Dylan J. Altschuler

Dylan J. Altschuler is a Research Fellow in the Department of Mathematical Sciences at Carnegie Mellon University, mentored by Konstantin Tikhomirov. He completed his PhD in Mathematics at New York University (Courant Institute) under Jonathan Niles-Weed and holds a B.A. in Mathematics from Princeton University, advised by Allan Sly. His research focuses on probability theory, particularly high-dimensional phenomena, with applications to statistical physics, combinatorics, algorithm design, and geometric analysis.

**Education**:

• PhD in Mathematics, New York University (Courant Institute), 2023, advised by Jonathan Niles-Weed
• B.A. in Mathematics, Princeton University, 2018, senior thesis advised by Allan Sly

**Research Interests**: Dylan’s work explores the interplay between probability, geometry, and combinatorics, addressing challenges in metric embeddings, random matrix theory, and phase transitions in high-dimensional systems. His recent contributions include resolving long-standing gaps in dimension reduction modulus, analyzing nonlinear spectral gaps, and studying critical phenomena in random graphs and perceptrons.

**Key Contributions**: His publications span topics such as universal thresholds for tree embeddings, non-embeddability of random regular graphs, and spectral properties of inhomogeneous matrices. He has also contributed to foundational results in discrepancy theory and the development of combinatorial frameworks for nonlinear spectral analysis.

**Grants & Awards**: While no explicit awards are listed, his research has been recognized through collaborations with leading institutions and his active participation in academic seminars, including the UPenn Optimization Seminar. His work frequently involves interdisciplinary approaches, bridging theoretical mathematics with applications in data science and algorithm design.

**Labs/Teams**: Dylan collaborates extensively with researchers in probability and geometry, including Pandelis Dodos, Konstantin Tikhomirov, and Konstantinos Tyros. His current research is supported by his postdoctoral fellowship at CMU.