Ioannis Diamantis (I.D.)

I am a geometric-topologist specializing in knot theory, braid groups, and 3-manifolds. My research primarily focuses on constructing Jones-type invariants for knots and links in 3-manifolds using knot algebras and Markov traces. These mathematical tools reveal deep connections within low-dimensional topology and its applications.

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A significant focus of my current work is on doubly periodic structures, a rich topic at the intersection of pure mathematics and applied science. These structures, which exhibit repeating patterns in two independent directions, have profound applications across disciplines:

• Material Science: Modeling lattice structures in crystallography, polymers and nanomaterials.
• Biology and Chemistry: Understanding molecular entanglements, protein folding and DNA topology.
• Mathematics and Physics: Analyzing periodic solutions in differential equations and physical systems.

In addition to their inherent mathematical beauty, doubly periodic structures offer practical tools for solving complex problems in real-world systems.

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I am also deeply engaged in Topological Data Analysis (TDA), leveraging topology to extract meaningful insights from complex datasets. My recent TDA work explores applications in Economics and Finance (Time series analysis, market behavior modeling and anomaly detection).

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Editorial and Organizational Roles

Guest Editor: Special Issue Mathematical Modeling of Complex Entangled Structures in the journal Mathematics (Q1, 2024-2025).

Upcoming Events:

• Co-organizing the international conference "The Theory of Periodic Tangles and Their Interdisciplinary Applications" at Tohoku University, Japan (2025).

• Local organizer of the first Knot Theory Congress, celebrating Prof. Louis Kauffman’s 80th birthday in February 2025.

   

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  Current Projects

• Book in Progress: Co-authoring a monograph for the De Gruyter Expositions in Mathematics series with international collaborators.
• Recent Research Highlights:
  • Published works on doubly periodic tangles in Symmetry and other leading journals.
  • Papers submitted on pseudo tangles and their equivalences.
  • A study on Symbolic Aggregate Approximation and TDA, published with my MSc student Fredrik Hobbelhagen.

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My research bridges pure mathematics and applications, offering a unique perspective on solving interdisciplinary problems. The study of doubly periodic structures and TDA exemplifies this approach, combining theoretical rigor with practical relevance.