# About me

I am currently a temporary assistant professor at the University of Hawai‘i at Mānoa. Previously I was a postdoctoral scholar in mathematics at the University of California, San Diego, where I was working with Professor Kiran Kedlaya. I finished my PhD in 2015 at Indiana University under the supervision of Professor Matthias Strauch. I completed my BA at Swarthmore College.

You can view my curriculum vitae.

###### Contact

Department of Mathematics

University of Hawai‘i at Mānoa

2565 McCarthy Mall (Keller Hall 401A)

Honolulu, HI 96822

*E-mail* atcarter@hawaii.edu

# Teaching

I am currently a temporary assistant professor at the University of Hawai‘i at Mānoa, where I have taught the following courses:

- MATH 243 Calculus III (spring 2019)
- MATH 420 Introduction to the Theory of Numbers (spring 2019)
- MATH 242 Calculus II (fall 2018)
- MATH 321 Introduction to Advanced Mathematics (fall 2018)

I was previously a postdoctoral scholar at the University of California, San Diego, where I taught the following courses:

- MATH 103A Modern Algebra I (summer 2018, fall 2016)
- MATH 20D Introduction to Differential Equations (spring 2018)
- MATH 109 Mathematical Reasoning (winter 2018)
- MATH 20B Calculus for Science and Engineering (fall 2017)
- MATH 103B Modern Algebra II (spring 2017)
- MATH 10C Calculus III (winter 2017)
- MATH 10B Calculus II (spring 2016)
- MATH 10A Calculus I (winter 2016)
- MATH 20C Calculus and Analytic Geometry for Science and Engineering (fall 2015)

Prior to that I was an associate instructor at Indiana University, where I taught the following courses:

- MATH-J 113 Introduction to Calculus with Applications (spring 2015, spring 2014)
- MATH-J 110 Introduction to Problem Solving (summer 2014, summer 2013)
- MATH-D 116 Introduction to Finite Math I (fall 2013)
- MATH-T 103 Math for Elementary Teachers 3 (spring 2013, fall 2012)
- MATH-J 010 Introduction to Algebra (summer 2012, summer 2011)
- MATH-M 025 Pre-Calculus Mathematics (spring 2011, summer 2010)

I also served as LaTeX consultant for Indiana’s Research Experience for Undergraduates.

# Research

My research belongs to the field of algebraic number theory. Specifically, I study (*φ*,*Γ*)-modules, a concept used to study *p*-adic Galois representations via Jean-Marc Fontaine’s equivalence between étale (φ,Γ)-modules and continuous **Z**_{p}-representations. Recently, I have been working with Kiran Kedlaya and Gergely Zábrádi to extend Fontaine’s equivalence to multivariate (φ,Γ)-modules, and to show that such modules are overconvergent. In my PhD thesis, I examined whether there exists a theory of (φ,Γ)-modules for the Lubin-Tate tower of deformation spaces of formal modules. This work drew on recent work of Anthony Scholl, which gives criteria under which such a theory of (φ,Γ)-modules exists.

For more details, see my research statement.

# Papers

###### Preprints

- Drinfeld’s Lemma for Perfectoid Spaces and Overconvergence of Multivariate (φ,Γ)-Modules, with Kiran Kedlaya and Gergely Zábrádi, submitted
- Lubin-Tate Deformation Spaces and Fields of Norms, with Matthias Strauch, in preparation