Stephen Mackes

I successfully defended my PhD thesis at UIC in Mathematics in December 2024 (graduated 2025).

My thesis advisor was Emily Dumas and the main result of my thesis guarantees that a (not necessarily convex) pleated surface is embedded (corresponds to a quasifuchsian representation) given locally small enough bending data. I have plans to prove a similar result for d-pleated planes.

I now work as a math researcher at Rampart Communications. This work is on security and efficiency of digital signals at the physical layer. Most recently, we have been innovating in coded modulations on dense lattice constellations. There is some interesting recent work on this aiming to simultaneously achieve the shaping gains due to lattice voronoi shaping as well as efficient coding gains using FEC and lattice density, and we are currently working to publish our research in this area.

Research interests:

I am interested in pleated planes, higher Teichmüller theory, character varieties for surface groups to complex Lie groups (mostly PSL(d, C)), and hyperbolic geometry.

I am also interested in dense lattices, theta functions on integral lattices, and using geometric tools from lattices and Lie groups (mostly O(n) and U(n)) to innovate physical layer signal protocols like coded modulation.

Preprints:

"Multilevel Coset Codes on Lattices," (with Matt Robinson, Chloe Makdad, Leo Bertholet, and Dan Chew). Preprint, 2026.

This work is through my Rampart affiliation, and it presents a powerful coded modulation scheme on AWGN using nonbinary polar codes in a particularly efficient way in a lattice valued and voronoi shaped signal constellation. The results presented are in the D4 lattice and are throughput-equivalent to a coded modulation on a 16 QAM.

Teaching:

I was a teaching assistant at UIC for

Math 125, 192, and 210 each of which was repeated for a few semesters.

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