Luciena Xiao (肖霄)

(Pronouns: they/them)

Department of Mathematics
MC 253-27
1200 E California Blvd
Pasadena, CA 91106
Office: 302 Linde Hall

E-mail:  xxiao at caltech dot edu

I graduated in June 2020 from Caltech with a PhD in Mathematics. My advisor is Elena Mantovan.

My research interests include Shimura varieties, Langlands program, and arithmetic geometry.

Here is my CV (updated July 2020).




Invited Talks:

Number Theory Seminar, UCSD, March 2020

Number Theory Seminar, UCLA, January 2020

Number Theory Seminar, Caltech, October 2019

Geometry & Arithmetic of Surfaces Workshop, UW-Madison, WI, USA, 2019

Algebraic Groups and Geometrization of the Langlands Program, ENS Lyon, France, 2018

The 11th annual WiMSoCal Symposium, Pepperdine University, CA, USA, 2018


Conferences attended:

Arizona Winter School 2020: Nonabelian Chabauty, March 7-11, 2020 at the University of Arizona, AZ, USA

Southern California Number Theory Day, February 22, 2020, UC San Diego, CA, USA

INdAM special research activity in Padova on "p-adic Langlands program", May 12 - July 12, 2019, University of Padua, Italy

AMS Spring Eastern Sectional Meeting, April 13-14, 2019, University of Connecticut Hartford, Hartford, CT, USA

Geometry & Arithmetic of Surfaces Workshop, February 9-10, 2019, UW-Madison, WI, USA

Conference on open questions in cryptography and number theory, Sept 17-21, 2018, UC Irvine, CA, USA

Algebraic Groups and Geometrization of the Langlands Program, April 23 - June 29, 2018, Univ Lyon 1 and ENS Lyon, France

Sino-French conference in Algebraic and Complex Geometry, April 23-27, 2018, Université Lyon 1, France

Anachronism(s) in the History of Mathematics, April 13-14, 2018, Caltech, CA, USA

The 11th annual WiMSoCal Symposium, March 24, 2018,  Pepperdine University, CA, USA

Arizona Winter School 2018: Iwasawa Theory, March 3-7, 2018, University of Arizona, AZ, USA

UNCG Summer School: Modular Forms, May 22-26, 2017, UNC at Greensboro, NC, USA

Arizona Winter School 2017: Perfectoid Spaces, March 11-15, 2017, University of Arizona, AZ, USA

Women and Math: Aspects of Algebraic Geometry, May 11-22, 2015, Institute for Advanced Study, NJ, USA


In July 2020, I received a Certificate of Practice in University Teaching from the Caltech Project for Effective Teaching.

Ma 1d Sequence and Series (Instructor): Winter 2019, Winter 2018. Lecture Notes.

Ma 1a Calculus of One and Several Variables and Linear Algebra (Recitation Instructor, Grader): Fall 2017, Fall 2018, Fall 2019

Ma 5/105b: Introduction to Abstract Algebra (Teaching Assistant): Winter 2017

Ma 5/105a: Introduction to Abstract Algebra (Teaching Assistant): Fall 2016

Ma 1c: Calculus of Several Variables (Recitation instructor, Grader): Spring 2016, Spring 2020

Ma 1b: Linear Algebra (Recitation instructor, Grader): Winter 2015

Ma 2/102a: Differential Equations (Recitation instructor, Grader): Fall 2015


I'm a certified Mental Health First Aider by Mental Health First Aid USA. Feel free to reach out to me if you are experiencing a mental health or substance use challenge. I'm not a therapist, but I can provide initial help until appropriate professional resources are available.

During the last two years of my undergraduate studies, I translated Brian P. Copenhaver's English translation of the Hermetica into Chinese. My translation was published in July 2019 as a volume in the "经典与解释"(Hermes: Classici et commentarii) book series.

Here's a commentary (in Chinese) I wrote for the first Chinese translation of the prose Edda, where I give some background on the Eddas and explain Old Norse poetic forms via two examples.