Research
Research
Below, you’ll find my publications, CV, and slides/notes from recent talks and learning experiences. I’m always happy to discuss my work or answer questions—please reach out to me at prerna.dhankhar@uky.edu.
I am a student of Professor Bert Guillou.
Curriculum Vitae
Click here for a copy of my CV.
Recent Talks
Computing Effective Algebraic K-theory of Classifying space BC_2?
Summer Collaborative Workshop, Virginia – June 21st, 2025
In this short collaborative talk, I presented the calculation of kgl_{**}(BC_2) using the Adams spectral sequence, leveraging the E(1)E(1)E(1)-module structure of the motivic cohomology of BC_2. My work involved solving hidden extensions in the Atiyah–Hirzebruch spectral sequence, highlighting computational techniques in motivic homotopy theory.
When is S^n an H-space?
UK Topology Seminar – November 21st, 2024
This talk investigated the results of complex vector bundles and K-theory, specifically to prove that S^n is an H-space only for n = 0,1,3, and 7. This result addresses a significant algebraic question (R^n is a division algebra or TS^n is trivial bundle) and highlights the connections between topology and algebraic structures. I introduced equivalence classes of vector bundles as commutative rings and discuss their properties in relation to K(S^n). Ultimately, this exploration sheds light on the role of K-theory in algebraic topology and their topological implications.
Publications
TBD
Important Books and Notes
TBD