# Research and Conferences

"Without mathematics, there’s nothing you can do. Everything around you is mathematics. Everything around you is numbers " - Shankuntala Devi

My research interests lie in p-adic numbers and the structure of valuations of special sequences, special functions, polynomials over finite fields and p-adic analysis. Currently, I'm working on p-adic valuations of integer sequences with Dr Victor Moll.

# PAPERS :

**Filter Integrals for orthogonal polynomials***(**Hardy-Ramanujan Journal 2021)**Tewodros Amdeberhan**, Ad**riana Duncan,**Victor H. Moll**, and**Vaishavi Sharma**,***Arithmetic properties of the sum of divisors***(Journal of Number Theory 2021)**Tewodros Amdeberhan**,**Victor H. Moll**,**Vaishavi Sharma**,**Diego Villamizar***Filter Integrals for orthogonal polynomials***Tewodros Amdeberhan**, Ad**riana Duncan,**Victor H. Moll**, and**Vaishavi Sharma**,***Solving Quadratic and Cubic Diophantine Equations using 2-adic Valuation Trees***(Pre-Print)**Maila Brucal-Hallare, Eva G. Goedhart, Ryan Max Riley, Vaishavi Sharma, and Bianca Thompson.***The integrals in Grashsteyn and Ryzhik. Part 31: Forms containing binomials***(Pre print)**Poly Mathews Jr., Victor H Moll, Vaishavi Sharma*

# Research talks:

Southern Regional Number Theory Conference, LSU, Baton Rouge (March 2022)

AWM Pitt Grad Seminar, University of Pittsburgh, virtual (March 2022)

WCNT: Problems in Number theory, virtual

*(**Dec**2021)*Invited speaker at virtual AMS Fall Southeastern Sectional Meeting

*(Nov 2021)*Graduate student mentor at Polymath Jr REU.

*(June-Aug 2021)*Short research talk at Southern Regional Number Theory Conference,

*LSU (March 2020)(Cancelled due to COVID)*Short research talk at Math For All,

*Tulane University, (March 2020)*Research talk at Math Graduate Student Colloquium,

*Tulane University, (**Fall**2021, Spring 2020, Spring 2019, Spring 2018)*

# Conferences :

Joint Math Meetings, Virtual (April 2022)

IMBM Number Theory Seminar

*,**Istanbul Center for Mathematical Sciences**,*Virtual (April 2021)Joint Math Meeting, Virtual (Jan 2021)

Joint Math Meetings,

*Denver (Jan 2020)*p-adic Modular forms and Galois representations,

*University of Sheffield (July 2019)*Southern Regional Number Theory Conference,

*LSU (April 2019*)AWM Research Symposium,

*Rice University (April 2019)*