Marta Pavelka
My research is in geometric and topological combinatorics.
I study simplicial complexes and triangulated manifolds, developing higher-dimensional analogues of classical graph concepts — Hamiltonicity, interval graphs, chordality, shellability, and Turán problems — with connections to topology and commutative algebra.
Postdoctoral researcher in the QMATH group at the University of Copenhagen; previously at Carnegie Mellon University. Ph.D. in Mathematics, University of Miami, 2023, under Bruno Benedetti.
Research
My work follows three connected directions: extending graph theoretic properties to higher dimensions, studying the structure of triangulated manifolds, and relating combinatorial properties of simplicial complexes to topology and commutative algebra.
Higher-dimensional graph theory
I study extensions of graph theoretic properties, including chordality, Hamiltonicity, interval structures, and Kneser graphs, to simplicial complexes and polytopes.
Triangulated manifolds
I investigate structural and extremal questions for triangulated manifolds, including enumeration, dual graphs, reduced balls, and efficient triangulations.
Combinatorial topology and algebra
I study how combinatorial properties of simplicial complexes interact with shellability, vertex decomposability, Alexander duality, and commutative algebra.
Current projects
Joint work in progress, each project carrying a classical combinatorial question into higher dimensions.
Reduced balls and dual graphs
With Bergfinnur Durhuus, I study structural properties of reduced triangulated balls and their dual graphs. This project is motivated by the problem of estimating the number of triangulated 3-spheres with a given number of tetrahedra.
Higher dimensional chordality
With Bruno Benedetti, I study extensions of chordal graph theory to simplicial complexes. We seek higher dimensional analogues of several classical characterizations of chordal graphs, with particular emphasis on properties that are structurally meaningful and efficiently testable. The first part of this project is available on arXiv, while the second is in progress.
Kneser graphs of polytopes
With Florian Frick, I study Kneser graphs associated with polytopes and the relationship between their geometric structure and edge-criticality and vertex-criticality.
Cubical complexes and efficient triangulations
With Hailun Zheng, I study cubical complexes and small triangulations of manifolds satisfying desirable combinatorial and topological properties.
Publications
A complete list is available in my CV.
Skeleton Chordalities
with Bruno Benedetti, 2026
Introduces and compares higher-dimensional notions of chordality, with applications to vertex decomposability, decompositions, simplicial vertices, and Alexander duality.
Chordality, syzygies, and shellability for hypergraphic analogues of interval graphs
with Anton Dochtermann and Bennet Goeckner, 2026
Connects underclosed complexes and cointerval hypergraphs, also with chordality, shellability, vertex decomposability, and linear quotients.
Vertex orders in higher dimensions
with Bennet Goeckner, 2025
Studies higher-dimensional analogues of interval graphs and structural properties arising from vertex orders.
A conditional lower bound for the Turán number of spheres
with Andrew Newman · Combinatorics, Probability and Computing 34, no. 6, 848–856, 2024
Studies extremal questions for triangulated spheres and gives lower bounds for their Turán numbers.
Higher-dimensional counterexamples to Hamiltonicity
with Bruno Benedetti · Graphs and Combinatorics 42, no. 1, Article 14, 2023
Constructs higher-dimensional counterexamples showing that classical Hamiltonian phenomena do not extend directly from graphs to simplicial complexes.
2-LC triangulated manifolds are exponentially many
with Bruno Benedetti · Annales de l’Institut Henri Poincaré D 11, 363–382, 2022
Proves exponential bounds for a broad class of triangulated manifolds defined through local constructibility.
On-line algorithms for multiplication and division in real and complex numeration systems
with Christiane Frougny, Edita Pelantová, and Milena Svobodová · Discrete Mathematics and Theoretical Computer Science 21, no. 3, 2019
Develops online algorithms for arithmetic in real and complex numeration systems.
Teaching and mentoring
Teaching mathematics is in some ways like teaching yoga.
Teaching. Students improve through regular practice, clear guidance, and carefully chosen challenges. In first-year courses, my focus is on building confidence, fluency, and persistence, while helping students understand why the methods they use work.
Mentoring. Here my focus is on helping students move toward independence. This includes choosing productive examples, learning how to formulate questions, testing conjectures, and presenting mathematical ideas clearly.
Teaching Excellence Award, University of Miami, Math Department (2022)
Mentor at University of Copenhagen
I lead a course in which first year bachelor’s students work in small groups on their first mathematical projects and produce a written manuscript. I taught the course in Spring 2026 and will teach it again in 2027.
Instructor at Carnegie Mellon University
I taught Integration and Approximation to approximately 80 students per section in Fall 2023, Spring 2024, and two sections in Spring 2025. Each semester, I also coordinated a team of three to six teaching assistants.
Instructor at University of Miami
Between Fall 2020 and Spring 2022, I taught several undergraduate courses, including Precalculus II, Calculus I, and Calculus II, with approximately 40 students per section. My responsibilities included both lectures and recitations.
Recitation Instructor at University of Miami and Czech Technical University
Between Fall 2016 and Spring 2020, I led recitations for undergraduate courses including Calculus II, Calculus I, Precalculus II, and Foundations of Mathematical Analysis.
Selected talks
A complete list of talks is available in my CV.
Interval clutters and their duals
- Midsummer Combinatorial Workshop XXXI, Charles University, July
- Combinatorics and Geometry in Mytilene, May
A conditional lower bound for the Turán number of spheres
Geometric and Topological Combinatorics, Joint Mathematics Meetings in Seattle, January
Vertex orders: From graphs to complexes
Colloquium at University of Hawaii, November
Service
Contributions to the mathematical community through seminar organization and refereeing for journals and conferences.
Organization
Seminars I have co-organized for the community.
- Algorithms, Combinatorics, and Optimization Seminar
- Carnegie Mellon University
- 2023 to 2024
Refereeing
Journals and conferences I referee for.
- Discrete & Computational Geometry
- The Electronic Journal of Combinatorics
- FPSAC 2024
- Publications Mathématiques de Besançon, “Women in Numbers Europe 5”
Contact
I am happy to hear about possible collaborations, talks, and visits.