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.

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. "Pythagoras Numbers for Ternary Forms" (with Greg Blekherman and Rainer Sinn ). To appear in Proceedings of the AMS ArXiv Preprint
  2. "A Topological Approach to Simple Descriptions of Convex Hulls of Sets Defined by Three Quadrics" (with Greg Blekherman). To appear in SIAM Journal on Applied Algebra and Geometry ArXiv Preprint
  3. "Alternating Minimization for Regression with Tropical Rational Functions" (with Lars Ruthotto ). Algebraic Statistics . Published Version Code ArXiv Preprint
  4. "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. "Tensor-Tensor Products, Group Representations, and Semidefinite Programming", with (Elizabeth Newman)

Conference Presentations

  1. "Alternating Minimization for Regression with Tropical Rational Functions" SIAM Conference on Mathematics of Data Science 2024 ( Poster )
  2. "A Topological Approach to Simple Descriptions of Convex Hulls of Sets Defined by Three Quadrics". MEGA (Effective Methods in Algebraic Geometry) 2024 (slides)
  3. "Tensor-Tensor Products, Group Representations, and Semidefinite Programming". JM Invariant @ 60 Conference on Tensor Invariants in Geometry and Complexity Theory 2024, Poster Session
  4. "Alternating Minimization for Regression with Tropical Rational Functions". SIAM Conference on Applied Algebraic Geometry 2023, Minisymposium on Real Algebraic Geometry and Optimization.
  5. "Alternating Minimization for Regression with Tropical Rational Functions". AMS Spring Southeastern Sectional Meeting 2023, Special Session on Algebraic Methods in Algorithms
  6. "An Alternating Minimization Algorithm for Regression with Tropical Rational Functions". Combinatorial, Computational, and Applied Algebraic Geometry 2022 (CCAAGS-22), Poster Session
  7. "Relaxation and Duality for Multiobjective Integer Programming". INFORMS Annual Meeting 2020, Undergraduate Operations Research Prize Session A

Upcoming Conferene Travel

  1. International Conference on Continuous Optimization (ICCOPT) 2025

I am not teaching in Spring 2025.

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)

Contact: alex.dunbar (at) emory.edu

Office: MSC N408

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