Vaibhav Pandey

I am a fourth year graduate student studying commutative algebra at the University of Utah. My advisor is Anurag Singh . I like to think about Local cohomology modules and rings of invariants under group actions on polynomial rings. I have used these techniques to determine the cohomological dimension of ideals defining Veronese subrings in arbitrary characteristic. Currently, I am working on applying these techniques to better understand the structure of the classical determinental rings as subrings of polynomial rings.

From 2011-2016, I did my undergrad at the National Institute of Science Education and Research (NISER), Bhubaneswar in India with an Integrated M.Sc (MS equivalent) in Mathematics.

In Fall 2020, I am teaching Math 2200-001 Discrete Mathematics.

Publications

  • "Cohomological dimension of ideals defining Veronese subrings" (To be published in Proceedings of the American Mathematical Society).
  • "A Dedekind Domain with Nontrivial Class Group"; with Sagar Shrivastava and B.Sury . The American Mathematical Monthly. Volume 125, Issue 4 (2018), pp. 356-359.
  • "On the prime ideals of C[0,1]"; Reasonance May (2016), pp. 439-446. (I published this as an undergrad in NISER, Bhubaneswar.)

    • Teaching

    1. Fall 2018 : Business Algebra (Math 1090)
    2. Spring 2019 : Business Algebra (Math 1090)
    3. Spring 2020 : Busines Calculus (Math 1100)
    4. Summer 2020 : Linear Algebra (Math 2270)
    5. Fall 2020 : Discrete Mathematics (Math 2200)

    Lab instruction

    1. Fall 2017 : Differential Equations and Linear Algebra (Math 2250)
    2. Spring 2018 : Engineering Calculus 2 (Math 1320)

    Service

  • I organized 'BIKES' - the commutative algebra student seminar at the University of Utah in Fall 2019 and Spring 2020. Here is the link of the current "BIKES" page.
  • I mentored for the 'Summer High School Mathematics Program' held at the University of Utah in Summer 2019. The aim was to introduce Number Theory to some bright high school kids.

    • Invited Talks

  • "Cohomological dimension of Veronese ideals"; Algebra seminar, Purdue University - March 11, 2020
  • "Cohomological dimension of Veronese ideals"; AMS Fall Eastern Sectional Meeting (online) - October 3, 2020