Research Cluster
Algebra, Geometry &
Number Theory
The Algebra, Geometry & Number Theory cluster at Tulane is dedicated to the study of fundamental algebraic, geometric, and arithmetic structures. Our research explores the deep and classical interplay within pure mathematics, investigating the interactions between these fields and their applications in areas such as combinatorics, coding theory, and cryptography.
Faculty in this cluster share common tools and a common mathematical language, with diverse research interests that include semigroups, rings and modules, category theory, and commutative algebra.
Key Research Focus: In algebraic geometry and combinatorics, we investigate syzygies, monomial ideals, and edge ideals of hypergraphs. Our geometers and topologists study questions related to the curvature properties of Riemannian manifolds, transformation groups, and surgery theory, providing a comprehensive view of modern pure mathematics.
Affiliated Faculty
Our faculty's expertise in pure mathematics drives the department's contributions to the field. Explore their profiles to learn more about their specific research.
Tewodros Amdeberhan
Primary
Professor Amdeberhan's research is in combinatorics and number theory, with a focus on q-series, special functions, and partition theory.
Olivia Beckwith
Primary
A number theorist, Professor Beckwith's research centers on modular forms, including mock modular and Maass forms, and their connections to combinatorics.
Daniel Irving Bernstein
Secondary
Professor Bernstein's work sits at the intersection of combinatorics, discrete geometry, and applied algebraic geometry, with a focus on structures arising in science.
Mahir Can
Primary
Professor Can's research spans algebraic groups, representation theory, and algebraic geometry, with applied interests in error-correcting codes and cryptography.
Alessandra Costantini
Primary
Professor Costantini's research is in commutative algebra, focusing on Rees algebras of ideals and modules with connections to singularity theory and toric geometry.
Maurice Joseph Dupre
Secondary
Professor Dupre applies topological and differential geometric methods and bundle theory to problems in functional analysis and mathematical physics.
Tài Huy Hà
Primary
Professor Hà's research lies at the intersection of commutative algebra, algebraic geometry and combinatorics, studying algebraic invariants and combinatorial structures.
Michael Joyce
Primary
Professor Joyce's research is in algebraic combinatorics, where he explores combinatorial models for algebraic varieties using objects like barred permutations.
Rafal Komendarczyk
Primary
Professor Komendarczyk's work is in geometry and topology, with a focus on knot theory, finite type invariants, and modern applications in topological data analysis.
Kalina Mincheva
Primary
Professor Mincheva's research is in tropical geometry and its connections to algebraic geometry and commutative algebra, including vector bundles on tropical schemes.
Victor Moll
Primary
A classical analyst, Professor Moll's research includes symbolic computation, special functions, and number theory, with a focus on the evaluation of definite integrals.
Norbert Riedel
Secondary
Professor Riedel's work connects functional analysis and operator algebras with the theoretical foundations of statistical learning theory.
David DaGang Yang
Primary
Professor Yang's research is in differential geometry, focusing on Riemannian manifolds, curvature and topology, rigidity theorems, and eigenvalue estimates.
Seminars & Activities
- Faculty and students in this cluster are active participants in the department's weekly Algebra Seminar and Topology-Geometry Seminar.
- The prestigious international journal Semigroup Forum was founded and is still edited at Tulane, reflecting our longstanding research strength in algebraic semigroups.
- Explore all faculty profiles in the Mathematics Department Directory.
