Yulia Alexandr

Yulia Alexandr is a Hedrick Assistant Adjunct Professor (Adjunct Assistant Professor) in the Department of Mathematics at the University of California, Los Angeles (UCLA) and a Postdoctoral Fellow in Applied Mathematics at Harvard University. Her research centers on algebraic statistics, applied algebraic geometry, and mathematical machine learning, with current focus on geometric structures in statistical models and neural networks. She is actively on the academic job market for the 2025-26 cycle.

Education:

• Ph.D. in Mathematics, University of California, Berkeley (2023). Advisors: Bernd Sturmfels and Serkan Hoşten. Thesis: From Voronoi Cells to Algebraic Statistics.
• B.A. in Mathematics (high honors), Wesleyan University (2019). Advisor: Karen Collins. Thesis: Combinatorial Nullstellensatz: Various Proofs, Extensions and Applications.

Dr. Alexandr's research develops algebraic and geometric frameworks for statistical modeling and machine learning. She pioneers methods for analyzing logarithmic Voronoi cells in Gaussian and discrete models, investigates structural properties of graphical models and mixture distributions, and establishes algebraic constraints in neural network architectures. Her work bridges abstract algebra with practical machine learning applications, particularly in understanding geometric constraints of ReLU networks and information divergence in statistical models.

Analysis of her 15 most recent publications (2018-2025) reveals three dominant research thrusts: (1) geometric foundations of statistical models through Voronoi structures and moment varieties, (2) algebraic analysis of graphical models including decomposable and context-specific variants, and (3) mathematical theory of neural networks with emphasis on ReLU constraints. Her publications demonstrate consistent progression from combinatorial foundations to advanced applications in machine learning, with increasing focus on computational implementations using tools like HomotopyContinuation.jl.

Scientific Awards:

No scientific awards were documented in the provided materials.

Dr. Alexandr has mentored undergraduate researchers through Berkeley's Directed Reading Program (Spring 2020), focusing on algebraic combinatorics and graph theory. Her teaching portfolio includes instructing programming courses (PIC 10A/B, PIC 16A) at UCLA and serving as Graduate Student Instructor for mathematics courses at UC Berkeley. While no specific grants are listed, her participation in workshops at IMSI, AIM, and MPI MIS indicates collaborative research funding support.

She co-organizes the Berkeley Nonlinear Algebra Seminar and maintains active research collaborations with Guido Montúfar (UCLA), Anna Seigal (Harvard), and her doctoral advisors. Her work is regularly presented at premier venues including SIAM AG, ISSAC, and JMM. Additionally, Dr. Alexandr is a published Russian-language poet with a 2017 collection Лирическое Наступление and contributions to The Birch journal, reflecting her interdisciplinary engagement beyond mathematics.