Aryan Ghobadi's Website
My name is Aryan Ghobadi. I obtained my PhD in Mathematics in 2022 at Queen Mary University of London, under the supervision of Prof. Shahn Majid. Following my PhD, I was a Research Assistant role within the Queen Mary Mathematics department until end of September 2022. Previously, I graduated from Part III at University of Cambridge, after finishing my bachelors in Mathematics at UCL (University College London). This website should contain any other information which you might be wondering about, but if not don't hesitate to contact me via email.
My Researchgate profile is also active.
Latest: I am no longer employed in academia and my previous email address has been disactivated! However, I am happy to answer any queries regarding my research.
Please use the form at the bottom of the page to send me a message:)
My Research
My current focus is on using techniques from the theory of Hopf algebras and monoidal categories to study contemporary problems in Quantum Algebra. In noncommutative geometry, I am interested in the study of bimodule connections, as presented in the work of Beggs and Majid and investigating the category of such connections. Having built the Hopf algebroid of differential operators in this setting, I aim to extend results on Lie algebroids to these structures. Additionally, this work provides interesting examples of Hopf algebroids over noncommutative bases and allows for further study into the algebraic properties of Hopf algebroids, as well as Hopf monads. Another interest of mine are set-theoretical solutions to the Yang-Baxter equation. I have developed an approach to study these solutions and their associated skew braces via Hopf algebraic techniques in the appropriate category of lattices. Other topics which interest me include higher categories and higher categorical generalisations of the mentioned structures as well as TQFTs and quantum invariants of knots.
Some Keywords: Hopf Algebroids, Noncommutative Geometry, Hopf Monads, Tensor Categories, Yang-Baxter Equation, Skew Braces, Diagrammatic Algebra, Hopf Monads, Monoidal Bicategories, Crossed Modules, Deformation Theory
Previous Interests: My Part III Essay was focused on Gerstenhaber's theory of deformations of algebras and modern deformation theory via DGLAs. During the summer of 2017, I spent time working on representations of Artinian algebras, Morita equivalences and dualities. In 2016, I worked on Ralph H. Fox's derivatives on groups and presentations of groups as a summer project, and later wrote my first paper in this topic .
Publications and Pre-prints
(Hopefully one day there will be enough of them, for me to put a link to another page!)
Hopf algebroids, Bimodule Connections and Noncommutative Geometry
Isotopy Quotients of Hopf Algebroids and the Fundamental Groupoid of Digraphs
Published in Journal of Algebra, Volume 610, Pages 591-631, 2022
Skew Braces as Remnants of Co-quasitriangular Hopf Algebras in SupLat (Links: pre-print / published )
Published in Journal of Algebra, Volume 586, Pages 607-642, 2021
Published in Theory and Applications of Categories, Vol. 37, No. 11, pp. 287–325. Mar 2021
Published in Advances in Group Theory and Applications, Volume 6, Pages 3-21. Dec 2018
Conferences and meetings attended/attending
New Trends in Hopf Algebras and Monoidal Categories, Turin, September 2022
Hopf algebras, Monoidal Categories and related Topics, Bucharest, July 2022 [Contributing Speaker]
Bicategories, categorification and quantum theory, Leeds, July 2022 [acting as Teaching Assistant]
Biannual Congress of Royal Spanish Mathematics Society, Ciudad Real, January 2022
Lie Theory and Poisson Geometry, CIRM - Luminy, January 2022
Bracelets in Bracelet Bay, Online, January 2022
Categories Novemberfest, Online, November 2021
Unifying Themes in Geometry, Online, September 2021
Advances in Hopf Algebroids, Online, 7th July 2021 [ORGANISER]
Toposes Online, Online, June 2021
Categories and Companions Symposium, Online, June 2021 [Contributing Speaker]
