The page reproduced above is from Gauss,
and concerns what we now call Gauss sums,
which crop up often in my work.

Daniel J. Katz

Postdoctoral Fellow
Department of Mathematics
Simon Fraser University
I work with Jonathan Jedwab and his group,
among the Discrete Mathematicians of SFU.
I investigate number-theoretic and combinatorial
problems, often motivated by information theory.
Both algebra and analysis play crucial roles.

A recent highlight is a proof for finite fields of
characteristic 2 of a conjecture of Hellesth (1976)
concerning cross-correlations of maximal linear
recursive sequences (equivalent to a conjecture
about Weil sums of binomials or a statement
about weights in certain error-correcting codes).
Jonathan Jedwab, Kai-Uwe Schmidt, and I have
settled conjectures of Høholdt-Jensen (1988)
Borwein-Choi-Jedwab (2004), Parker (2005),
Yu-Gong (2007), and Jedwab-Schmidt (2010) on
the asymptotic L4 norm of certain families of
Littlewood polynomials. In doing so, we break a
record (which stood for over two decades) for the
lowest known asymptotic mean-square autocorrelation
for binary sequences.

Curriculum Vitae Research Statement Teaching Statement

Papers

  1. Asymptotic L4 Norm of Polynomials Derived from Characters
          arXiv:1205.1069 [math.NT], to appear in Pacific Journal of Mathematics

  2. (with J. Jedwab and K.-U. Schmidt) Advances in the Merit Factor Problem for Binary Sequences
          arXiv: 1205.0626 [math.CO], submitted for publication

  3. (with J. Jedwab and K.-U. Schmidt) Littlewood Polynomials with Small L4 Norm
          arXiv: 1205.0260 [math.NT], submitted for publication

  4. Weil Sums of Binomials, Three-Level Cross-Correlation, and a Conjecture of Helleseth
          Journal of Combinatorial Theory Series A, 119(8): 1644-1659 (2012).

  5. Proof of a Conjecture of Helleseth: Maximal Linear Recursive Sequences of Period 22n-1
          Never Have Three-Valued Cross-Correlation arXiv:1105.2291v1 [math.CO]


  6. On Theorems of Delsarte-McEliece and Chevalley-Warning-Ax-Katz
          Designs, Codes and Cryptography, 65(3): 291--324 (2012).

  7. Point Count Divisibility for Algebraic Sets over Z/p Z and Other Finite Principal Rings
          Proceedings of the American Mathematical Society, 137(12): 4065-4075 (2009).

  8. Sharp p-Divisibility of Weights in Abelian Codes over Z/pdZ
          IEEE Transactions on Information Theory, 54(12): 5354-5380 (2008).
         with a correction

  9. (with J. Zahl) Bounds on Degrees of p-Adic Separating Polynomials
         Journal of Combinatorial Theory Series A, 115(7): 1310-1319 (2008).

  10. p-Adic Estimates of Hamming Weights in Abelian Codes over Galois Rings
         IEEE Transactions on Information Theory, 52(3), 964-985 (2006).

  11. p-Adic Valuation of Weights in Abelian Codes over Zpd
         IEEE Transactions on Information Theory, 51(1), 281-305 (2005).

Ph.D. Thesis

On p-Adic Estimates of Weights in Abelian Codes over Galois Rings
      Ph.D. thesis, California Institute of Technology (2005).

Teaching

Spring 2012 at SFU: Math 232, Applied Linear Algebra

Some materials from past classes:

Calculus Lecture Slides (Princeton, Math 103)
Lecture 1 Lecture 9 Lecture 17 Lecture 25
Lecture 2 Lecture 10 Lecture 18 Lecture 26
Lecture 3 Lecture 11 Lecture 19 Lecture 27
Lecture 4 Lecture 12 Lecture 20 Lecture 28
Lecture 5 Lecture 13 Lecture 21 Lecture 29
Lecture 6 Lecture 14 Lecture 22 Lecture 30
Lecture 7 Lecture 15 Lecture 23 Lecture 31
Lecture 8 Lecture 16 Lecture 24

Graph Theory Two-Week Unit (Princeton, Applied and Computational Math 199)
Graph Theory Notes, part 1 (fundamentals, Eulerian cycles, flows in networks)
Graph Theory Notes, part 2 (coloring, planar graphs, coloring maps)

Putnam Preparation Class (Caltech, Math 17)
Problem Set 1 Solution Set 1
Problem Set 2 Solution Set 2
Problem Set 3 Solution Set 3
Problem Set 4 Solution Set 4
Problem Set 5 Solution Set 5
Problem Set 6 Solution Set 6
Problem Set 7 Solution Set 7
Problem Set 8 Solution Set 8
Problem Set 9 Solution Set 9

Contact Information

      Department of Mathematics
      Simon Fraser University
      8888 University Drive
      Burnaby, BC V5A 1S6, Canada

      email: [my first name]_[my last name]_2 [at] sfu [dot] ca (all lowercase)