• Ehrhart Theory
  • Lattice Polytopes
  • Spherical Varieties
  • Representation Theory

Johannes Hofscheier

I am a Nottingham Research Fellow at The University of Nottingham, UK, my academic mentor is Alexander Kasprzyk. Before I was a postdoctoral fellow at McMaster University in Hamilton, Canada, where my postdoctoral mentors were Megumi Harada and Adam Van Tuyl. Prior to that I was at Otto-von-Guericke-Universität Magdeburg in the Discrete, Convex and Toric Geometry research group of Benjamin Nill. I did my PhD at Eberhard Karls Universität Tübingen under the guidance of Victor Batyrev.

Research Interests

My research interests include spherical geometry, Ehrhart theory and lattice polytopes. These theories give rise to a rich interplay of algebraic geometry, representation theory, number theory, combinatorics, discrete and convex geometry, and the geometry of numbers. In particular, I am interested in the classification of Fano varieties, mirror symmetry, the Mukai conjecture, spherical varieties, h*-polynomials, combinatorics of lattice polytopes, Cayley polytopes and moduli spaces of (lattice) polytopes.

My preprints are on the arXiv.


  1. Cohomology rings of toric bundles and the ring of conditionspreprint

    In collaboration with: Askold Khovanskii, Leonid Monin

  2. Generalized flatness constants, spanning lattice polytopes, and the Gromov width preprint

    In collaboration with: Gennadiy Averkov, Benjamin Nill

  3. Splittings of Toric Ideals preprint

    In collaboration with: Giuseppe Favacchio, Graham Keiper, Adam Van Tuyl

  4. The Ring of Conditions for Horospherical Homogeneous Spaces accepted

    in Proceedings of the Workshop Interactions with Lattice Polytopes, Magdeburg, Germany September 14 - 16, 2017

  5. Introduction to toric geometry with a view towards lattice polytopes published

    in Proceedings of the Summer Workshop on Lattice Polytopes, Osaka, Japan, 23 July – 10 August 2018, WORLD SCIENTIFIC (2019), pp. 1–37

  6. Betti numbers of toric ideals of graphs: A case study published

    In collaboration with: Federico Galetto, Graham Keiper, Craig Kohne, Miguel Eduardo, Uribe Paczka, Adam Van Tuyl

    J. Algebra Appl. 18 (2019), no. 12, 1950226, 14 pp.

  7. Containment Relations among Spherical Subgroups preprint

    Comments Welcome!

  8. Smooth centrally symmetric polytopes in dimension 3 are IDP published

    In collaboration with: Matthias Beck, Christian Haase, Akihiro Higashitani, Katharina Jochemko, Lukas Katthän, Mateusz Michałek

    Ann. Comb. 23 (2019), no. 2, 255–262

  9. Spanning Lattice Polytopes and the Uniform Position Principle preprint

    In collaboration with: Lukas Katthän, Benjamin Nill


  10. On Ehrhart polynomials of lattice triangles published

    In collaboration with: Benjamin Nill, Dennis Öberg

    Electron. J. Combin. 25 (2018), no. 1, Paper #P1.3

  11. Ehrhart Theory of Spanning Lattice Polytopes published

    In collaboration with: Lukas Katthän, Benjamin Nill

    Int. Math. Res. Not. IMRN 2018, no. 19, 5947–5973

  12. The generalized Mukai conjecture for symmetric varieties published

    In collaboration with: Giuliano Gagliardi

    Trans. Amer. Math. Soc. 369 (2017), 2615-2649

  13. Homogeneous spherical data of orbits in spherical embeddings published

    In collaboration with: Giuliano Gagliardi

    Transform. Groups 20 (2015), no. 1, 83-98

  14. Lattice polytopes, finite abelian subgroups in \(\mathrm{SL}(n,\mathbb{C})\) and coding theory preprint

    In collaboration with: Victor Batyrev

  15. Gorenstein spherical Fano varieties published

    In collaboration with: Giuliano Gagliardi

    Geom. Dedicata 178 (2015), no. 1, 111-133

  16. A generalization of a theorem of G. K. White preprint

    In collaboration with: Victor Batyrev


Upcoming Activities

  • Online Algebraic Geometry Seminar

    Weekly, typically on ThursdayNottingham "Algebraic Geometry Group"

  • Online Reading Group on Tropical Combinatorics and Geometry

    Weekly, Mon 13:30 (SE time)Nottingham "Algebraic Geometry Group"

