Ioannis Diamantis (I.D.)
I am a geometric-topologist and my primary area of research is knot theory, braid groups and 3-manifolds. My research focuses on the construction of Jones-type invariants for knots and links in 3-manifolds other than the 3-sphere (skein modules), using knot algebras and Markov traces.
-- Participation In Conferences (Research Presentations) 2021-2024,
- Joint Meeting UMI (Unione Matematica Italiana)- AMS (American Mathematical Society), special session devoted to "Knot theory and applications", Palermo, Italy, July 23--26, 2024. Title of talk: tba.
- 12th International Conference on Mathematical Modeling in Physical Sciences. August 28--31, 2023, Belgrade, Serbia (by invitation). Title of e-talk: Skein modules via braids.
- Inverse Problems Virtual Meeting, 22—24 July 2022. This meeting was part of the AMS-EMS-SMF 2022, 2nd Joint Congress of Mathematics co-organized by the American Mathematical Society, the European Mathematical Society and the Société Mathématique de France, 18—22 July 2022, Grenoble, France. Video of talk: Skein modules: A braid theoretic approach.
- "Second Congress of Greek Mathematicians SCGM-2022", July 4--8, 2022, Athens, Greece. Title of talk: Kauffman bracket skein modules via braids.
- Mathematisches Forschunginstitute Oberwolfach, Germany, November 21--27, 2021. Hybrid Seminar/ Advanced School: Combinatorial and Geometric Knot Theory. Title of talk: The Kauffman bracket skein module of the complement of the (2, 2p+1)-torus knots via braids.
- I was one of the organizers for the “Circuit Topology III” Workshop, 2023 @Leiden University, The Netherlands, November 29, 2023.
- I am curently organizing an international conference in Tohoku University in Japan; to take place in 2025.
-- Seminar-Talks 2021-2024
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2024 Lab's seminar "Knot theory and Low-dimensional topology" of the National Technical University of Athens, Greece. Title of talk: Topological Graphs.
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2023 Mathematics Development Forum, Southeast University, School of Mathematics, Nanjing, P.R. China, Feb. 2023. Title of Talk: Skein modules via braids.
- 2023 Lab's seminar "Knot theory and Low-dimensional topology" of the National Technical University of Athens, Greece. Title of talk: Skein modules.
- "Knots and representation theory", e-Seminar on Knot Theory and Related Topics, June 20, 2022. Video of talk: Skein modules: A braid theoretic approach.
- University of Ioannina, Department of Mathematics, Ioannina, Greece, September 2021. Title of talk: The knot theory of 3-manifolds.
---------- Research ----------
-- I am currently writing a book for the series De Gruyter Expositions in Mathematics for De Gruyter Publishers, together with Boštjan Gabrovšek (Slovenia), Sofia Lambropoulou (Greece) and Maciej Mroczkowski (Poland).
-- My latest papers submitted for publication:
- Equivalence of Doubly Periodic Tangles, arXiv: 2310.00822, together with Prof. Sofia Lambropoulou & Dr. Sonia Mahmoudi.
- A survey on skein modules via braids, arXiv:2311.06556. Chapter for the Contemporary Mathematics (CONM) book series published by the American Mathematical Society (AMS); by invitation.
- The Kauffman bracket skein module of S1xS2 via braids arXiv.math[GT] (submitted for publication) 2023.
- The Kauffman bracket skein module of the lens spaces via unoriented braids, to appear @Communications in Contemporary Mathematics (2024).
-- My paper "The Kauffman bracket skein module of the complement of (2, 2p+1)-torus knots via braids" was published in the journal "Topology and Its Applications" (2023).
-- My paper "Knotoids, pseudo knotoids, braidoids and pseudo braidoids on the Torus" was published in the journal "Communications of the Korean Mathematical Society". It is among the most read papers within this journal.
--My latest research on KNOTOIDS has been published with @SpringerNature in Mediterr. J. Math. (Oct.2021). Read here!
--My latest research paper on HOMFLYPT Skein Modules has been published with @Elsevier in "Topology and its Applications" (Sept. 2021). Read here!
-- My latest research on Tied links, has been published with @World Scientific in "J.Knot Theory and it's Ramifications" (June 2021). Read here!
-- My paper "Pseudo links and singular links in the solid torus" was published @Communications in Mathematics, @DeGruyter publishers.
-- My latest research on Pseudo links, has been published with @Bulletin of the Hellenic Mathematical Society" (Oct.2021). Read here!
Geometric Topology & Quantum Topology
- Braids and braid equivalences in various diagrammatical settings. Alexander and Markov theorems.
- Knot algebras, braid groups and Jones-type invariants.
- Skein modules and related algebras; HOMFLY-PT skein modules and their combinatorics, Kauffman bracket skein modules and related algebras (combinatorics and representations).
- Other knot theories such as Knotoids, Pseudo Links, Tied Links, Singular Links etc. & related knot algebras such as the generalized singular Iwahori-Hecke algebras of type B, Pseudo Iwahori-Hecke algebras of type A and B and algebras related to tied links in 3-manifolds.
- Knot theory and the topology of low-dimensional manifolds. Jones polynomials for various types of links, invariants of 3-manifolds.
Applications of Topology
- Periodic Structures.
- Knots and braids in Chemistry and Biology (DNA topology and the topology of proteins).
Maastricht University, Lecturer, Since Sept. 2021
China Agricultural University, Visiting Professor, Sept. 2015 – August 2021
National Technical University of Athens, Postdoctoral Fellow, Jan. 2015 – Dec. 2015
