Curriculum Vitae

Click here for a copy of my CV.

Upcoming Talks

• Abstract-TBD

A special session on “Computational Homotopy Theory” 

At the AMS Sectional Meeting at Arizona State University – November 7-8, 2026

• Abstract-TBD

AMS Special Session on Recent Developments in Algebraic Topology" 

At the Joint Mathematics Meetings (JMM) 2027 in Chicago – January 13, 2027

• Abstract-TBD

AWM Special Session on Recent Developments in Algebraic Topology" 

At the Joint Mathematics Meetings (JMM) 2027 in Chicago – January 15, 2027

Recent Talks

• Computing the RO(C_2)- graded homotopy groups of an equivariant spectrum ko_{C_2}

UK Topology Seminar – March 5th, 2026

In this talk I computed the RO(C_2)-graded homotopy groups of the  C_2- equivariant connective cover of real K-theory, ko_{C_2}. The main computational tool is the C_2-equivariant Adams spectral sequence, whose input is the cohomology of the subalgebra A(1)^[C_2} of the equivariant Steenrod algebra A^[C_2}. A surprising feature of this story is that the C_2-equivariant cohomology of a point looks very similar to the cohomology of Spec(R) in real motivic homotopy theory. This resemblance both motivates the use of ρ-Bockstein Spectral Sequence and helps organize the Adams spectral sequence in a useful way. Although the details of the calculation can get quite intricate, beyond the bookkeeping there are some genuinely nice patterns and pictures that emerge, and I tried to emphasize those.

• Computing real K-theory homology of Classifying space BC_2^n, for n>1

UK Topology Seminar – November 6th, 2025

In this talk, I computed the connective real K-theory homology of the classifying spaces of cyclic 2-groups. Classifying spaces of finite groups serve as fundamental test cases for understanding how the generalized homology theories behave, and these computations illuminate how ko-theory detects 2-torsion phenomena. Using spectral sequences, I described the process of carrying out the computation and explained the resulting structure of ko*(BC_2^n). I also discussed how analogous methods can be applied in the motivic setting to compute kq*(BC_2^n), the very effective cover of Hermitian K theory over C and R.

• 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)-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.

Important Books and Notes

TBD