Prof. Dr.

Martina Juhnke

Discrete Mathematics

Research Interests

Algebraic combinatorics

I am interested in the combinatorics of simplicial complexes, in particular in problems concerning the enumeration of their faces and in topics related to the g-conjecture, i.e., the face enumeration of spheres or also more general complexes. 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. The aim is to understand how algebraic invariants and properties are influenced by combinatorial properties and vice versa.

Topological combinatorics

The idea of topological combinatorics is to use topological methods in combinatorics. Roughly speaking, one shows that a combinatorial object, such as a graph, a simplicial complex or a matroid exhibits a certain topology property, in order to apply technologies from topology and then to deduce a combinatorial property.

Combinatorics of posets

The combinatorics of partially ordered sets shows several relations to other areas of combinatorics and combinatorial commutative algebra such as order complexes and face lattices of simplicial complexes. Currently, I am also interested in the study of certain monomial ideals associated to isotone maps between posets.

Real algebraic geometry

In this area, my main interest lies in the study of the difference of the cone of non-negative polynomials and the cone of sums of squares. Here, the focus is on the investigation of dimensional differences of exposed faces of those cones, not only in the classical setting but also for general projective varieties.

Discrete and convex geometry

My interests in discrete and convex geometry mainly lie in the study of combinatorics and geometry of polytopes and polyhedra, including e.g., the enumeration of lattice points and subdivisions of polytopes. I am also interested in possible generalizations of Ehrhart theory to a “mixed” setting.

Short CV

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 2021: Diskrete Mathematik, Universität Osnabrück

Summer term 2021: Seminar Elemente der Mathematik, Universität Osnabrück

Winter term 2020/21: Elemente der Diskreten Mathematik, Universität Osnabrück

Winter term 2020/21: Seminar Topologische Kombinatorik und Geometrie, Universität Osnabrück

Winter term 2019/20: Kryptographie und Codierung, Universität Osnabrück

Winter term 2019/20: Lineare Algebra und Analytische Geometrie I, Universität Osnabrück

Summer term 2019: Probabilistische Kombinatorik, Universität Osnabrück

Summer term 2019: Diskrete Mathematik, Universität Osnabrück

Winter term 2018/19: Tropische Kombinatorik, Universität Osnabrück

Winter term 2018/19: Elemente der Diskreten Mathematik, Universität Osnabrück

Summer term 2018: Kombinatorische kommutative Algebra, Universität Osnabrück

Winter term 2017/18: Codierungstheorie und Kryptographie, Universität Osnabrück

Winter term 2017/18: Diskrete Geometrie, Universität Osnabrück

Summer term 2017: Mathematik für Anwender 2, Universität Osnabrück

Winter term 2016/17: Mathematik für Anwender 1, Universität Osnabrück

Summer term 2016: Diskrete Geometrie, Universität Osnabrück

PhD Students

Tarek Emmrich (joined with Stefan Kunis, since 10/2021)

Justus Bruckamp (joined with Markus Chimani, since 10/2021)

Alexander Nover (joined with Markus Chimani, since 10/2017)

Daniel Köhne (since 10/2019)

Jan-Marten Brunink (10/2016 – 2020)

Lorenzo Venturello (10/2016 – 09/2019)

Publications

M. Chimani, M. Juhnke-Kubitzke and A. Nover
On the Dominant of the Multicut Polytope.
2021 [ 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.
2021 [ 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.
Accepted by Women in Commutative Algebra Volume, Springer, 2020 [ 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 45th IEEE LCN Symposium on Emerging Topics in Networking LCN, 2020 [ http ]

C. Athanasiadis, J.-M. Brunink and M. Juhnke-Kubitzke
Combinatorics of antiprism triangulations.
Accepted by Discrete & Computational Geometry, 2020 [ 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, 2020 [ http ]

M. Chimani, M. Juhnke-Kubitzke, A. Nover and T. Römer
Cut-Polytopes of Minor-free Graphs.
Accepted by Bulletin Mathematique, 2019 [ 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

06/2022: 75 + 80 = 155 years of commutative algebra, Universität Osnabrück, organized with A. Conca, S. Iyengar and T. Römer. [ http ]

05/2022: Ehrhart polynomials: inequalities and extremal constructions, American Institute of Mathematics, San Jose. [ http ]

03/2022: Mini-Symposium on Lattice Polytopes, online. [ http ]

03/2022: Combinatorial Coworkspace – a session in algebraic and geometric combinatorics, Haus Bergkranz, Riezlern, Österreich, organized with T. Kahle, R. Sanyal and C. Stump. [ http ]

09/2021: Lecture Series on combinatorics of symmetric edge polytopes, 86th Séminaire Lotharingien de Combinatoire, Bad Boll.

