Qi Zhu

Current Projects

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1. Quotients of Real Bordism (joint with Ryan Quinn)

We provide an E_σ-algebra structure on quotients of Real bordism.

2. Real Snaith Theorems (joint with Ryan Quinn)

We provide an E_ρ-equivalence between Real periodic complex bordism and BUR after inverting a Bott class.

3. More Multiplication on BP (joint with Ryan Quinn)

The best known multiplicative structure on BP is E_4 obtained by Basterra-Mandell. We have ongoing work to improve on this structure.

4. Equivariant Commutative Orientations [poster]

Hopkins-Lawson describe an obstruction theory about lifting complex orientations MU ---> E to coherently multiplicative maps. I'm hoping to generalize this to an equivariant setting.​

5. Real Equivariant Commutative Orientations (joint with Ryan Quinn) ​​​​

Hopkins-Lawson describe an obstruction theory about lifting complex orientations MU ---> E to coherently multiplicative maps. We hope to lift it to the Real equivariant setting and obtain highly structured Real orientations from it.

6. Monoidal Parametrized Unstraightening (joint with Ryan Quinn & Siddharth Gurumurthy)

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.

7. Multiplicative Equivariant Morita Theory

In the language of parametrized higher algebra, we wish to prove a multiplicative equivariant Schwede-Shipley theorem. The aim is to apply this to a good theory of equivariantly inverting elements in a multiplicative (but not fully multiplicative) setting.