I am a mathematician studying algebraic number theory and algebraic geometry; I also have a long-standing interest in cryptography. I am currently a Rankin–Sneddon Fellow at the University of Glasgow; I was previously a postdoc and Imperial College Research Fellow, and prior to that, I was an NSF postdoc at UC Berkeley and a graduate student at Stanford. I received my Ph.D. in 2013 under the supervision of Brian Conrad, and my thesis was on p-adic Hodge theory in rigid analytic families.
I visited Bonn for the special trimester on the Langlands program during the summer of 2023, and I will be at IAS for the special year on p-adic arithmetic geometry for the 2023-24 academic year.
Here is my academic cv and here is my industry cv.
My e-mail address is my first name dot my last name at glasgow dot ac dot uk.
Preprint. Trianguline lifts in positive characteristic. Preprint.
Preprint. Irregular loci in the Emerton-Gee stack for GL_2. Submitted.
arXiv, journal. Modularity of trianguline Galois representations. Forum of Mathematics, Sigma. 12 (2024), e3.
arXiv, journal. Cohomology of (phi, Gamma)-modules over pseudorigid spaces. International Mathematics Research Notices 2023.
arXiv, journal. Galois representations over pseudorigid spaces. Journal de Théorie des Nombres de Bordeaux 35 (2023) no. 1, pp. 283-334.
arXiv, journal G-valued local deformation rings and global lifts (with T. Gee). Algebra & Number Theory 13 (2019), no. 2, pp. 333-378.
arXiv, journal Wach modules, regulator maps, and epsilon-isomorphisms in families (with O. Venjakob). International Mathematics Research Notices 2019, no. 16, pp. 5127-5204.
arXiv, journal p-adic Hodge theory in rigid analytic families. Algebra & Number Theory 9 (2015), no. 2, pp. 371-433.
arXiv, journal Generic smoothness for G-valued potentially semi-stable deformation rings. Annales de l'Institut Fourier 66, no. 6 (2016), pp. 2565-2620.
arXiv Newton polygons for a variant of the Kloosterman family (with S. Garthwaite, E. Ozman, R. Pries, C. Williams, and H.J. Zhu). Women in numbers 2: research directions in number theory 2013, pp. 47-63.
In Spring 2023, I taught 1C at the University of Glasgow to first-year undergraduates.
In Autumn 2022, I taught 2C Introduction to Real Analysis at the University of Glasgow to second-year undergraduates.
In Spring 2022, I taught 4H/5E Galois Theory at the University of Glasgow.
In Spring 2017, I taught M3/4/5P12 Group Representation Theory at Imperial College London.
Raynaud's results on F-vector group schemes. These are notes I wrote for a talk in the learning seminar on Faltings's proof of the Mordell conjecture. They are actually part 2; part 1 was given by Melanie Wood.
Mordell conjecture. These are notes I wrote for another talk in the learning seminar on Faltings's proof of the Mordell conjecture.
Notes on Galois Cohomology. These are notes I wrote for a talk in the modularity lifting seminar.
Calculating Deformation Rings, for \ell \neq p. These are notes I wrote for another talk in the modularity lifting seminar.
Cryptography: Authentication, Blind Signatures, and Digital Cash. These are notes I wrote up for a talk on David Chaum's amazing work on digital cash. I've given the talk twice, once to high school students (at PROMYS) and once to undergraduates (at Stanford).
Cracking the Enigma. These are the slides for a talk I gave to Stanford undergraduates on an early Polish break of Enigma.