinda Lato
| Title: | Distance-biregular graphs and spectral bounds |
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Abstract: |
The Moore bound is an upper bound on the number of vertices a regular graph with fixed diameter can have. Fiol and Garriga gave a local version, using the spectrum to bound the number of vertices that can be at the maximal distance from a fixed vertex in a regular graph. Cioabă, Koolen, Nozaki, and Vermette gave a spectral Moore bound to upper bound the number of vertices of a regular graph with fixed second-largest eigenvalue, and subsequently Cioabă, Koolen, and Nozaki improved this bound for bipartite regular graphs. When any of those bounds are tight, the graph has the strong algebraic and combinatorial structure of a distance-regular graph. In this talk, we present extensions of these bounds to semiregular bipartite graphs, and characterize the extremal examples meeting these bounds as distance-biregular graphs. |
| PDF: | Abstract (PDF) |
11:00 - 11:30, Coffeee break
11:30 - 11:55, Andrea Švob
| Title: | On some new directed strongly regular graphs and their orbit matrices |
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Abstract: |
In this talk, we describe a construction of certain regular digraphs using finite simple groups. We prove the existence of some directed strongly regular graphs. Further, we introduce the notion of orbit matrices of directed strongly regular graphs. The talk is based on joint works with A. E. Brouwer, D. Crnković, M. Zubović Žutolija and T. Zrinski. |
| PDF: | Abstract (PDF) |
12:00 - 12:25, Nour Alnajjarine
| Title: | Linear Complete Symmetric Rank-Distance Codes in M3×3(𝔽q) |
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Abstract: |
An 𝔽q-linear code of minimum distance d is said to be complete if it is not contained in any larger 𝔽q-linear code with the same minimum distance. Studying such extremal objects is a natural problem in coding theory. In this talk, we classify 𝔽q-linear complete symmetric rank-distance (CSRD) codes in M3×3(𝔽q) up to equivalence. In particular, we show that there exist exactly 3 such codes when q is odd, and 6 when q is even of minimum distance 2, up to equivalence. This classification reveals a fundamental distinction between odd and even characteristic. When q is odd, every CSRD code in M3×3(𝔽q) is in fact a maximum symmetric rank-distance (MSRD) code. In contrast, when q is even, there exist 3-dimensional CSRD codes that are not MSRD. Our approach is geometric. By interpreting symmetric rank-distance codes as subspaces of PG(5,q), the problem translates into the study of linear systems of conics in PG(2,q), in particular pencils and nets of conics corresponding to 1- and 2-dimensional subspaces of the projective space of quadratic forms in 𝔽q[X,Y,Z]. We conclude by discussing consequences of this correspondence and provide new insight toward the long-standing open problem of classifying and characterizing nets of conics in PG(2,q). |
| PDF: | Abstract (PDF) |
12:30 - 14:00, Lunch, Innorenew CoE, Livade 6a, Izola
14:00 - 14:25, Akihiro Munemasa
| Title: | Roux: a refined approach to antipodal covers of complete graphs |
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Abstract: |
The concept of voltage assignment on graphs has been used to construct regular coverings of graphs. In particular, certain voltage assignments on the set of arcs of a complete graph give rise to antipodal distance-regular covers of complete graphs, as shown by Godsil and Hensel in 1992. Klin and Pech regarded voltage assignments on a complete graph on n vertices as an n × n matrix with entries in the group algebra in 2011, and it was axiomatized using the theory of association schemes by Iverson and Mixon in 2022. The terms roux matrix and roux scheme, introduced by Iverson and Mixon, capture not only antipodal distance-regular covers of complete graphs, but also complex equiangular lines. In this talk, I will introduce the so-called local construction of roux schemes, and how the remarkable set of 64 equiangular lines discovered by Hoggar in 1998 can be characterized as an association scheme. This is based on joint work with Jesse Lansdown, Alexander Gavrilyuk and Sho Suda. |
| PDF: | Abstract (PDF) |
14:30 - 14:55, Sanja Rukavina
| Title: | On some recent results on distance-biregular graphs |
