August 26, 2016

Teaching

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


Teaching

University of Maryland

Cryptography (MATH/CMSC 456) [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]

    • 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.