- Ehrhart Theory
- Lattice Polytopes
- Spherical Varieties
- Representation Theory
Johannes Hofscheier
Address
School of Mathematical
Sciences
The University of Nottingham
University Park
Nottingham, NG7 2RD
United Kingdom
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.
Articles
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Generalised Flatness Constants: A Framework Applied in Dimension \(2\) preprint
In collaboration with: Giulia Codenotti, Thomas Hall
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Polytopes and Machine Learning preprint
In collaboration with: Jiakang Bao, Yang-Hui He, Edward Hirst, Alexander Kasprzyk, Suvajit Majumder
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Hilbert Series, Machine Learning, and Applications to Physics accepted
In collaboration with: Jiakang Bao, Yang-Hui He, Edward Hirst, Alexander Kasprzyk, Suvajit Majumder
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Cohomology rings of toric bundles and the ring of conditionspreprint
In collaboration with: Askold Khovanskii, Leonid Monin
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Generalized flatness constants, spanning lattice polytopes, and the Gromov width accepted
In collaboration with: Gennadiy Averkov, Benjamin Nill
Manuscripta math. (2021). https://doi.org/10.1007/s00229-021-01363-x
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Splittings of Toric Ideals published
In collaboration with: Giuseppe Favacchio, Graham Keiper, Adam Van Tuyl
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The Ring of Conditions for Horospherical Homogeneous Spaces accepted
in Proceedings of the Workshop Interactions with Lattice Polytopes, Magdeburg, Germany September 14 - 16, 2017
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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
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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
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Containment Relations among Spherical Subgroups preprint
Comments Welcome!
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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
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Spanning Lattice Polytopes and the Uniform Position Principle preprint
In collaboration with: Lukas Katthän, Benjamin Nill
submitted
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On Ehrhart polynomials of lattice triangles published
In collaboration with: Benjamin Nill, Dennis Öberg
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Ehrhart Theory of Spanning Lattice Polytopes published
In collaboration with: Lukas Katthän, Benjamin Nill
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The generalized Mukai conjecture for symmetric varieties published
In collaboration with: Giuliano Gagliardi
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Homogeneous spherical data of orbits in spherical embeddings published
In collaboration with: Giuliano Gagliardi
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Lattice polytopes, finite abelian subgroups in \(\mathrm{SL}(n,\mathbb{C})\) and coding theory preprint
In collaboration with: Victor Batyrev
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Gorenstein spherical Fano varieties published
In collaboration with: Giuliano Gagliardi
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A generalization of a theorem of G. K. White published
In collaboration with: Victor Batyrev
Activities
Upcoming Activities
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Online Algebraic Geometry Seminar
Weekly, typically on ThursdayNottingham "Algebraic Geometry Group"
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Oberwolfach Workshop on "Toric Geometry"
27 March - 2 April 2022Oberwolfach Research Institute for Mathematics, Germany
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Together with D. Maclagan and G. G. Smith, I co-organise the LMS-Bath Workshop on "Combinatorial Algebraic Geometry"
1 - 5 August 2022University of Bath, UK
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Ehrhart polynomials: inequalities and extremal constructions
May 9-13, 2022American Institute of Mathematics, USA
Selected Past Activities
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Speaker at Oldenburg Mini-Workshop "Constructive Approaches to Varieties with Group Actions"
17 March 2022 Online conference
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Together with K. Jochemko, I co-organise the Mini-Symposium on Lattice Polytopes
3-4 March 2022Online conference
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Speaker at Western's Geometry and Combinatorics seminar
01 November 2021 University of Western Ontario, Canada
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Speaker at Workship "Newton-Okounkov bodies and Fanosearch"
5 - 8 October 2021 Levico Terme, Trentino, Italy
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DANGER: Data, Numbers, and Geometry
25-26 August 2021 University of Nottingham
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Together with D. Maclagan and G. G. Smith, I co-organised the LMS-Bath Summer school on "Combinatorial Algebraic Geometry"
26 July - 6 August 2021 University of Bath, UK
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(Polytop)ics: Recent advances on polytopes
06 - 09 April 2021 MPI MiS Leipzig, Germany
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Fano Varieties and Birational Geometry
23-26 February 2021 University of Nottingham
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Sanya Workshop on Algebraic Geometry and Machine Learning
26-29 January 2021 Tsinghua Sanya International Mathematics Forum, China
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Online Reading Group on Tropical Combinatorics and Geometry
24 August - 30 November 2020, MondaysNottingham "Algebraic Geometry Group"
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Online Reading Group on Birational Geometry
1 September - 24 November 2020, TuesdaysNottingham "Algebraic Geometry Group"
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McKay correspondence, mutation and related topics
July 10 - August 14, 2020Online, hosted by Kavli IPMU, Japan
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Online Reading Group on the Geometry of Numbers