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Abstract: |
Let Γ be a connected bipartite graph with vertex set partitioned as Y ∪ Y′. The graph Γ is called distance-biregular if, for any pair of vertices u and v, the number of neighbors of v that lie closer to u depends only on the distance d(u,v) and on whether u belongs to Y or to Y′. In this talk, we present recent results on distance-biregular graphs, specifically the classification of 2–Y-homogeneous (Y, Y′)-distance-biregular graphs with eccentricity D ∈ {3, 4, 5}. The talk is based on joint work with colleagues from the University of Primorska, Blas Fernández and Safet Penjić, and the University of Rijeka, Marija Maksimović and Emma Šepić. |
| PDF: | Abstract (PDF) |
15:00 - 15:30, Coffeee break
15:30 - 15:55, Giusy Monzillo
| Title: | On dual adjacency matrix (candidate) and (weakly) uniform structure |
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Abstract: |
In this talk, we investigate the connection between two properties of bipartite graphs: Q-polynomiality and uniform structure. To this end, we introduce the concept of a dual adjacency matrix candidate and define a weakly uniform structure by slightly relaxing the standard conditions for a uniform structure [1]. Our main result [2] establishes a one-to-one correspondence between these two concepts: Main Theorem. A bipartite graph Γ admits a dual adjacency matrix candidate with respect to x and corresponding parameters β, ρ if and only if Γ admits a weakly uniform structure with respect to x; in particular, for β = 2, the weakly uniform structure coincides with a standard uniform structure. References [1] P. Terwilliger. The incidence algebra of a uniform poset, Coding Theory and Design Theory 20(1) (1990), 193–212. [2] B. Fernández, R. Maleki, Š. Miklavič, G. Monzillo. On the uniform structure of bipartite graphs admitting a dual adjacency matrix candidate, Journal of Algebraic Combinatorics (2026). |
| PDF: | Abstract (PDF) |
16:00 - 16:25, Pascal Gollin
| Title: | A coarse Erdős–Pósa theorem |
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Abstract: |
An induced packing of cycles in a graph is a set of vertex-disjoint cycles with no edges between them. We generalise the classic Erdős–Pósa theorem to induced packings of cycles. More specifically, we show that there exists a function f(k) = O(k log k) such that for every positive integer k, every graph G contains either an induced packing of k cycles or a set X of at most f(k) vertices such that the closed neighbourhood of X intersects all cycles in G. Our proof is constructive and yields a polynomial-time algorithm finding either the induced packing of cycles or the set X. As a corollary, we prove that every graph with no K1,t induced subgraph and no induced packing of k cycles has tree-independence number at most O(tk log k), and one can construct a corresponding tree-decomposition in polynomial time. This resolves a special case of a conjecture of Dallard et al. (arXiv:2402.11222), and implies that on such graphs, many NP-hard problems, such as Maximum Weight Independent Set, Maximum Weight Induced Matching, Graph Homomorphism, and Minimum Weight Feedback Vertex Set, are solvable in polynomial time. |
| PDF: | Abstract (PDF) |
16:30 - 16:55, Jihye Jeong
| Title: | Ramanujan Graphs from Simplicial Complexes with few blockers |
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Abstract: |
In this talk, we discuss how to find a construction method for Ramanujan graphs from simplicial complexes with one or two blockers, where blocker mean minimal elements of the complement of a simplicial complex. To obtain this, we completely find all the binary linear codes obtained from simplicial complexes with one or two blockers. Furthermore, we explicitly compute their weight distributions using the corresponding multivariable functions. From the few-weight binary linear codes found, we construct 14 families of nonbipartite Ramanujan graphs; their eigenvalues are computed by using the weight distributions of the corresponding codes. We verify that our families of Ramanujan graphs are different from the previous families in terms of eigenvalues and regularity. This is a joint work with Yoonjin Lee (Ewha Womans University) and Jong Yoon Hyun (Konkuk University). |
| PDF: | Abstract (PDF) |
