Zijian Yao
Zijian Yao

Department of Mathematics
Harvard University
Science Center 242f
1 Oxford Street
MA 02138, USA

E-mail:  zyao[at]math[dot]harvard[dot]edu

Hi! I am a fifth year graduate student at Harvard. My advisor is Mark Kisin.

I work in number theory and arithmetic geometry (p-adic cohomology, automorphic forms and various parts in the Langlands program).

I co-organize the Harvard Number Theory Seminar this year.

Research

Automorphic forms and Galois representations

Higher coherent cohomology and symplectic Galois representations.   In preparation.

The Breuil-Mézard conjecture for function fields.   (arXiv preprint). 2018.

p-adic geometry and p-adic Hodge theory

The logarithmic prismatic cohomology and semistable comparison.   In preparation. 2019
With Appendix by L. Chen.

The crystalline comparison of Ainf-cohomology: the case of good reduction.   Preprint. 2019.

The log crystalline specialization of Ainf-cohomology in the semistable case.   Preprint. 2018.

Logarithmic de Rham-Witt complexes via the Décalage operator.   (arXiv preprint). 2018.  

Perfectoid covers of abelian varieties   (arXiv preprint). 2018.
With C. Blasestad, D. Gvirtz, B Heuer, D Shchedrina, K. Shimizu and P. Wear.

Some undergraduate stuff on dynamics and combinatorics

Peckness of Edge Posets.   2015.
With D. Hemminger and A. Landesman

Something about the Pentagram map and its point of collapse.   2014.

Something about Devil's staircase and rotation numbers.   2014.


Teaching

Fall 2019 -- Abstract algebra.   Session & OH: Sunday @7pm in SC Hall A.  (Additional sessions are announced on FB group ).

Fall 2018 -- Calculus 21A (multivariable calculus).

Fall 2017 -- Arithmetic of Elliptic Curves.

Summer 2017 - Binary quadratic forms and class field theory.

Fall 2016 -- Arithmetic of Elliptic Curves.


Seminars (co-)organized

Harvard Number Theory Seminar - Fall 2019

Current Notions Seminar - Fall 2019

Harvard Number Theorists Seminar - Spring 2019

Prismatic cohomology - Winter 2019

Harvard Number Theorists Seminar - Fall 2018

Current Notions Seminar - Fall 2018

Integral p-adic Hodge theory - summer 2017

Torsion in cohomology - Spring 2017

Seminar on Faltings's Theorem - Spring 2016


Expository notes

More to appear

The schematic Fargues-Fontaine curve

Notes on modularity lifting

Extremely rough notes on Mordell's conjecture

Representation theory at infinity

(again) Extremely rough notes on Local Langlands

Short notes on mod l representations






Last revised Sep 2019