Martina Juhnke

Research Interests

Discrete and convex geometry

My interests in discrete and convex geometry mainly lie in the study of combinatorics and geometry of polytopes and polyhedra. This includes the enumeration of lattice points via Ehrhart theory but also the existence of nicely behaved subdivisions and triangulations. I often use toric geometry, e.g., Gröbner degenerations to study these objects. I am also interested in the typical behavior of combinatorial properties of polytopes which can be studied via random polytopes.

Applications to Physics

Lately, I started to study connections between physics, in particular cosmology, and discrete geometry. Key words in this area are cosmological polytopes, cosmohedra, canonical forms, positive geometries, dual volumes, Bergman fans and the flat space wavefunction.

Algebraic and geometric combinatorics

I am interested in the combinatorics of simplicial complexes, in particular in problems concerning the enumeration of their faces. In particular, I recently got interested in properties (and new variants) of the cd-index of a (semi)-Eulerian poset. Often algebraic methods turn out to be useful for this type of problems.

Combinatorial commutative algebra

I am interested in the study of algebraic and combinatorial properties of (monomial) ideals associated to combinatorial objects such as graphs, posets and simplicial complexes. In particular, I am interested in families of these objects that are invariant under a certain symmetry, e.g., the symmetric group or the Inc-monoid. In this setting, though objects might be a priori infnite, up to symmetry, one can often reduce to a finite situation.

Matroids

During the last years I also gained increasing interest in matroid theory. In particular, I am interested in the polytope of all matroids and projections of it.

Short CV

since 2023 member of the steering committee of the DFG priority programme Combinatorial Synergies

since 10/2018 Professor (W2) for Discrete Mathematics at University of Osnabrück

04/2015–09/2018 Juniorprofessor at University of Osnabrück

02/2014–03/2015 Akademischer Rat at Goethe-Universität, Frankfurt am Main

05/2012–02/2014 postdoctoral researcher at Goethe-Universität, Frankfurt am Main

09/2010–04/2012 postdoctoral researcher at University of Vienna, Vienna (Austria)

09/2009–08/2010 postdoctoral researcher at Háskólin í Reykjavík, Reykjavík (Iceland)

08/2007–02/2008 visiting PhD student Cornell University (Ithaca), host: Irena Peeva

10/2006–07/2009 PhD student Philipps-Universität Marburg/Lahn

10/2001–08/2006 Diploma Study Philipps-Universität Marburg/Lahn (Diploma Thesis)

Teaching

Summer term 2026: Elements of discrete Mathematics, Universität Osnabrück (a discrete math class for students who want to become teachers in primary school)
Lattice polytopes, Universität Osnabrück (a course for Master and PhD tudents)

Winter term 2025/2026: Coding theory and cryptography, Universität Osnabrück (a course for Bachelor students)
Seminar Combinatorics, Universität Osnabrück
Seminar Elements of Mathmatics, Universität Osnabrück (Proofs from the Book)

Former classes
I have been teaching can be found on the University webpage and on stud.IP. I am responsible for the organization of the seminar of the Algebra and Discrete Mathematics group of the University of Osnabrück. Please contact me if you are interested in giving a talk. Moreover, together with Hanna Döring and Stefan Kunis, I organize the Maryam Mirzakhani Lectures, where usually female or non-binary researchers give a talk for Bacehlor/Master/PhD students and discuss career questions afterwards.

Research Group

Current Members

Jhon Bladimir Caicedo de Portilla (PhD student on a DFG project)

Torben Donzelmann (jointly supervised PhD student on a DFG project)

Mieke Fink (jointly supervised PhD student with Graham Denham on the basis of a Cotutelle agreement)

Germain Poullot (postdoc) [ GitHub ]

Steffen Schlie (jointly supervised PhD student)

Former members

Justus Bruckamp (jointly supervised PhD student)

Alessio D'Alì (postdoc, now Professore Associato at Politecnico di Milano) [ GitHub ]

Jan-Marten Brunink (PhD student)

Tarek Emmrich (jointly supervised PhD student)

