# Guchuan Li

 Northwestern University Department of Mathematics Office: Locy 212 Email:   guchuanli2013 at u dot northwestern dot edu CV

I am a sixth-year graduate student in the Mathematics Department at Northwestern University. My advisor is Paul Goerss. My main research interests are in stable homotopy theory.

## Publications and Preprints

• Picard groups and duality for Real Morava E-theories (with Drew Heard, XiaoLin Danny Shi).
We show, at the prime $2$, that the Picard group of invertible modules over $E^{hC_2}_n$ is cyclic. Here, $E_n$ is the height $n$ Lubin-Tate spectrum and its $C_2$-action is induced from the formal inverse of its associated formal group law. We further show that $E^{hC_2}_n$ is Gross-Hopkins self-dual and determine the shift to be $n+4$. Our results generalize the well-known results when $n=1$.

• Hurewicz Images of Real Bordism Theory and Real Johnson-Wilson Theories (with XiaoLin Danny Shi, Guozhen Wang, and Zhouli Xu). To appear in Advances in Mathematics.
We show that the Hopf elements, the Kervaire classes, and the $\bar{\kappa}$-family in the stable homotopy groups of spheres are detected by the Hurewicz map from the sphere spectrum to the $C_2$-fixed points of the Real Brown-Peterson spectrum. A subset of these families is detected by the $C_2$-fixed points of Real Johnson-Wilson theory $E\mathbb{R}(n)$, depending on $n$.

## Teaching

• Spring 2018: Math 240-0: 31A & 41A Linear Algebra (two sections)
• Winter 2017: Math 331-2 MENU: Abstract Algebra & Math 334-0 Linear Algebra: Second Course
• Fall 2016: Math 331-2 MENU: Abstract Algebra & Math 334-0 Linear Algebra: Second Course
• Spring 2016: Math 440-3 Geometry/Topology & Math 470-3 Algebra
• Winter 2016: Math 440-2 Geometry/Topology & Math 470-1 Algebra
• Fall 2015: Math 440-1 Geometry/Topology & Math 470-1 Algebra
• Spring 2015: Math 440-3 Geometry/Topology
• Winter 2015: Math 410-2 Analysis; Math 470-2 Algebra

## Other

• From 2018 Fall, I am a co-organizer for the Electronic Computational Homotopy Theory Seminar (with D. Isaksen), an online international research seminar on the topic of computational homotopy theory. I send out the notification emails and record the attendance of the seminars.