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.

I am a postdoctoral researcher in the QMATH group at the University of Copenhagen. Previously, I held a postdoctoral position at Carnegie Mellon University. I received my Ph.D. in Mathematics from the University of Miami in 2023 under the supervision of Bruno Benedetti.

Curriculum vitae

Curriculum vitae, including a full publication and talk list.

Software

Enter the facets of a simplicial complex to test the properties shown below—and more.

Research

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

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

Preprint

Skeleton Chordalities

with Bruno Benedetti, 2026

Introduces and compares higher-dimensional notions of chordality and relates them to simplicial vertices, decompositions, vertex decomposability, and Alexander duality.

Preprint

Chordality, syzygies, and shellability for hypergraphic analogues of interval graphs

with Anton Dochtermann and Bennet Goeckner, 2026

Identifies underclosed complexes with complements of cointerval hypergraphs and connects them to chordality, shellability, vertex decomposability, and linear quotients.

Preprint

Vertex orders in higher dimensions

with Bennet Goeckner, 2025

Studies higher-dimensional analogues of interval graphs and structural properties arising from vertex orders.

Published article

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.

Published article

Higher-dimensional counterexamples to Hamiltonicity

with Bruno Benedetti · Graphs and Combinatorics 42, no. 1, Article 14, 2023

Characterizes the dimensions in which every polytope graph is line-Hamiltonian, showing that dimension three is the unique exception.

Published article

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.

Published article

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.

Thesis

On t-LC manifolds and on Hamiltonian complexes

Ph.D. thesis, University of Miami, 2023 · Supervisor: Bruno Benedetti

Teaching and mentoring

Teaching Excellence Award, University of Miami, Math Department (2022)

Teaching mathematics is, in some ways, like teaching yoga: progress comes through regular practice, clear guidance, gradual development, and challenges matched to the student’s level.

Project Mentor at the 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 the 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 the 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.