Lukas Katthän (postdoc)

Daniel Köhne (PhD student)

Alexander Nover (jointly supervised PhD student)

Sara Saeedi Madani (postdoc, now Associate Professor at Amirbakir University of Technology, Iran)

Richard Sieg (jointly supervised PhD student, now Professor at Cologne University of Applied Sciences)

Dinh Van Le (postdoc, now FPT University Hanoi, Vietnam)

Lorenzo Venturello (PhD student, now tenure track researcher at University of Siena)

Mentoring

I serve as a mentor for international scholars at the University of Osnabrück, providing guidance to both incoming and established researchers.

Formal mentoring programmes. I have supervised numerous (predominantly female) PhD candidates and postdoctoral researchers through university-affiliated mentorship initiatives. Several of these mentees have already secured permanent academic positions at other institutions.

Informal mentorship. Beyond structured programmes, I regularly advise PhD students and postdoctoral fellows who seek support on research, career development, or integration into the academic community.

My commitment to fostering inclusive, high-quality mentorship contributes to the long-term success of emerging scholars across disciplines.

Publications

T. Donzelmann, M. Juhnke, B. Rednoß, C. Thäle
Central limit theorems for high dimensional lattice polytopes: symmetric edge polytopes.
2026 [ http ]

A. Birkemeyer, T. Donzelmann, M. Fink, M. Juhnke
On cosmological polytopes, their canonical forms and their duals.
2026 [ http ]

T. Donzelmann, T. Holleben, M. Juhnke
Symmetric (co)homology polytopes.
2026 [ http ]

M. Juhnke, L. Solus, L. Venturello
Triangulations of cosmological polytopes.
In: Algebr. Comb. 8, No. 4, 1141–1168, 2025 [ http ]

J. Bruckamp, M. Chimani, M. Juhnke
On the connected blocks polytope.
In: Discrete Comput. Geom. 73, No. 4, 946–972, 2025 [ http ]

T. Emmrich, M. Juhnke, S. Kunis
Sparse graph signals – uncertainty principles and recovery.
In: GAMM-Mitt. 48, No. 2, Article ID e70002, 13 p., 2025 [ http ]

T. Emmrich, M. Juhnke, S. Kunis
Two subspace methods for frequency sparse graph signals.
In: Appl. Comput. Harmon. Anal. 74, Article ID 101711, 9 p., 2025 [ http ]

J. B. Caicedo, M. Juhnke, G. Poullot
Ehrhart non-positivity and unimodular triangulations for classes of s-lecture hall simplices.
2025 [ http ]

M. Juhnke, G. Poullot
Unimodality of the number of paths per length on polytopes: Examples, counter-examples, and a central limit theorem.
2025 [ http ]

M. Juhnke, R. M. Miró-Roig
List of problems.
In: Lefschetz properties. Current and new directions. Springer INdAM Ser. 59, 211–225, 2024

A. D'Alì, M. Juhnke-Kubitzke, M. Koch
On a generalization of symmetric edge polytopes to regular matroids.
In: Int. Math. Res. Not. 2024, No. 14, 10844–10864, 2024 [ http ]

J. Bruckamp, L. Goltermann, M. Juhnke, E. Landin, L. Solus
Ehrhart theory of cosmological polytopes.
2024 [ http ]

J. Bruckamp, M. Chimani, M. Juhnke
Two-edge-connected (not necessarily spanning) subgraphs and polyhedra.
2024 [ http ]

M. Juhnke-Kubitzke, J. Alejandro Samper, L. Venturello
The cd-index of semi-Eulerian posets.
Accepted by SIAM Journal on Discrete Mathematics, 2024 [ http ]

M. Juhnke-Kubitzke, D Köhne
Laplacian polytopes of simplicial complexes.
2023 [ http ]

A. D'Alì, M. Juhnke-Kubitzke, D. Köhne, L. Venturello
On the gamma-vector of symmetric edge polytopes.
In: Int. Math. Res. Not. 2024, No. 14, 10844–10864 (2024) [ http ]

