Edit (7/25/2021): I now have my own professional website at sohailfarhangi.com that I will be updating in place of this website.
My mathematical works from before I started my Ph.D.
Complements Through Cevian Triangles A problem of my own about Cevian Triangles of a given Triangle.
Sawayama Thebault An expository article about the internal and external Sawayama Thebault Theorems.
Centroids And Circumcenters A problem of my own relating some Centroids and Circumcenters.
Some Interesting Collinearities A problem of my own about some interesting collinearities that arise from Cevian Triangles.
Inequalities And Quadratic Forms A technique I developed to solve Olympiad inequalities through the use of linear algebra and quadratic forms.
On Refinements of Van der Waerden’s Theorem My master’s thesis on Ramsey Theory.
The Fibonacci Numbers are Not 2 Large A result that I discovered at the 2014 University of West Georgia REU. I formally wrote up this result in July of 2021 since it is amusing and slightly related to the content of my second publication.
Publications
1) Pointwise Ergodic Theorems For Higher Levels Of Mixing To appear in Studia Mathematica
2) Distance Graphs And Arithmetic Progressions (joint work with J. Grytczuk) Integers, 21A(Ron GrahamMemorial Volume):Paper No. A11, 6, 2021.
Preprints
3) Enhancements of van der Corput’s Difference Theorem and Connections to the Hierarchy of Mixing Properties of Unitary Operators Submitted
4) Classifying Partition Regular Polynomial Equations in a Nonlinear Family Submitted (joint work with R. Magner)