Daniel Shankman

I am a fourth year graduate student at Purdue University. My advisor is Freydoon Shahidi.

Mathematical Interests:
  • Algebraic number theory
  • Algebraic geometry
  • Representation theory
  • Bruhat-Tits building theory

    My general area of interest is the Langlands Program, a body of work encompassing many areas of mathematics, following
    a series of influential conjectures by Robert Langlands. My advisor invented something called local coefficients in the 80s,
    based off of an idea of Langlands. I'm currently working on the problem of the stability of local coefficients under highly
    ramified twists.

    I've been an instructor or taught recitation for the following:
  • Math 158 (Precalculus and trigonometry) instructor
  • Math 162 (Calculus II) recitation
  • Math 261 (Calculus III) recitation
  • Math 262 (Differential equations and linear algebra) recitation.

  • I've graded for the following:
  • Math 266 (Differential equations)
  • Math 351 (Linear algebra)
  • Math 546 (Functional analysis)

  • Support: Since Spring 2016, I have been supported by a research assistantship from Dr. Shahidi.

  • Class field theory: Notes typed by me and Dongming She based on Dr. Shahidi's Math 684 course.

  • Honors and awards:
  • 2015 Maclane Award.

  • Qualifying exams: I completed my qualifying exams in August 2015.
    Here are the exams I took.
  • August 2014: Abstract algebra (failed, miserably)
  • January 2015: Real analysis, abstract algebra, topology
  • August 2015: Complex analysis

  • Advanced topics: This is an oral exam based on subjects of your advisor's choosing.
    My advanced topics exam was on class field theory and linear algebraic groups.
    I took the advanced topics exam in August 2016.