M. Chimani, M. Juhnke-Kubitzke and A. Nover
On the Dominant of the Multicut Polytope.
in: Discrete Comput. Geom. 72, No. 3, 1169–1198, 2024 [ http ]

M. Juhnke-Kubitzke, D. Köhne and J. Schmidt
Counting Horizontal Visibility Graphs.
2021 [ http ]

M. Chimani, M. Juhnke-Kubitzke and A. Nover
On the Bond Polytope.
In: Adv. Geom. 23, No. 4, 461–480, 2023 [ http ]

M. Juhnke-Kubitzke and L. Venturello
Balanced shellings and moves on balanced manifolds.
In: Advances in Mathematics 379, Paper No 107571, 45 pp, 2021 [ http ]

M. Juhnke-Kubitzke and L. Venturello
Graded Betti numbers of balanced simplicial complexes.
In: Acta Mathematica Vietnamica 46, 839–871, 2021 [ http ]

E. Faber, M. Juhnke-Kubitzke, H. Lindo, C. Miller, R. R.G. and A. Seceleanu
Canonical Resolutions over Koszul Algebras.
In: Proceedings of the 2019 WICA workshop, Banff, Alberta, Canada, October 20–25, 2019. Cham: Springer. Assoc. Women Math. Ser. 29, 281-301, 2022 [ http ]

B. Schütz, N. Aschenbruck, S. Bussmann, H. Döring and M. Juhnke-Kubitzke
The Impact of Bit Errors on Intra-Session Network Coding with Heterogeneous Packet Lengths.
In: Proceedings of the 45^th IEEE LCN Symposium on Emerging Topics in Networking LCN, 2020 [ http ]

C. Athanasiadis, J.-M. Brunink and M. Juhnke-Kubitzke
Combinatorics of antiprism triangulations.
In: Discrete Comput. Geom. 68, No. 1, 72–106, 2022 [ http ]

M. Juhnke-Kubitzke and U. Nagel
Balanced squeezed Complexes.
2020 [ http ]

J. Grygierek, M. Juhnke-Kubitzke, M. Reitzner, T. Römer and O. Röndigs
Gigantic random simplicial complexes.
In: Homology, Homotopy and Applications 22(1), 297–318, 2020 [ http ]

M. Juhnke-Kubitzke, D. Van Le and T. Römer
Asymptotic behavior of symmetric ideals: a brief survey.
In: Combinatorial structures in algebra and geometry, Springer Proc. Math. Stat. 331, 73–94, 2020 [ http ]

M. Chimani, C. Dahn, M. Juhnke-Kubitzke, N. M. Kriege, P. Mutzel and A. Nover
Maximum Cut Parameterized by Crossing Number.
In: Journal of Graph Algorithms and Applications 24, 155–170, 2020 [ http ]

M. Juhnke-Kubitzke and U. Nagel
Squeezed Complexes.
In: Journal of the London Mathematical Society, In: J. Lond. Math. Soc., II. Ser. 101, No. 1, 110–135, 2020 [ http] ]

M. Chimani, M. Juhnke-Kubitzke, A. Nover and T. Römer
Cut-Polytopes of Minor-free Graphs.
In: Bull. Math. Soc. Sci. Math. Roum., Nouv. Sér. 66(114), No. 1, 97–112, 2023 [ http ]

M. Juhnke-Kubitzke and L. Venturello
A balanced non-partitionable Cohen-Macaulay complex.
In: Algebraic Combinatorics 2(6), 1149–1157, 2019 [ http ]

M. Juhnke-Kubitzke, S. Murai and R. Sieg
Local h-vectors of Quasi-Geometric and Barycentric Subdivisions.
In: Discrete & Computational Geometry 61(2), 364–379, 2019 [ http ]

M. Juhnke-Kubitzke and S. Murai
Balanced generalized lower bound inequality for simplicial polytopes.
In: Selecta Mathematica 24(2), 1677–1689, 2018 [ http ]

