Research

List of preprints/papers
  1. Interpolation in Weighted projective space. (In prepration.)
  2. An Isomorphism Theorem for Arithmetic Complexes (With Luca Fiorindo, Ethan Reed, and Hongmiao Yu) submitted.
  3. Axial Constants and Sectional Regularity of Homogeneous Ideals (With M. DeBellevue, A. Lebovitz, Y.Li, M. Lotfi, S. Mohite, X. Pan, M.S. Pathak, A. Seceleanu,S.X Zhang), Proceedings of American Mathematical Society
  4. Subgroups of Groups of Units Modulu n , Mathematics Magazine. (This article is based on my Master's Thesis can also be found on my website Here.
Upcoming travel/talks

Commutative Algebra is my main area of research. Below is a more specific list of topics/questions I am currently looking at.

  • Interpolation in the weighted projective space. To apply algebro-geometric techniques to compute the hilbert function of schemes of fat points and to understand the concept of "unexpected curves" in the weighted projective space
  • The containment problem a.k.a Harbourne-Huekene containment problem. (These are separate questions, excuse my impreciseness.) It asks for if/when the third symbolic power of an ideal is contained in the second ordinary power. This is the original form of the question asked by Hueneke in 2000. The conjecture in it's original form is false, but variations of it, namely the stable containment problem remains open. I am Trying to fully understand an infinite family of counter examples to the original conjecture and see if they satisfy the stable conjecture.
  • A problem I am interested in is given a property P of an ideal, when does the radical or the integral closure of I also has that property. For example, P can be taken to be complete intersection i.e. R/I is a c.i., or Gornstein. (Or homological c.i. etc.) Over a fixed ring, classify all ideals whose radical or integral closure is also c.i. or Gornstein etc. This has been done for monomial ideals and their radical. I believe? The c.i. property fails for a monomial ideal and its integral closure (there are counter examples.) Can results to the radical be improved? What can be said about the integral closure? Classify all monomial ideals whose integral closure is not c.i.
  • One more broad theme I am interested in: proving analogoues of theorems about the projective space in the weighte projective space, i.e. commutative algebra in non-standard graded setting. This is the gist of my first project above.

I am also interested in cross-sections of mathematics and humanities, specifically the portrayal of mathematicians in 20th century movies. Here is a link to a talk I gave on this topic. I hold a graduate minor in Liberal Studies from University of Minnesota Duluth. As part of this degree, I investigated the portrayal of mathematicians in 21st century movies. The work is still unpublished but I have been using the following extra credit assignment to collect data points. It relates to a documentray I made. For more info see service section. Please feel free to use this assignment for your class. It'd be greatly appreciated if you could please send the responses in a single file to me at sroshanzamir2@huskers.unl.edu.