Publications/Preprints
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2. Fractured Structures in Condensed Mathematics (joint with Nima Rasekh)
preprint (submitted), 17 pages, arXiv:2603.09618
talk by myself
1. Multiplicative ​Equivariant Thom Spectra & Structured Real Orientations (joint with Ryan Quinn)
preprint, 91 pages, arXiv:2512.15573
​talk by Ryan
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
We provide an E_ρ-equivalence between Real periodic complex bordism and BUR after inverting a Bott class. To do so, we work out an equivariant version of Morita theory, in particular a monoidal equivariant Schwede-Shipley result.
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.