Current and former courses. Lecture notes. Advising and supervision.
Teaching
University of Maryland
Cryptography (MATH/CMSC 456) [Spring 2026]
Cryptography (MATH/CMSC 456) [Spring 2025]
Introduction to Quantum Computing(MATH/CMSC 457) [Spring 2024]
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]
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- 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:
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Representation Theory [Fall 2015] [lecture notes]
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- 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
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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.