August 26, 2016

Teaching

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


Teaching

I was fortunate enough to teach all of the below courses as sole instructor. The Math Department at the University of Copenhagen allowed me to design and run my courses as I pleased. The courses at the University of Connecticut, on the other hand, were largely standardized “general ed” affairs.

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.
    Alexander Poremba: post-quantum cryptography (2016-2017);
      MSc student in Physics.
    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.