Research

 

Some Questions

Most recently I’ve been thinking about the following problems In no particular order (okay, maybe they aren’t all so different):

    1. Under what conditions can we guarantee a form of the disjunction theorem for G-manifolds? [Edit: this now has a partial answer 🙂 ]
    2. Does the equivariant algebraic K-theory of a smooth manifold split into stable homotopy and the smooth whitehead spectrum? [Edit: this is (hopefully) appearing in forthcoming work.]
    3. What is the equivariant involution on the concordance space?
    4. Is there a form of equivariant block diffeomorphisms that maps to equivariant algebraic K-theory?


In Preparation

 

An Equivariant Embedding Calculus

Spherical Group Ring Models for Equivariant A-theory

Joint withMaxine CalleDavid Chan, and Anish Chedalavada

Previous Research Articles

 

A Genuine Linearization Map for Equivariant Algebraic K-Theory

Joint with Maxine Calle and David Chan

The Generalized Makeev Problem Revisited, 2023

Joint with Steven Simon and Jialin Zhang

Admissibility and the C_2 Spider, 2018

Joint with Wade Bloomquist

Classically Integral Quadratic Forms Excepting at Most Two Values, 2018

Joint With Madeleine Barowsky, William Damron, Frederick Saia, Nolan Schock, and Katherine Thompson