Zhen HuanZhen Huan

School of Mathematics
Sun Yat-sen University
Xingangxi Road 135, Haizhu
Guangzhou, Guangdong, China


Email:   xunzhen(at)mail.sysu.edu.cn

 

Personal information

Currently I’m a Research Associate at School of Mathematics, Sun Yat-sen University, Guangzhou, China.

I received my PhD from University of Illinois at Urbana-Champaign. May, 2017. My advisor was Charles Rezk. My dissertation defense was on May 5th, 2016.

I completed my BS in mathematics at Peking University.

Here is my CV.

Research

My research interests are in algebraic topology, homotopy theory and related field. The main subject I'm working on is quasi-elliptic cohomology.

Here is my research statement.

Here is a draft of my dissertation. My work is on several topics:

We introduce and construct quasi-elliptic cohomology.

We construct its complete power operation, and prove the Tate K-theory of symmetric groups modulo a certain transfer ideal classify the finite subgroups of the Tate curve. This conclusion motivates the construction of the universal finite subgroup of the Tate curve.

We construct an orthogonal G-spectrum weakly representing quasi-elliptic cohomology, which cannot arise from an orthogonal spectrum.

We construct a new global homotopy theory which contains the orthogonal G-spectrum for quasi-elliptic cohomology.

Preprint

Quasi-Elliptic Cohomology and its Power Operations. Submitted for publication.

Quasi-Elliptic Cohomology and its Spectra. Submitted for publication.

Universal Finite Subgroup of Tate Curve. Submitted for publication.

Almost Global Homotopy Theory. In preparation.

Invited Talks

AMS Special Session on Homotopy Theory, Riverside, CA. Quasi-elliptic cohomology, November 5, 2017.

Parallel Session, Conference "Homotopy theory: tools and applications", University of Illinois at Urbana-Champaign, Quasi-elliptic Cohomology, July 17, 2017

Informal Session, Conference on invertible objects and duality in derived algebraic geometry and homotopy theory, the University of Regensburg, Germany. Quasi-elliptic Cohomology, April 3, 2017.

AMS Special Session on Homotopy Theory, Bloomington, IN. Quasi-elliptic Cohomology, April 1, 2017.

AMS Special Session on Topology and Arithmetic, Minneapolis, MN. Quasi-elliptic Cohomology, October 30, 2016.

University of Chicago Algebraic Topology Seminar, Quasi-elliptic cohomology, November 25, 2014.

Northwestern University Topology Seminar, Quasi-elliptic cohomology, November 24, 2014.

Teaching at University of Illinois at Urbana-Champaign

2016 Summer: teaching assistant for Netmath MATH 231-Calculus II.

2016 Spring: the main instructor of MATH 124-Finite Mathematics.

2015 Fall: the main instructor of MATH 124-Finite Mathematics.

2015 Spring: the main instructor of MATH 124-Finite Mathematics.

2013 Fall: the main instructor of MATH 119-Ideas in Geometry.

 

2016 Fall: led discussion session for MATH 221-Calculus I.

2012 Fall: led discussion session for MATH 231-Calculus II.

2012 Spring: led discussion session for MATH 234-Calculus for Business I.

2011 Fall: led discussion session for MATH 231-Calculus II.

 

2012 Spring, 2013 Spring, 2014 Spring, 2014 Summer, 2014 Fall, 2015 Summer, 2016 Summer, 2017 Spring: I was a research assistant.

Here is my teaching statement.

Useful links