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.
• 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.

-- Seminar-Talks 2021-2024

• 2023 Mathematics Development Forum, Southeast University, School of Mathematics, Nanjing, P.R. China, Feb. 2023. Title of Talk: Skein modules via braids.

• 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

i. 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).

ii. a chapter to the volume based on the AMS Special Session on Algebraic Structures in Knot Theory, for the series Contemporary Mathematics (CONM) of the American Mathematical Society (AMS).

-- My latest papers on Kauffman bracket skein modules:

• The Kauffman bracket skein module of S1xS2 via braids arXiv.math[GT] 2023.
• The Kauffman bracket skein module of the lens spaces via unoriented braids @Communications in Contemporary Mathematics (2023).
• The Kauffman bracket skein module of the complement of (2, 2p+1)-torus knots via braids; @Topology and Its Applications (2023).

-- My paper "Pseudo links and singular links in the solid torus" was published @Communications in Mathematics, @DeGruyter publishers.

-- My paper "Knotoids, pseudo knotoids, braidoids and pseudo braidoids on the Torus" was published in the journal "Communications of the Korean Mathematical Society".

--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 latest research on Pseudo links, has been published with @Bulletin of the Hellenic Mathematical Society" (Oct.2021). Read here!