Schedules

On the mutually commuting $n$-tuples with respect to an automorphism

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Independence Complexes of Finite Groups

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Cayley Graphs over Cyclic Groups of Particular Valencies
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Matrix-Based Representation of $Z$-Fuzzy Soft $\beta$-Covering Multi Granulation Fuzzy Rough Sets and Its Application to MAGDM Using AHP

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Equivariant Persistent Homology via Group Actions

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This presentation explains how we can use group actions to improve persistent homology. We start by reviewing basic concepts like simplicial complexes, usual homology, and persistence modules. Then, we show how to include symmetries (group actions) by using a more advanced algebraic structure called a module over $\mathbb{Z}[x] \otimes \mathbb{Z}[G],$ where  $G$ is a group. This allows us to study data with repeating patterns or symmetrical shapes. We give simple examples to explain the ideas clearly and compare the usual persistence with the new method. Some real applications are also shown, such as image analysis and shape recognition.

Three Methods of Group Generations

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On Relation Between Representation Of Group $G$ Over an $F$-Vector Space $V$ and Representation of Group $G$ over The $F[x]$-Module $V$ via a Linear Transformation $T : V → V$

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Self-normalizing Subgroups

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We consider groups with few conjugacy classes of self normalizing subgroups.

The Classification of Finite Simple Groups from the perspective of “Big Mathematics”

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Structure-Preserving Transformations: Recent Updates on the Homological Analysis of Bieberbach Groups

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A Generalization of Perfect Group Under an Automorphism

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Generalizing the Enhanced Power Graph of a Group with respect to Automorphisms

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The enhanced power graph of a finite group G, sometimes also called as the cyclic graph  of the group G  has the set G-{1} as the set of vertices and a subset of the vertex set with exactly two elements is an edge if and only if that set generates a cyclic subgroup of G . We consider the following generalization of this construction which was previously called the cyclic graph of A-orbits of the group G:  For given group G and and another group A acting on G by automorphisms we define the vertex set as the set of A-orbits  on the set of nonidentity elements of G with two different vertices being adjacent if and only they contain elements which generate a cyclic group. We show that the connectivity and diameter of this generalized graph is similar to that of the enhanced power graph. We consider the universal vertices of this generalized graph and the question when this graph is a complete graph. Finally, we classify the groups for which this graph is the empty graph.