M. Juhnke-Kubitzke, S. Murai, I. Novik and C. Sawaske
A generalized lower bound theorem for balanced manifolds.
In: Mathematische Zeitschrift, 289(3–4), 921–942, 2017 [ http ]

M. Juhnke-Kubitzke, R. M. Miró-Roig, S. Murai and A. Wachi
Lefschetz properties for complete intersection ideals generated by products of linear forms.
In: Proceedings of the AMS, 146, 3249–3256, http://dx.doi.org/10.1090/proc/14009, 2018 [ http ]

D. Cook II, M. Juhnke-Kubitzke, S. Murai and E. Nevo
Lefschetz properties of balanced 3-polytopes.
In: Rocky Mountain J. Math 48(3), 769–790, 2018 [ http ]

M. Juhnke-Kubitzke and Le Van Dinh
Flawlessness of h-vectors of broken circuit complexes.
In: International Mathematical Research Notices, 2018(5), 1347–1367, 2018 [ http ]

A. Conca, M. Juhnke-Kubitzke and V. Welker
Asymptotic syzygies of Stanley-Reisner rings of iterated subdivisions.
In: Transactions of the AMS 370, 1661–1691, 2017 [ http ]

C. Haase, M. Juhnke-Kubitzke, R. Sanyal and T. Theobald
Mixed Ehrhart polynomials.
In: The Electronic Journal of Combinatorics 24(1), 2017 [ http ]

M. Juhnke-Kubitzke and S. Saeedi Madani
Ideals associated to poset homomorphisms: A survey.
In: Homological and Computational Methods in Commutative Algebra, Springer INdAM Series, 2016 [ http ]

M. Juhnke-Kubitzke, L. Katthän and S. Saeedi Madani
Algebraic properties of ideals of poset homomorphisms.
In: Journal of Algebraic Combinatorics, 44(3), 757–784, 2016 [ http ]

M. Juhnke-Kubitzke and T. de Wolff
Intersections of Amoebas.
2015 [ http ]

G. Blekherman, S. Iliman, M. Juhnke-Kubitzke and M. Velasco
Gap vectors of real projective varieties.
In: Advances in Mathematics, 283, 458–472, 2015 [ http ]

G. Blekherman, S. Iliman and M. Kubitzke
Dimensional Differences Between Faces of the Cones of Nonnegative Polynomials and Sums of Squares.
In: International Mathematical Research Notices, 2015(18), 8437–8470, 2015 [ http ]

M. Kubitzke and A. Olteanu
Algebraic properties of classes of path ideals of posets.
In: Journal of Pure and Applied Mathematics 218(6), 1012–1033, 2014 [ http ]

I. Fischer and M. Kubitzke
Spectra and eigenvectors of the Segre transformation.
In: Advances In Applied Mathematics 56, 1–19, 2014 [ http ]

M. Kallipoliti and M. Kubitzke
A Poset Fiber Theorem for Doubly Cohen-Macaulay Posets and Its Applications.
In: Annals of Combinatorics 17, 711–731, 2013 [ http ]

M. Kubitzke and S. Murai
Lefschetz properties and the Veronese construction.
In: Mathematical Research Letters 19(5), 1–11, 2012 [ http ]

M. Kubitzke and V. Welker
Enumerative g-theorems for the Veronese construction for formal power series and graded algebras.
In: Advances in Applied Mathematics 49 (3–5), 307–325, 2012 [ http ]

F. Breuer, A. Dall and M. Kubitzke
Hypergraph Coloring Complexes.
In: Discrete Mathematics 312, 2407–2420, 2012 [ http ]

G. Kämpf and M. Kubitzke
Exterior depth and exterior generic annihilator numbers.
In: Communications in Algebra 40(1), 1–25, 2012 [ http ]

M. Kallipoliti and M. Kubitzke
Doubly homotopy Cohen-Macaulayness for the poset of injective words and the classcial NC-partition lattice.
In: DMTCS, proceedings of FPSAC 2011, Reykjavík, 575–586, 2011/p>