  • Online Reading Group on Birational Geometry

    Weekly, Tue 15:00 (UK time)Nottingham "Algebraic Geometry Group"

  • Ehrhart polynomials: inequalities and extremal constructions

    May 9-13, 2022American Institute of Mathematics, USA

Selected Past Activities

  • McKay correspondence, mutation and related topics

    July 10 - August 14, 2020Online, hosted by Kavli IPMU, Japan

  • Online Reading Group on the Geometry of Numbers

    March 31 - June 9, 2020, WeeklyNottingham "Algebraic Geometry Group"

  • Combinatorial Coworkspace

    March 8-15, 2020Haus Bergkranz, Kleinwalsertal, Austria

  • Research visit and speaker at Algebra and Geometry Seminar

    February 18-23, 2020University of Bristol, UK

  • Research visit and speaker at Discrete Geometry Seminar

    January 14-18, 2020Freie Universität Berlin, Germany

  • Together with A. Kasprzyk, B. Nill, and B. Shapiro, I co-organised the conference "Lucia Geometrica - a celebration of geometry"

    December 9–13, 2019Department of Mathematics, Stockholm University

  • Speaker at Einstein Workshop on Polytopes and Algebraic Geometry

    December 2-4, 2019Freie Universität Berlin

  • Speaker at Workshop on Discrete Geometry with a View on Symplectic and Tropical Geometry

    September 23–27, 2019University of Cologne

  • Speaker at Lattice polytopes, with a view towards Geometry and Applications

    September 18–20, 2019ICMS, University of Edinburgh

  • Together with A. Higashitani and A. Kasprzyk I organised a Workshop titled "Mutations: Mirror Symmetry, Deformations, and Combinatorics"

    August 11 - 16 2019Banff International Research Station, Banff, Canada

More Past Activities

  • Speaker at Special Session on "Algebraic Geometry" of 2018 CMS Winter Meeting

    December 7-10, 2018Vancouver, Canada

  • Research visit, University of Nottingham

    October 7-12, 2018Nottingham, United Kingdom

  • Teaching course at summer school Summer Workshop on Lattice Polytopes

    July 23 - August 10, 2018Osaka University, Osaka, Japan

  • Combinatorial Algebraic Geometry Retrospective Workshop

    June 18 - 22, 2018The Fields Institute, Toronto, Canada

  • Teaching course at Graduate Summer School in Algebraic Group Actions

    June 11 - 15, 2018McMaster University, Hamilton, Canada

  • Speaker at the Algebraic Geometry Seminar of the Ohio State University

    March 20, 2018Columbus, USA

  • Speaker at Special Session on "Convex Bodies in Algebraic Geometry and Representation Theory" of AMS Spring Central Sectional Meeting

    March 16-18, 2018Ohio State University, Columbus, USA.

  • Speaker at Special Session on "Applications of Combinatorial Topology in Commutative Algebra" of 2017 CMS Winter Meeting

    December 8-11, 2017Waterloo, Canada

  • Speaker at the Algebra, Combinatorics, and Geometry Seminar of University of Pittsburgh

    November 16, 2017Pittsburgh, USA

  • Speaker at Oberwolfach Mini-Workshop "Lattice Polytopes: Methods, Advances, Applications"

    September 17-23, 2017Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach, Germany

  • Together with C. Borger, A. Kasprzyk and B. Nill I organized a Workshop titled "Interactions with Lattice Polytopes"

    September 14-16, 2017Otto-von-Guericke-Universität Magdeburg, Magdeburg, Germany

  • Speaker at the minisymposium "Core Algorithms in Algebra and Geometry", SIAM Conference on Applied Algebraic Geometry

    July 31 - August 4, 2017Atlanta, USA

  • Speaker at Forschungsseminar Discrete Mathematics/Geometry

    July 19, 2017TU Berlin, Berlin, Germany

  • Speaker at Emmy-Noether-Seminar

    June 2, 2017Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany

  • Speaker at Einstein Workshop on Lattice Polytopes

    December 12-15, 2016Harnack-Haus of the Max Planck Institute, Berlin, Germany

  • Speaker at International Conference on Spherical Varieties

    November 7-11, 2016Tsinghua Sanya International Mathematics Forum of Yau Mathematical Sciences Center, Sanya, China

  • Speaker at conference on Computational Commutative Algebra and Convex Polytopes

