Alex McDonald

About Me

I am an Assistant Professor at Kennesaw State University.  From 2021 to 2024 I was a postdoc at The Ohio State University working with Krystal Taylor, and prior to that I was a graduate student at University of Rochester where my advisor was Alex Iosevich.  My CV can be found here.

Research

My primary research interests lie in the intersection of harmonic analysis and geometric measure theory.  These fields have proved to be closely tied to each other; major results about the geometry of fractal sets have been proved using tools and techniques from harmonic analysis.  My research centers around two major sticking points between these fields: the existence of point configurations in sufficiently large fractal sets, and measure theoretic properties of projections.  I also work on related problems in geometric combinatorics.

Publications and Preprints (listed newest to oldest)

• In preparation: The VC-dimension and point configurations in R^d (joint with Alex Iosevich, Akos Magyar, and Brian McDonald)

• Prescribed projections and efficient coverings of sets by curves (joint with Alan Chang and Krystal Taylor)

• Point configurations in sets of sufficient topological structure and a topological Erdos similarity conjecture (joint with Krystal Taylor), Res. Math. Sci. 12 (2025), no. 3, Paper No. 45.

• Infinite constant gap length trees in products of thick Cantor sets (joint with Krystal Taylor), Proc. Roy. Soc. Edinburgh Sect. A 154 (2024), no. 5, 1336–1347.  

• Finite point configurations in products of thick Cantor sets and a robust nonlinear Newhouse Gap Lemma (joint with Krystal Taylor), Math. Proc. Cambridge Philos. Soc. 175(2023), no. 2, 285-301.

• Volumes spanned by k-point configurations in R^d (joint with Belmiro Galo), J. Geom. Anal. 32 (2022), no. 1, 23. 

• Areas spanned by point configurations in the plane, Proc. Amer. Math. Soc., 149(5):2035-2049, 2021.

• Distinct distances from points on a circle to a generic set (joint with Brian McDonald, Jonathan Passant, and Anurag Sahay), Integers 21 (2021), Paper no. A55

• Congruence classes of large configurations in vector spaces over finite fields, Funct. Approx. Comment. Math., Volume 62, Number 1 (2020), 131-141. 

• Areas of triangles and SL_2 actions in finite rings, BULLETIN of the L.N. Gumilyov Eurasian National University Mathematics Series, Computer science, Mechanics, No.2 (127) / 2019 

Outreach and other activities

• As of Spring 2025, I am co-organizing the Analysis and Applied Mathematics Seminar at Kennesaw State (co-organized with Emanuel Indrei)

• Organized HAFS2023: Harmonic Analysis and Fractal Sets conference at Ohio State in March 2023 (co-organized with Eyvindur Palsson and Krystal Taylor).

• Taught a mini-course for the Ross Mathematics Program, a summer math program for high school students, in summer 2022 (see lecture notes below).

• Graduate assistant for Grad STEM for All, a summer undergraduate research and mentoring program at the University of Rochester, in summer 2019.

Expository Writing (not published)

• My lecture notes on the Erdos-Falconer distance problem in vector spaces over finite fields, given at the Ross Mathematics Program, Summer 2022.

Teaching

• Fall 2025: I am teaching Real Analysis II (Math 4382) and Graph Theory (Math 3322)

• Spring 2025: I taught Discrete Mathematics (Math 2345) and Real Analysis II (Math 4382).

• Fall 2024: I taught Discrete Mathematics (Math 2345).

My earlier teaching experience as a graduate student and postdoc can be found in my CV.