A. Claesson, M. Dukes and M. Kubitzke
Partition and composition matrices: two matrix analogues of set partitions.
In: DMTCS, proceedings of FPSAC 2011, Reykjavík, 221–232, 2011

M. Dukes, V. Jelinek and M. Kubitzke
Composition matrices, (2+2)-free posets and their specializations.
In: Electronic Journal of Combinatorics 18(1), P44, 2011 [ http ]

A. Claesson, M. Dukes and M. Kubitzke
Partition and composition matrices.
In: Journal of Combinatorial Theory Series A 118(5), 1624–1637, 2011 [ http ]

M. Kubitzke and E. Nevo
The Lefschetz property for barycentric subdivisions of shellable complexes.
In: Transact. AMS 361, 6151–6163, 2009 [ http ]

G. Kämpf and M. Kubitzke
Notes on symmetric and exterior depth and annihilator numbers.
In: Le Matematiche 63(2), 179–211, 2008 [ http ]

M. Kubitzke and V. Welker
The Multiplicity Conjecture for Barycentric Subdivisions.
In: Comm. Alg., 36, 4223–4248, 2008 [ http ]

Upcoming and Recent Events

04/2027: Oberwolfach Workshop Geometric, Algebraic and Topological Combinatorics (organizer)

03/2027: Intersection of Commutative Algebra, Combinatorial Topology, and Discrete Geometry, Chennai Mathematical Institute

09/2026: Priority Program Annual Conference, Frankfurt [ http ]

07/2026: invited speaker at FPSAC 2026, Seattle [ http ]

06/2026: invited speaker at Discrete Mathematics Days, Granada [ http ]

06/2026: Commutative Algebra and Computation (a birthday conference for Winfried Bruns), Osnabrück (organizer)

03/2026: Combinatorial Coworkspace, Austria (organizer) [ http ]

01/2026: Oberwolfach Workshop Enumerative Combinatorics

11/2025: Closing conference on Combinatorial Geometries and Geometric Combinatorics, Barcelona [ http ]

11/2025: invited speaker at Cosmology meets Non-Linear Algebra, Amsterdam [ http ]

09/2025: Priority Program Annual Conference, Hannover [ http ]

08/2025: invited speaker at Combinatorics and Geometry in Istanbul [ http ]

Editorial Boards

Electronic Journal of Combinatorics. Editorial board member since 2025.
Scope: all branches of discrete mathematics, including combinatorics, graph theory, and algorithms for combinatorial problems. [ http ]

Combinatorial Theory. Editorial board member since 2024.
Scope: additive, Algebraic, Analytic, Enumerative, Extremal, Geometric, Probabilistic and Topological Combinatorics, as well as theoretical aspects of their applications to other areas of mathematics and the sciences. [ http ]

Beiträge zur Algebra und Geometrie. Editorial board member since 2024.
Scope: classical areas of algebra, algebraic geometry and geometry, including algorithmic, computational, combinatorial, topological, differential and number theoretic topics with a distinct algebraic or geometric flavor. [ http ]

Miscellaneous

Academic Distinctions and Grants

2024–2027: DFG Research Grant for a PhD student

since 2023: Member of steering committee of DFG priority programme 2458 Combinatorial Synergies. (I am one of the five applicants applying for the programme. It was granted 2023 and started 2024.) [ http ]

2023–2026: DFG Research Grant for a PhD student

2019: Hans-Mühlenhoff prize for excellent teaching (University of Osnabrück)

2016/17: DAAD Vigoni (PI): Combinatorial and Computational Methods in Commutative Algebra

2007/08: DAAD grant for PhD students (Cornell University, USA)

Activities in the field of academic self-governance and further education

2020–2026: Participant in the EmpowHer Leadership Programme for Women with Management. Responsibility of the University of Osnabrück [ http ]

since 2024: Member of the senat of the University of Osnabrück and the Fachbereichsrat of the department of Mathematics, Computer Science and Physics

2015–2023: Member of the faculty committee for teaching and research

2018–2021: Deputy chairman of the graduate school Graphen und Netzwerke