British Mathematics Colloquium and BAMC at Glasgow, Online, April 2021 [Presenting Poster]
Motivic, Equivariant and Non-commutative Homotopy Theory, Online, July 2020
57th ARTIN Meeting: Tensor Categories, Quantum Groups and Related Topics, Online, July 2020
Topics in Category Theory: A Spring School, Edinburgh, 11-13 March 2020 [ORGANISER]
Is Logic A Physical Variable?, Krakow, November 2019
Quantum Flag Manifolds, Prague, September 2019
Talking Mathematics in Public, Cambridge, August 2019
Representations of Monoidal Categories and 2-Categories, Norwich, July 2019
Rings, modules, and Hopf algebras, Almeria, May 2019
Aspects of Higher Representation Theory: Quantum Groups and Categorification, Brussles, Jan 2019
Talks
- Hopf Algebraic Point of View on Skew Braces, Bracelets in Bracelet Bay, Jan 2022 [Slides / References]
- Skew Braces and Hopf algebras in SupLat, Categories Novemberfest, Nov 2021 [Slides / Video Link]
- Hopf Algebroids and Noncommutative Geometry, Geometric Methods Seminar at TU Dresden , Nov 2021
- Set-theoretical YBE solutions: Hopf algebras to the rescue, QMUL PGR Day, Jun 2021 [Slides]
- Hopf algebras in the category SupLat, Categories and Companions Symposium, Jun 2021 [Slides / Video Link]
- Hopf algebras in SupLat and set-theoretical YBE solutions, Quantum Groups Seminar, Jun 2021 [Slides / References]
- From Yang-Baxter Equation to Quantum Groups , QUIPS at QMUL, Mar 2021
- Tannakian Categories I, II, QMUL Reading group on Categorical Galois Groups, Feb 2021
- Skew Braces as Hopf Algebras in SupLat, QMUL Quantum Algebra Seminar, Oct 2020
- Hopf Algebroids in Noncommutative Geometry, 57th ARTIN Meeting, Jul 2020 [Slides]
- Noncommutative Differential Geometry, Southampton PGR Seminar, Jun 2020
- DG-Categories, Study Group on Simplicial Homotopy and DG-Categories at QMUL, Dec 2019
- Bialgebroids and Graphs, QMUL Quantum Algebra Seminar, Nov 2019
- Diagrammatic Algebra and Higher Category Theory, QUIPS at QMUL, Oct 2019
- From knots and topology to quantum groups and tensor categories, QUIPs at QMUL, Feb 2019
- Hopf Monads, QMUL Quantum Algebra Seminar, Feb 2019
- Some talks on basics of Category theory: Adjunctions, limits and colimits, Reading groups at QMUL, Dec 2018
- Morita Equivalences in Module Categories, Part III Seminars, Dec 2017
Public Outreach/Engagement
Article titled "Diagrammatic algebra: On the road to category theory" appearing in issue 13 of Chalkdust
Short YouTube Videos on “Proofs” and “Data Presentation and Interpretation” in "A-Level Maths Explained” series by QMUL School of Mathematics
Talking Mathematics in Public, Cambridge, August 2019
I supervised projects on Permutations and Trianulations during the QMUL Math summer School, July 2019
I was an assistant to Dr Kathrin Glau, in the fantastic Art/Math project: Creating the Mathematical Universe at the Tate Modern, June 2019
Teaching
2020/21 2nd Term: SEF041B Mathematics Foundations B, Introduction to Algebra
2020/21 1st Term: SEF041B Mathematics Foundations B
2019/20 2nd Term: SEF041B Mathematics Foundations B, Introduction to Algebra, Vectors and Matrices
2019/20 1st Term: SEF041B Mathematics Foundations B, Linear Algebra I, Linear Algebra II
2018/19 2nd Term: Introduction to Algebra
Many moons ago I organised:
Reading group (Virtual) on Categorical Aspects of Galois Groups at QMUL
(Notes from every talk will be uploaded here)
Week 1: Tannakian Categories I by Me, Notes
Week 2: Group Schemes by Luka, Notes
Week 3: Tannakian Categories II by Me, Notes
Week 4: Grothendieck's Fundamental Group, by Itamar, Notes
Week 5: Grothendieck's Fundamental Group II, by Arthur, Notes
Week 6: Categorical Galois Theory, by Ivan
Week 7-11: Stacks, by Behrang, Notes 1, Notes 2, Notes 3 , Notes 4
Week 12: Differential Galois Theory, by Michael Wibmer, Notes
Week 13: Categorical Galois Theory II, by Ivan
Since links are fashionable, here are some links!
Chalkdust Magazine (Which I used to work on as an Undergrad)
Me:)
You can contact me at through the below contact form:)