31 March - 7 July 2020, TuesdaysNottingham "Algebraic Geometry Group"
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Combinatorial Coworkspace
March 8-15, 2020Haus Bergkranz, Kleinwalsertal, Austria
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Research visit and speaker at Algebra and Geometry Seminar
February 18-23, 2020University of Bristol, UK
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Research visit and speaker at Discrete Geometry Seminar
January 14-18, 2020Freie Universität Berlin, Germany
More Past Activities
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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
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Speaker at Einstein Workshop on Polytopes and Algebraic Geometry
December 2-4, 2019Freie Universität Berlin
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Speaker at Workshop on Discrete Geometry with a View on Symplectic and Tropical Geometry
September 23–27, 2019University of Cologne
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Speaker at Lattice polytopes, with a view towards Geometry and Applications
September 18–20, 2019ICMS, University of Edinburgh
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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
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Speaker at Special Session on "Algebraic Geometry" of 2018 CMS Winter Meeting
December 7-10, 2018Vancouver, Canada
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Research visit, University of Nottingham
October 7-12, 2018Nottingham, United Kingdom
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Teaching course at summer school Summer Workshop on Lattice Polytopes
July 23 - August 10, 2018Osaka University, Osaka, Japan
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Combinatorial Algebraic Geometry Retrospective Workshop
June 18 - 22, 2018The Fields Institute, Toronto, Canada
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Teaching course at Graduate Summer School in Algebraic Group Actions
June 11 - 15, 2018McMaster University, Hamilton, Canada
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Speaker at the Algebraic Geometry Seminar of the Ohio State University
March 20, 2018Columbus, USA
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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.
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Speaker at Special Session on "Applications of Combinatorial Topology in Commutative Algebra" of 2017 CMS Winter Meeting
December 8-11, 2017Waterloo, Canada
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Speaker at the Algebra, Combinatorics, and Geometry Seminar of University of Pittsburgh
November 16, 2017Pittsburgh, USA
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Speaker at Oberwolfach Mini-Workshop "Lattice Polytopes: Methods, Advances, Applications"
September 17-23, 2017Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach, Germany
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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
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Speaker at the minisymposium "Core Algorithms in Algebra and Geometry", SIAM Conference on Applied Algebraic Geometry
July 31 - August 4, 2017Atlanta, USA
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Speaker at Forschungsseminar Discrete Mathematics/Geometry
July 19, 2017TU Berlin, Berlin, Germany
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Speaker at Emmy-Noether-Seminar
June 2, 2017Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany
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Speaker at Einstein Workshop on Lattice Polytopes
December 12-15, 2016Harnack-Haus of the Max Planck Institute, Berlin, Germany
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Speaker at International Conference on Spherical Varieties
November 7-11, 2016Tsinghua Sanya International Mathematics Forum of Yau Mathematical Sciences Center, Sanya, China
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Speaker at conference on Computational Commutative Algebra and Convex Polytopes
August 2016RIMS, Kyoto University, Kyoto, Japan
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Speaker at the conference Géométrie Algébrique en Liberté
June 13-17, 2016Nesin Mathematics Village, Şirince, Turkey
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Speaker at Mini-Symposium "Combinatorial algebraic geometry" of 7ECM Berlin
July 19-24, 2016Berlin Germany
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Speaker at Reinhold-Baer-Kolloquium
May 21, 2016Otto-von-Guericke-Universität Magdeburg, Magdeburg, Germany
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Speaker at Seminar on Fano varieties
February 2, 2016Johannes Gutenberg-Universität Mainz, Mainz, Germany
Teaching
PhD Students
- Iqra Khan, 2022-present (joint supervision with A. Kasprzyk)
- Girtrude Hamm, 2020-present (joint supervision with A. Kasprzyk)
- Thomas Hall, 2019-present (joint supervision with A. Kasprzyk)
Postdoc students
- Tim Grange, 2021-present
The University of Nottingham
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Autumn 2021
MATH3022/4059
Rings and Modules (MATH3022)/Further Topics in Rings and Modules (MATH4059): rings, ideals, and fields; Noetherian modules and rings; unique factorisation domains and principal ideal domains; Gröbner bases; elimination and extension theorems.
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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
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Winter 2019
Math 3U03
Combinatorics: Inversion formulae, systems of distinct representatives, block designs and other configurations; other topics.
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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.
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Winter 2017/18
Math 1ZC3-1B03
Introduction to linear algebra for engineers. We cover linear independence, dimension, determinants, eigenvalues, diagonalisation, and complex numbers.
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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
11/2015
PhD in Mathematics at Eberhard Karls Universität Tübingen
09/2010
Diploma in Mathematics at Eberhard Karls Universität Tübingen
09/2006
Bachelor in Mathematics at Università degli Studi di Trento