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

Johannes Hofscheier


McMaster University 1280 Main Street West Hamilton Hall 218 Hamilton, ON L8S 4K1 Canada

I am a postdoctoral fellow at McMaster University in Hamilton, Canada, my postdoctoral mentors are Megumi Harada and Adam Van Tuyl. Before 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.



Upcoming Activities

  • Research visit, University of Nottingham

    October 7-12, 2018Nottingham, United Kingdom

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

    December 7-10, 2018Vancouver, Canada

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

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

Selected Past Activities

  • 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.

More Past Activities

  • 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


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

09/2017 - current
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