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.