Mingcong Zeng's page

Written in Chinese, my name is 曾鸣聪。

Interests

I do computation in equivariant stable homotopy theory. I am particularly interested in slice spectral sequence computation and homological algebra around Mackey functors. My thesis is about computation around the slice filtration and equivariant Eilenberg-Mac Lane spectra.

Research

The Z-Homotopy Fixed Points of C_n Spectra with Applications to Norms of MUR. (joint with Michael Hill) Preprint. Submitted.

We introduce a computationally tractable way to describe the Z-homotopy fixed points of a C_n-spectrum E, producing a genuine C_n spectrum E^{hnZ} whose fixed and homotopy fixed points agree and are the Z-homotopy fixed points of E. These form a piece of a contravariant functor from the divisor poset of n to genuine C_n-spectra, and when E is an N_∞-ring spectrum, this functor lifts to a functor of N_∞-ring spectra. For spectra like the Real Johnson–Wilson theories or the norms of Real bordism, the slice spectral sequence provides a way to easily compute the RO(G)-graded homotopy groups of the spectrum E^{hnZ}, giving the homotopy groups of the Z-homotopy fixed points. For the more general spectra in the contravariant functor, the slice spectral sequences interpolate between the one for the norm of Real bordism and the especially simple Z-homotopy fixed point case, giving us a family of new tools to simplify slice computations.

Equivariant Eilenberg-Mac Lane spectra in cyclic p-groups. Preprint. Submitted.

In this paper we compute $RO(G)$-graded homotopy Mackey functors of $H\underline{\mathbb{Z}}$, the Eilenberg-Mac Lane spectrum of the constant Mackey functor of integers for cyclic $p$-groups and give a complete computation for Cp2. We also discuss homological algebra of $\underline{\mathbb{Z}}$-modules for cyclic $p$-groups, and interactions between these two. The goal of computation in this paper is to understand various slice spectral sequences as $RO(G)$-graded spectral sequences of Mackey functors.

A poster of my thesis for Equivariant and motivic homotopy theory of Homotopy Harnessing Higher Structures program in Isaac Newton Institute.

About Me

Here is my CV.

I was a graduate student under Doug Ravenel and defended my thesis in May, 2018. I am in the Isaac Newton Institute for the Homotopy Harnessing Higher Structures program from August to December, and then I will be a postdoc in Universiteit Utrecht in the Netherlands, starting from January 2019.

You can email me at lastnamefirstname@gmail.com