Research

My mathematical interests are discussed in my research statement.

 

You can find a list of talks that I have given here

 

 

Preprints

a

4) Enhancements of van der Corput’s Difference Theorem and Connections to the Hierarchy of Mixing Properties of Unitary Operators, Submitted, arxiv

a

a

a

Publications

a

3) On the partition regularity of ax+by = cwmzn (joint work with R. Magner), Integers, 23: Paper No. A18, 52, 2023.

 

2.5) Ph.D. Thesis: Topics in ergodic theory and ramsey theory. [Permalink] [PDF]

 
2) Distance Graphs and Arithmetic Progressions (joint work with J. Grytczuk), Integers, 21A (Ron GrahamMemorial Volume): Paper No. A11, 6, 2021. [DOI] [2nd Ed.]

 

1) Pointwise Ergodic Theorems For Higher Levels Of Mixing, Studia Math., 261(3):329–344, 2021. [DOI] [arxiv]

a

a

Topics I have unpublished results in

  1. Sets of recurrence
  2. Van der Corput sets
  3. Central sets
  4. Topological variants of van der Corput’s difference theorem

    a

    If any of these topics interest you and you have ideas for further research that may result in a publication, feel free to get in touch with me so that we can consider a collaborative effort.

a

a

My Pre-Ph.D. Mathematical Works

a

1) Complements Through Cevian Triangles A problem of my own about Cevian Triangles of a given Triangle.

2) Sawayama Thebault An expository article about the internal and external Sawayam The Bault Theorems.

3) Exeter Point An expository article about the existence of the Exeter Point as well as the fact that it lies on the Euler Line.

4) Centroids and Circumcenters A problem of my own relating some Centroids and Circumcenters.

5) Some Interesting Collinearities A problem of my own about some interesting collinearities that arise from Cevian Triangles.

6) Inequalities and Quadratic Forms A technique I developed to solve Olympiad inequalities through the use of linear algebra and quadratic forms.

7) Triangle Center X(8043) While playing around on Geogebra I accidentally discovered a new construction in Euclidean geometry that is now referred to as the Farangi-cyclocevian image of a point. When applied to the incenter (also referred to as X(1)) of a triangle, it produces a new triangle center.

8) On Refinements of Van der Waerden’s Theorem My master’s thesis on Ramsey Theory.

9) 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.