# Josip Smolcic

### jsmolcic@waterloo.ca

Hello! I am a Canadian graduate student at the University of Waterloo in the Combinatorics and Optimization department supervised by Dr. Stephen Melczer.
I am currently working in the area of Analytic Combinatorics in Several Variables (ACSV).
I completed my undergraduate degree in Mathematics at the University of Lethbridge in 2020.

## Research & Projects

Algorithms for Analytic Combinatorics in Several Variables

I am currently working on my master's thesis on Algorithms for ACSV.

Competitive Programming (ICPC)

I started competitive programming in 2017 and I have saved nearly all of my codes since then. There is over 95k lines of c++ code in my personal competitive programming repository!

*Photo from 2020 ICPC North American Championship!.*

Presentation: Algorithms for ACSV

Slides and code demo for a presentation about work on developing new algorithms for extracting asymptotic formulas of bivariate generating functions.

Notebooks:
Main Slides,
Homotopy Continuation,
ACSVMath Software Demo

Homotopy Continuation for ACSV (GitHub)

An application of the Julia library HomotopyContinuation.jl to the problem of computing asymptotic formulas for rational multivariate generating series. The conference paper regarding the work can be found on arxiv.

*Sketch of one step in the algorithm for solving polynomial systems using homotopy continuation (HC.jl Guide Link).*

Computing Euler-Kronecker Constants (GitHub)

Program written during an undergraduate research assistantship with Dr. Amir Akbary at the University of Lethbridge. The program computes the Euler-Kronecker constant of a given cyclotomic field. The Euler-Kronecker constants are a generalization of the well studied Euler's constant.

*The area of the blue region is Euler's constant (Wikipedia).*

Euler's Gamma Function

A short essay about the famous Gamma function.

*Hand drawn plot of the Gamma function from 1909.*

Two families of graphs that are Cayley on nonisomorphic groups (arxiv)

A summer undergraduate research assistantship with Dr. Joy Morris at the University of Lethbridge. The research is about finite groups and their cayley graph representations.

*Circulant graphs from MathWorld.*