William Hart's Blog

What I am working on in the short term (next three months)

  1. Writing paper on new factoring algorithm I discovered - majority done
  2. Studying L-series/theta series of number fields - partly done
  3. Parallel implementation of polynomial multiplication in FLINT using multimodular method and Montgomery multiplication (with Tornaria, Watkins, Elkies)
  4. Class number project with Michael Jacobson (Calgary)
  5. Write paper on algorithm for computing Hermite Normal Form over ZZ which I have been working on

Medium term projects (within the next year)

  1. Port of GMP/MPIR to Cell processor
  2. Linear algebra in FLINT (specifically over Z/pZ and Q)
  3. Put FLINT FFT into MPIR
  4. Fast point counting code and p-adic Elkies (with Ronald van Luik)
  5. Finish paper with Chapman and Toh on theta series
  6. Finish paper on computing special values of Weber functions
  7. Working with Peter Shrimpton on sieve based primality testing

Long term objectives (next five years)

  1. Compute tables of symmetric Hilbert modular forms
  2. Compute modular equations for Hilbert modular forms and investigate Shimura reciprocity as it applies to HMF's
  3. Develop new algorithms for computing group structure using sieving (e.g. class groups)
  4. Test Vandiver conjecture further than Harvey/Buhler
  5. Implement number field sieve
  6. Organise conference with Samir Siksek on L-series

Things that are done or that I am working on right now