Josip Smolcic

Hello, I am a computer programmer and mathematics enjoyer from the frigid plains of western Canada! The picture is me and my cat Mary c:
I graduated from the University of Waterloo with a MMath in combinatorics and optimization and from the University of Lethbridge with a BSci in mathematics.

Research / Personal Projects

Algorithms for Analytic Combinatorics in Several Variables

My masters thesis on Algorithms for analytic combinatorics in several variables. Source code on github.

Different types of non-crossing configurations on 18 vertices and random lattice walks of length 50.

Paths of several sampled points along a gradient flow on a surface connected to the analysis of a bivariate generating function.

Competitive Programming (ICPC)

I started competitive programming in 2017 and I have saved nearly all of my codes since then. There is over 45k lines of c++ code in my personal competitive programming repository!

Photo from 2019 after the ICPC Regional competition and photo from 2020 ICPC North American Championship!

Homotopy Continuation for ACSV

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. Sides and code demos for a presentation about the work are: Slides, Slides Notebook, Homotopy Continuation Notebook, ACSVMath Software Demo Notebook

Illustration of the homotopy continuation method on univariate quintic polynomials.

Computing Euler-Kronecker Constants

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

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.