Linquan Ma

Linquan Ma is an Associate Professor in the Department of Mathematics at Purdue University, specializing in Commutative Algebra and Algebraic Geometry. His research focuses on singularities in mixed characteristic, perfectoid spaces, and homological conjectures. He earned his Ph.D. from the University of Michigan under Melvin Hochster. His work bridges algebraic and geometric perspectives, with applications to F-singularities, local cohomology, and multiplier ideals.

Education:

• Ph.D. in Mathematics, University of Michigan (2014), advised by Melvin Hochster

Research Interests:

• Commutative Algebra: F-singularities, tight closure, local cohomology, multiplier ideals, Hilbert-Kunz multiplicity
• Algebraic Geometry: Singularities in mixed characteristic, minimal model program, perfectoid methods
• Homological Algebra: Ulrich modules, Boij-Söderberg theory, homological conjectures

Recent Work Trends: Recent papers explore perfectoid spaces' role in resolving homological conjectures, behavior of test ideals in mixed characteristic, and structural properties of Cohen-Macaulay modules. His work often unifies characteristic p and mixed characteristic techniques.

Awards: None explicitly listed, though his contributions to F-singularity theory and mixed characteristic algebra highlight his field-leading impact.

Teaching:

• Purdue: Courses include Algebra Honors, Linear Algebra, and graduate topics in commutative algebra (e.g., 2024: Positive characteristic methods)
• Prior institutions: University of Utah (Calculus, Differential Equations), University of Michigan (undergraduate calculus)

Collaborations: Active collaborations with Bhargav Bhatt, Karl Schwede, Ilya Smirnov, and others on foundational problems in commutative algebra and algebraic geometry.