Juniorprof. Dr.

Martina Juhnke-Kubitzke

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 04/2015 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

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

Winter term 2016/17: Doktorandenseminar Algebraic Statistics, Universität Osnabrück

Winter term 2016/17: Oberseminar Algebra Universität Osnabrück

Summer term 2016: Diskrete Geometrie, Universität Osnabrück

Summer term 2016: Doktorandenseminar Algebraic Statistics, Universität Osnabrück

Summer term 2016: Oberseminar Algebra Universität Osnabrück

Winter term 2015/16: Elemente der Diskreten Mathematik, Universität Osnabrück

Summer term 2015: Algebraische Kombinatorik, Universität Osnabrück

Winter term 2014/15: Diskrete Geometrie, Goethe-Universität Frankfurt

Summer term 2014: Diskrete Mathematik, Goethe-Universität Frankfurt

Winter term 2013/2014: Proseminar Diskrete Mathematik, Goethe-Universität Frankfurt

Summer term 2013: Seminar Kombinatorik und Diskrete Mathematik, Goethe-Universität Frankfurt

Winter term 2012/13: Algebraische Kombinatorik und Anwendungen in der kommutativen Algebra, Goethe-Universität Frankfurt

Winter term 2011/12: Mathematik II für Lehramt Informatik, Universität Wien

Publications

M. Juhnke-Kubitzke, S. Murai, I. Novik and C. Sawaske
A generalized lower bound theorem for balanced manifolds.
In: Preprint, 2016 [ http ]

D. Cook II, M. Juhnke-Kubitzke, S. Murai and E. Nevo
Lefschetz properties of balanced 3-polytopes
In: Preprint, 2016 [ http ]

M. Juhnke-Kubitzke and Le Van Dinh
Flawlessness of h-vectors of broken circuit complexes.
In: Preprint, 2016 [ http ]

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

C. Haase, M. Juhnke-Kubitzke, R. Sanyal and T. Theobald
Mixed Ehrhart polynomials.
In: Preprint, 2015 [ http ]

M. Juhnke-Kubitzke, Lukas Katthän and S. Saeedi Madani
Algebraic properties of ideals of poset homomorphisms.
In: Journal of Algebraic Combinatorics, 2016 [ http ]

M. Juhnke-Kubitzke and S. Murai
Balanced generalized lower bound inequality for simplicial polytopes.
In: Preprint, 2015 [ http ]

A. Conca, M. Juhnke-Kubitzke and V. Welker
Asymptotic syzygies of Stanley-Reisner rings of iterated subdivisions.
In: Preprint, 2014 [ http ]

G. Blekherman, S. Iliman, M. Juhnke-Kubitzke and M. Velasco
Gap vectors of real projective varieties.
In: Advances in Mathematics, 2015, 458–472 [ 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, doi: 10.1093/imrn/rnu202, 2014 [ http ]

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

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

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

M. Kubitzke and S. Murai
Lefschetz properties and the Veronese construction.
In: Mathematical Research Letters 19 (5), 2012, 1–11 [ 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), 2012, 307–325 [ http ]

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

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

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

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

M. Kubitzke and A. Egilsson
A Generalization of nbc-Bases to Broken Circuit Complexes of Matroids.
In: Preprint, 2010 [ http ]

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

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

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

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

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

Recent and Upcoming Events

08/2015: SIAM Conference on Applied Algebraic Geometry, Daejeon, South Korea[ http ]

09/2015: Workshop in Discrete Geometry, MIPT, Moscow, Russia [ http ]

10/2015: Annual conference of the DFG priority project SPP 1489, Algorithmic & Experimental Methods, Osnabrück [ http ]

10/2015: Combinatorial and Experimental Methods in Commutative Algebra and Related Fields, Osnabrück [ http ]

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

11/2015: Algebraic and Stochastic Aspects in Graph Theory, Osnabrück [ http ]

03/2016: DMV/GAMM-Jahrestagung 2016, Braunschweig [ http ]

03/2016: Lefschetz Properties and Artinian Algebras, Banff, Canada [ http ]

04/2016: Free Resolutions, Representations, and Asymptotic Algebra, Banff, Canada [ http ]

06/2016: Homological and computational methods in commutative algebra, Cortona, Italy [ http ]

07/2016: 7th European Congress of Mathematics, Berlin [ http ]

08/2016: Conference on Combinatorial Structures in Geometry, Osnabrück [ http ]

08/2016: The 24th National School on Algebra – EMS Summer School on Multigraded Algebra and Applications, Moieciu, Romania [ http ]

11/2016: Topology and Geometry in a Discrete Setting, ICERM, Brown University, Providence, USA [ http ]

05/2017: Konstanz Women in Mathematics: Paths in Studies and Career [ http ]

07/2017: Workshop on Lefschetz Properties in Algebra, Geometry and Combinatorics, Mittag-Leffler Institue, Stockholm, Sweden [ http ]

Talks and Presentations

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