    August 2016RIMS, Kyoto University, Kyoto, Japan

  • Speaker at the conference Géométrie Algébrique en Liberté

    June 13-17, 2016Nesin Mathematics Village, Şirince, Turkey

  • Speaker at Mini-Symposium "Combinatorial algebraic geometry" of 7ECM Berlin

    July 19-24, 2016Berlin Germany

  • Speaker at Reinhold-Baer-Kolloquium

    May 21, 2016Otto-von-Guericke-Universität Magdeburg, Magdeburg, Germany

  • Speaker at Seminar on Fano varieties

    February 2, 2016Johannes Gutenberg-Universität Mainz, Mainz, Germany


The University of Nottingham

  • Autumn 2020 MATH3022/4059

    Rings and Modules (MATH3022)/Further topics in Rings and Modules (MATH4059): modules, Noetherian modules and rings; unique factorization domains and principal ideal domains; structure of modules over a a principal ideal domain; tensor products and multilinear maps; basic properties of free modules, flat modules; injective modules, projective modules; localization, completion, local rings, regular rings.

McMaster University

  • Winter 2019 Math 3U03

    Combinatorics: Inversion formulae, systems of distinct representatives, block designs and other configurations; other topics.

  • Fall 2018 MATH 1LS3

    Calculus For Life Sciences I: Topics from differential and integral calculus, differential equations, discrete-time dynamical systems, chosen for their relevance to the life sciences.

  • Winter 2017/18 Math 1ZC3-1B03

    Introduction to linear algebra for engineers. We cover linear independence, dimension, determinants, eigenvalues, diagonalisation, and complex numbers.

  • Fall 2017 MATH 1A03-1ZA3

    Calculus for Science I: For students in science: geared towards applications, with attention to underlying concepts. Functions: limits, continuity, derivatives, optimization, curve sketching. Antiderivative, definite integral, techniques of integration.

Otto-von-Guericke-Universität Magdeburg

  • Summer 2017 Mathematical Methods 2 (with Prof. Dr. C. Stump)
  • Winter 2016 Mathematical Methods 1 (with Prof. Dr. W. Meidl)
  • Winter 2016 Computeralgebra (with Jun.-Prof. Dr. T. Kahle)
  • Summer 2016 Mathematical Methods 2 (with Prof. Dr. G. Kyureghyan)
  • Winter 2015 Mathematical Foundations (with Prof. Dr. B. Nill)

Eberhard Karls Universität Tübingen: Teaching assistant for

  • Summer 2015 Lineare Algebra 2 (PD Dr. I. Radloff)
  • Winter 2014 Block-Seminar: Lie-Algebren (with Prof. Dr. V. Batyrev)
  • Summer 2014 Algebraische Geometrie (with Prof. Dr. V. Batyrev)
  • Winter 2013 Kommutative Algebra (with Prof. Dr. V. Batyrev)
  • Summer 2013 Algebra (with Prof. Dr. V. Batyrev)
  • Winter 2012 Block-Proseminar: Algebra (with Prof. Dr. V. Batyrev)3
  • Summer 2012 Lineare Algebra 2 (with Prof. Dr. V. Batyrev)
  • Winter 2011 Lineare Algebra 1 (with Prof. Dr. V. Batyrev)
  • Summer 2011 Algebra (with Prof. Dr. V. Batyrev)
  • Winter 2010 Algebraische Geometrie I (with Prof. Dr. J. Hausen)
  • Summer 2010 Algebra II (with Prof. Dr. W. Gubler)
  • Winter 2009 Algebraische Geometrie (with Prof. Dr. V. Batyrev)
  • Summer 2009 Kommutative Algebra (with Prof. Dr. V. Batyrev)
  • Summer 2008 Lineare Algebra II (with Prof. Dr. V. Batyrev)
  • Winter 2007 Lineare Algebra I (with Prof. Dr. V. Batyrev)
  • Summer 2007 Algebra II (with Prof. Dr. V. Batyrev)
  • Winter 2006 Algebra I (with Prof. Dr. V. Batyrev)

Short CV

10/2019 - current
Nottingham Research Fellow at The University of Nottingham
09/2017 - 08/2019
Postdoctoral fellow at McMaster University
10/2015 - 08/2017
Postdoctoral research fellow at Otto-von-Guericke-Universität Magdeburg
PhD in Mathematics at Eberhard Karls Universität Tübingen
Diploma in Mathematics at Eberhard Karls Universität Tübingen
Bachelor in Mathematics at Università degli Studi di Trento