06/2021: On gamma-vectors of symmetric edge polytopes, Discrete geometry seminar, TU Berlin, online.

04/2021: On the bond polytope, (Polytop)ics: Recent advances on polytopes, MPI Leipzig, online. [ http ]

04/2021: The antiprism triangulation, Fellowship of the Ring Seminar, MSRI, online. [ http ]

Talks and Presentations

09/2019: Graded Betti numbers of balanced simplicial complexes, Algebraic Combinatorics in Genova, Genova

07/2019: Graded Betti numbers of balanced simplicial complexes, Algebra meets combinatorics in Neuchatel, Neuchatel

05/2019: Balanced shellings and moves on balanced manifolds, Mathematisches Kollquium, Oldenburg

04/2019: Balanced shellings and moves on balanced manifolds, Workshop on Convexity, Szeged, Hungary

02/2019: Balanced manifolds or how to color a donut, BMS Student Conference

02/2019: Face Numbers of (balanced) manifolds, Workshop on singularities and homological aspects of commutative algebra, Oberwolfach

12/2018: How to decorate a Christmas tree, Weihnachtskolloquium Bochum

10/2018: Asymptotic syzygies of Stanley-Reisner rings of iterated subdivisions, Oberwolfach

08/2018: Squeezed complexes, National School on Algebra, Combinatorial structures in algebra and geometry, Constanta, Romania

06/2018: Betti numbers of balanced complexes, New Trends in Syzygies, Banff, Canada

05/2018: Moves on manifolds, Felix Klein Kolloquium, Universität Leipzig

04/2018: Balanced shellings on manifolds, Algebra seminar, University of Kentucky, Lexington, USA

03/2018: Balanced shellings on manifolds, Einstein Workshop Discrete Geometry and Topology, FU Berlin

09/2017: Lefschetz properties for balanced 3-polytopes, AMS Sectional Meeting, University of North Texas, Denton, USA

09/2017: f-vectors of simplicial complexes and polytopes, part II: methods, Introductory Workshop: Geometric and Topological Combinatorics, MSRI, Berkeley, USA

07/2017: Lower bound theorems for balanced manifolds, Workshop on Lefschetz Properties in Algebra, Geometry and Combinatorics, Mittag-Leffler Institute, Stockholm, Sweden

06/2017: Face numbers of balanced 3-polytopes, Tagung der Deutschen Sektion der European Women in Mathematics, Bielefeld

05/2017: Face numbers of (balanced) simplicial polytopes and manifolds, Konstanz Women in Mathematics, Konstanz

02/2017: h-Vectors of Broken Circuit Complexes, Algebra Seminar, University of Kentucky, USA

02/2017: Face Enumeration for (balanced) Manifolds, PEAK 2017, Workshop on Perspectives and Emerging Topics in Algebra and Konvexity, Riezlern, Austria

11/2016: Lefschetz properties for balanced 3-polytopes, Topology and Geometry in a Discrete Setting, ICERM, Brown University, Providence, USA

08/2016: Lefschetz properties for balanced 3-polytopes, The 24th National School on Algebra – EMS Summer School on Multigraded Algebra and Applications, Moieciu, Romania

07/2016: Intersections of Amoebas, 7th European Congress of Mathematics, Berlin

04/2016: Asymptotic syzygies of Stanley-Reisner rings of subdivisions, Free Resolutions, Representations, and Asymptotic Algebra, Banff, Canada

03/2016: An introduction to Mixed Ehrhart Theory, DMV/GAMM-Jahrestagung 2016, Braunschweig

