**Luciena Xiao (肖霄)
**

MC 253-27

1200 E California Blvd

Pasadena, CA 91106

Office: 302 Linde Hall

I am a fourth-year Ph.D. student in Mathematics at Caltech. My advisor is Elena Mantovan.

My research interests include Shimura varieties, the Langlands program, arithmetic geometry, and number theoretic cryptography.

Here is my CV (updated January 2019).

Abstract: For a prime p, the Hecke orbit conjecture asserts that every prime-to-p Hecke orbit in a PEL type Shimura variety is dense in the central leaf containing it. We prove that the conjecture holds for certain Newton polygon strata under assumptions on the splitting behavior of p.

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

NIST Post-Quantum Cryptography (PQC) Standardization Conference, August 22 - 24, 2019, Santa Barbara, CA, USA

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

*Hypersymmetric Abelian Varieties, *
Geometry
& Arithmetic of Surfaces Workshop, UW-Madison, WI, USA, 2019

*The Hecke
Orbit Conjecture,
Algebraic Groups and Geometrization of the Langlands Program,
*ENS Lyon, France, 2018

*The Hecke Orbit Conjecture for PEL Type
Shimura Varieties*,
The 11th annual WiMSoCal Symposium, Pepperdine University,
CA, USA, 2018

I am a participant of the Certificate of Practice in University Teaching program at Caltech.

Winter 2019 - Math 1d: Sequence and Series (Instructor)

Fall 2018 - Math 1a Section 1: Calculus of One and Several Variables (Recitation Instructor, Grader)

Winter 2018 - Math 1d: Sequence and Series (Instructor)

Fall 2017 - Math 1a Section 1: Calculus of One and Several Variables (Recitation Instructor, Grader)

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

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

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

Winter 2017 - Ma 1b: Linear Algebra (Recitation instructor, Grader)

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