Qi Zhu

Current Projects

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1. Norms of Real Algebraic K-Theory (joint with Kaif Hilman and Ryan Quinn)

The project is to endow Poincaré categories with a C_2-symmetric monoidal structure and realize Real algebraic K-theory as a normed algebra. This in particular yields a natural map K ---> L as well as parts of red- and whiteshift results.

2. Hermitian K-Theory through Real Homotopy Theory (joint with Christian Carrick and Ryan Quinn)

We start from Real analogs of Lee-Levy's THH computations leading to THR computations of Real chromatic spectra. The goal is to use this to make computations in Hermitian K-theory.

3. Equivariant Commutative Orientations (joint with Ryan Quinn) [poster]

Hopkins-Lawson describe an obstruction theory for lifting complex orientations MU ---> E to coherently multiplicative maps. I'm hoping to generalize this to a genuine equivariant setting. Likewise, I'm hoping to obtain a Real version together with Ryan Quinn.​

4. Monoidal Parametrized Unstraightening (joint with Siddharth Gurumurthy and Ryan Quinn)

Straightening-Unstraightening compares a slice construction to a functor category construction. Both of these acquire a natural monoidal structure through the slice monoidal structure and Day convolution. Classically, these are known to be equivalent as (symmetric) monoidal ∞-categories due to Ramzi. We wish to spell out a generalization to parametrized higher category theory.