Yujie Xu

Hi! I received my PhD from Harvard in May 2022, advised by Mark Kisin.

Starting Fall 2022, I will be a postdoc at MIT.

Starting Fall 2023, I will be a Joseph F. Ritt Assistant Professor at Columbia.

Previously, I was an undergraduate at Caltech.

E-mail: I can be reached at either yujiex[at]math[dot]harvard[dot]edu or yujiexu[at]mit[dot]edu

(Me at Windsor Castle, aka my Zoom profile)

Papers

Here are some of my most recent papers:

Papers in representation theory:

[New] The Explicit Local Langlands Correspondence for G2. (with A.-M. Aubert and C.-C. Tsai), 2022

On Hecke algebras for p-adic reductive groups: The example of G2. (with A.-M. Aubert), 2022

Papers in arithmetic geometry (Shimura varieties etc.),

[New] The connected components of affine Deligne--Lusztig varieties. (with I. Gleason and D.G. Lim), 2022.

A comparison of the Kisin-Pappas model with Rapoport-Smithling-Zhang model (Appendix to "Arithmetic modularity of special divisors and arithmetic mixed Siegel-Weil formula" by C. Qiu), 2022.

Normalization in integral models of Shimura varieties of Hodge type.

Finiteness of fppf cohomology.

On the Hodge embedding for PEL type integral models of Shimura varieties.

Bounding Selmer Groups for the Rankin-Selberg Convolution of Coleman Families (with A. Graham and D. Gulotta), Canadian Journal of Mathematics, 2020.

Surjectivity of Galois representations in rational families of abelian varieties (with A. Landesman, A. Swaminathan and J. Tao), Algebra & Number Theory, 2019.

Other Writings

Here is (the expository part of) my Harvard minor thesis on the Geometric Langlands Conjectures.

Teaching

Instructor/Lecturer for Math 21b Linear Algebra and Differential Equations, Harvard University (Awarded a Bok Center Certificate of Distinction and Excellence in Teaching)

Here you can find excerpts of some extremely positive student comments from the freshman linear algebra class I taught at Harvard.

Teaching Fellow for Math 221 Commutative Algebra, Fall 2019, Harvard University (Awarded a Bok Center Certificate of Distinction and Excellence in Teaching)

Teaching Fellow for Math 137 Algebraic Geometry, Spring 2020, Harvard University (due to the pandemic, this course switched to Zoom instruction halfway, and there was no quantitive student evaluation nor Bok Center Teaching Award given out)

Teaching Fellow, Math 122 Algebra I: Theory of Groups and Vector Spaces, Fall 2020 (Zoom instruction), Harvard University (Awarded a Bok Center Certificate of Distinction and Excellence in Teaching)

Elliptic Curves and Beyond, Summer Tutorial 2019, Harvard University

Seminars

I co-organized the STAGE seminar in Fall 2021 on Uniform Mordell. You can find notes for some of the talks here.

Conferences

I was a plenary speaker at Community-building in the Langlands Program, Bonn, Germany, August 2022.