11/2015: Antrittsvorlesung „Wie vielseitig sind Polytope?“, Osnabrück

10/2015: Gap vectors of real projective varieties, Combinatorial and Experimental Methods in Commutative Algebra and Related Fields, Osnabrück

09/2015: The generalized Balanced Lower Bound Conjecture, Workshop in Discrete Geometry, Moscow, Russia

08/2015: Gap vectors of real projective varieties, SIAM Conference on Applied Algebraic Geometry, Daejeon, South Korea

06/2015: The generalized Balanced Lower Bound Conjecture, Joint meeting of the AMS, EMS and SPM, Porto

06/2015: Algebraic properties of ideals of poset homomorphisms, Workshop on Minimal free resolutions, Betti numbers, and combinatorics, Edinburgh, UK

05/2015: Gap vectors of real projective varieties, Workshop on NonLinear Algebra, Berlin

03/2015: The generalized Balanced Lower Bound Conjecture, Workshop on Lefschetz properties, Georg-August-Universität Göttingen

10/2014: Lecture series on “Face enumeration of (subdivisions) of simplicial complexes“, summer school DFG GK1916 Kombinatorische Strukturen in der Geometrie, Universität Osnabrück

09/2014: Betti numbers of subdivision operations, MOCCA – Meeting on Combinatorial Commutative Algebra, Levico Terme, Italy

02/2014: Betti numbers of subdivision operations for simplicial complexes, seminar talk. Universität des Saarlandes, Saarbrücken

09/2013: Dimensional differences between the cone of nonnegative polynomials and sums of squares, CoMeTA – Combinatorial Methods in Topology in Algebra, Cortona, Italy

07/2013: Betti numbers of subdivision operations, Miniworkshop Discrete Mathematics, Goethe-Universität Frankfurt

11/2012: A brief introduction to classical and mixed Ehrhart theory, Kolloquium Mathematische Informatik, Goethe-Universität Frankfurt

09/2012: Lefschetz properties of Artinian algebras and Hilbert series, Commutative Algebra School, Mangalia, Rumania

03/2012: Veronese algebras, their h- and g-vectors, Lefschetz properties and connections to edgewise subdivisions, Arbeitsgemeinschaft Diskrete Mathematik, Universität Wien und TU Wien

11/2011: h- und g-Vektoren von Veronese-Algebren sowie Lefschetz-Eigenschaften, AG & Oberseminar Diskrete Mathematik, Goethe-Universität Frankfurt

11/2011: New poset fiber theorems and applications, Workshop on Algebraic Topology and Combinatorics, Buenos Aires, Argentina

10/2011: Veronese algebras, their Hilbert series and Lefschetz properties, International school on Commutative Algebra and Algebraic Geometry, Messina, Italy

06/2011: Doubly homotopy Cohen-Macaulayness for the poset of injective words, and the classical NC-partition lattice (poster), Conference on Formal Power Series and Algebraic Combinatorics, Reykjavík, Iceland

06/2011: Partition and composition matrices: two matrix analogues of set partitions (poster), Conference on Formal Power Series and Algebraic Combinatorics, Reykjavík, Iceland

03/2011: Poset Fiber Theorems and Applications, 66th Séminaire Lotharingien de Combinatoire, Ellwangen

01/2011: The multiplicity conjecture for barycentric subdivisions of simplicial complexes, “Geometry and Analysis on Groups” Research Seminar at Universität Wien

12/2010: A new poset fiber theorem and some applications, Aurora Borealis Conference, Abisko, Sweden

07/2010: Triangulations, the associahedron and gamma-vectors for planar lattices, University of Miami

06/2010: Triangulations, the associahedron and gamma-vectors for planar lattices, Arbeitsgemeinschaft Diskrete Mathematik at TU Wien and Universität Wien

05/2010: NBC bases for broken circuit complexes of matroids, 10th Nordic Combinatorial Conference, Reykjavík

11/2009: The Lefschetz property for barycentric subdivisions of simplicial complexes, Combinatorics Seminar at KTH, Stockholm

09/2009: The relation between the exterior shifting and the exterior depth of a simplicial complex, Biannual Meeting of the Icelandic Mathematical Society, Leirubakki, Iceland