Hi,

I am a fourth-year PhD student under the supervision of Dmitriy Rumynin in the area of Representation Theory. My current research focuses on Knutson's Conjecture on the Representation Ring and the Knutson Index of modules over different objects such as finite groups, algebraic groups, connected and disconnected reductive groups and bialgebras and Hopf algebras

Publications:

• The Knutson Index of the representation ringLink opens in a new window, Journal of Algebra 659 (2024): 516-541.

Preprints:

• Disconnected Reductive Groups: Classification and RepresentationsLink opens in a new window, joint with Dylan JohnstonLink opens in a new window and Dmitriy RumyninLink opens in a new window, submitted 10^th of September 2024

• Global Representation Ring and Knutson IndexLink opens in a new window, joint with Dylan JohnstonLink opens in a new window and Dmitriy RumyninLink opens in a new window, submitted 23^rd of May 2024
• Arithmetic Properties of Character Degrees and the Generalised Knutson IndexLink opens in a new window, submitted 21^st of June 2023

Past Talks:

• Global Representation Ring and Knutson Index. Warwick Algebra SeminarLink opens in a new window, 3^rd of October 2024
• Knutson's Conjecture on the Representation Ring. 14th Ukraine Algebra ConferenceLink opens in a new window, 6^th of July 2023
• Knutson's Conjecture on the Representation Ring. Oxford Junior Algebra and Representation Theory SeminarLink opens in a new window, 25^th of November 2022
• Knutson's Conjecture on the Representation Ring. Warwick Algebra SeminarLink opens in a new window, 21^st of November 2022
• From the Knutson - Savitskii Conjecture to the Knutson Index of characters. Postgraduate Group Theory ConferenceLink opens in a new window in London, 6^th of July 2022
• The Knutson - Savitskii Conjecture. Warwick Mathematics Postgraduate SeminarLink opens in a new window, 15^th of June 2022

Teaching Duties:

• Tutor for MA397 ConsolidationLink opens in a new window, Autumn 2021 - Autumn 2023
• Supervisor of first-year students, Autumn 2021 - Spring 2023
• Teaching assistant for MA453 Lie AlgebrasLink opens in a new window, Autumn 2022
• Teaching assistant for MA249 Algebra II: Groups and RingsLink opens in a new window, Spring 2022

Miscellaneous:

• Co-author of the Global Representation Ring complementary codeLink opens in a new window on GitHub
• Author of the integer sequences A363675Link opens in a new window, A363676Link opens in a new window and A363701Link opens in a new window on the OEIS
• Co-organiser of the Quantum Groups reading group, Autumn 2023
• Co-organiser of the junior AGATALink opens in a new window (Algebraic Geometry, Algebraic Topology and Algebra) seminar, 2023

Email: Diego dot Martin-Duro at warwick dot ac dot uk