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. Equivariant Commutative Orientations [poster]
   Hopkins-Lawson describe an obstruction theory about lifting complex orientations MU ---> E to coherently multiplicative maps. The current goal of my PhD project is to generalize this to a (global) equivariant setting.​

3. 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.​​​​

4. Real Snaith Theorems
   Snaith showed that inverting the Bott class in the unreduced suspension spectrum of BU(1) resp. BU yields KU resp. MUP. We give a new short proof for a Real equivariant analogue. In particular, we lift the MUP version to an E_ρ-equivalence.

5. Fractured Structure on Condensed Anima (joint with Nima Rasekh) [master's thesis, talk notes, talk] 
   The categorical foundation of condensed mathematics lies in topos theory. Our goal is to establish formal properties of Lurie's fractured topoi. One possible application is the study of condensed cohomology.