Current and former courses. Lecture notes. Advising and supervision.

**Teaching**

*University of Maryland*

Introduction to Quantum Information Processing (CMSC 657) [Fall 2020]

Cryptography (MATH/CMSC 456) [Spring 2020]

*University of Copenhagen*

Introduction to Modern Cryptography [Fall 2016] [webpage]

- Private-key cryptography: historical ciphers, perfect secrecy, computational security, chosen-plaintext and chosen-ciphertext attacks, authentication, one-way functions and pseudorandomness. Public-key cryptography: Diffie-Hellman key exchange, the El-Gamal cryptosystem, and discrete-log-based digital signatures; Learning with Errors and fully-homomorphic encryption. Primary text: Katz and Lindell.

Representation Theory [Fall 2015] [lecture notes]

- Complex linear representations of finite groups: Schur’s Lemma, Maschke’s theorem, tensor products and duals, character theory, the group algebra. The compact setting: Haar measure, Peter-Weyl theorem, basics of Lie theory in the matrix group approach, representations of Lie groups and Lie algebras, basic examples. We primarily used my lecture notes; see also the texts of Serre and Brian Hall.

*University of Connecticut*

Elementary Mathematical Modeling

Introductory Calculus

Problem Solving

**Students**

I’ve had the pleasure of doing research projects with many great students.

*University of Copenhagen*

Hector Hougaard: block ciphers on groups (2016-2017);

MSc student in Mathematics; now PhD student at Osaka University;

Alexander Poremba: quantum attacks on Learning with Errors (2016-2017);

MSc student in Physics; now PhD student at Caltech;

Erik Partridge: Time-reversible quantum programming languages (2016);

MSc student in Computer Science.

*Caltech*

Catharine Lo: Complexity theory and 3-manifold invariants (2014) [paper];

SURF fellow; now PhD student in Mathematics at Princeton.

Evan Patterson: Quantum algorithms for Fourier transforms on compact groups (2013);

SURF fellow; now PhD student in Statistics at Stanford.

Aniruddha Bapat: Classical simulation of Yang-Baxter gates (2012) [paper];

SURF fellow; now PhD student in Physics at University of Maryland.

*University of Waterloo*

Edgar Bering: Quantum algorithms for manifold invariants (2010) [paper];

REU fellow; now PhD student in Mathematics at University of Illinois at Chicago.