Alex Dunbar

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I'm a fifth-year PhD candidate in Mathematics at Emory University coadvised by Vicki Powers and Greg Blekherman (Georgia Tech). I graduated from Rice University in 2020 with a BS in Mathematics and a BA in Computational and Applied Math.

My research interests are broadly in algebraic methods for optimization and machine learning. Most recently, I have been thinking about applied aspects of real and tropical geometry.

I will be applying for postdoctoral positions to start in Summer/Fall 2025. Find my CV and Research Statement here.

Research Interests

My research interests are in applied algebraic geometry, real algebraic geometry, optimization, and machine learning. I am particularly interested in interactions between real algebraic geometry and semidefinite programming as well as applications of tropical geometry in machine learning.

Publications and Preprints

  1. "A Topological Approach to Simple Descriptions of Convex Hulls of Sets Defined by Three Quadrics" (with Greg Blekherman). ArXiv Preprint
  2. "Alternating Minimization for Regression with Tropical Rational Functions" (with Lars Ruthotto ). Algebraic Statistics . Published Version Code ArXiv Preprint
  3. "Relaxations and Duality for Multiobjective Integer Programming" (with Saumya Sinha and Andrew J. Schaefer). Mathematical Programming. Published Verison Optimization Online Preprint ArXiv Preprint

In Preparation

  1. "Pythagoras Numbers for Ternary Forms", with Greg Blekherman
  2. "Tensor-Tensor Products, Group Representations, and Semidefinite Programming", with Elizabeth Newman

Conference Presentations

  1. "Tensor-Tensor Products, Group Representations, and Semidefinite Programming". JM Invariant @ 60 Conference on Tensor Invariants in Geometry and Complexity Theory 2024, Poster Session
  2. "Alternating Minimization for Regression with Tropical Rational Functions". SIAM Conference on Applied Algebraic Geometry 2023, Minisymposium on Real Algebraic Geometry and Optimization.
  3. "Alternating Minimization for Regression with Tropical Rational Functions". AMS Spring Southeastern Sectional Meeting 2023, Special Session on Algebraic Methods in Algorithms
  4. "An Alternating Minimization Algorithm for Regression with Tropical Rational Functions". Combinatorial, Computational, and Applied Algebraic Geometry 2022 (CCAAGS-22), Poster Session (poster)
  5. "Relaxation and Duality for Multiobjective Integer Programming". INFORMS Annual Meeting 2020, Undergraduate Operations Research Prize Session A

Upcoming Conferene Travel

  1. MEGA (Effective Methods in Algebraic Geometry), 2024
  2. ICERM Workshop "Discrete Optimization: Mathematics, Algorithms, and Computation", 2024

I am teaching Advanced Calculus (MATH 211) at Emory in Fall 2024.

Some interactive graphs in Desmos which I used to supplement my Calculus I lecture notes can be found here.

Previous Teaching:

Emory Mathematics Directed Reading Program

I have been a graduate student mentor for the Emory Mathematics DRP since Fall 2021. In Spring 2022, I joined the steering comittee to help organize the program. In the 2023-24 academic year, I co-directed the program with Shilpi Mandal. For more information about the program, see the DRP website.

Past reading topics include:

2022LAHALF

When I am not doing math, I enjoy distance running. In college, I competed on the Rice Cross Country and Track & Field (5000m, 10000m) teams. Since graduating, I have participated in a variety of races on roads and trails. (Picture is from 2022 Lousiana Half Marathon)