**Speaker:**

Stefan Hollands

**Coordinator:**

Jörg Lehnert

**Address:**

Inselstraße 22

04103 Leipzig

Germany

**Contact:**

+49(0)341-9959-641

+49(0)341-9959-658* ***IMPRS**

# Geometry

## Scientific Members working in this area

- Daniele Agostini (MPI for Mathematics in the Sciences)
- Paul Breiding (MPI for Mathematics in the Sciences)
- Noémie Combe (MPI for Mathematics in the Sciences)
- Tobias Finis (Mathematical Institute of Leipzig University)
- Jürgen Jost (MPI for Mathematics in the Sciences)
- Michael Joswig (MPI for Mathematics in the Sciences)
- Raffaella Mulas (MPI for Mathematics in the Sciences)
- Hans-Bert Rademacher (Mathematical Institute of Leipzig University)
- Matthias Schwarz (Mathematical Institute of Leipzig University)
- Rainer Sinn (Mathematical Institute of Leipzig University)
- Bernd Sturmfels (MPI for Mathematics in the Sciences)
- André Uschmajew (MPI for Mathematics in the Sciences)

## Description of Research

We investigate the topology of manifolds and simplicial complexes and the geometry of locally symmetric spaces and Riemannian, Finslerian, algebraic and symplectic manifolds, together with extensions to general metric spaces. Abstract notions of curvature also link this area with stochastic and discrete structures. The geometry of locally symmetric spaces is connected with arithmetic problems. Geometrically defined variational problems, like harmonic maps, pseudoholomorphic curves or minimal submanifolds, require powerful tools from analysis. Some of these variational problems, in particular those involving Dirac operators, are inspired by quantum field and string theory.

## Current PhD Students

Surname, first name | Phone | Office | Homepage | |

Adams, Zachary | Zachary.Adams | 549 | B3 08 | |

Barth, Lukas | Lukas.Barth | 572 | B3 08 | group |

Eisenmann, Henrik | Henrik.Eisenmann | 769 | F3 07 | group |

Fevola, Claudia | Claudia.Fevola | 763 | F3 06 | group, personal |

Freund, Valerie | Valerie.Freund | 833 | G2 02 | |

Jiang, Shuhan | Shuhan.Jiang | 571 | B3 08 | |

Meroni, Chiara | Chiara.Meroni | 761 | F3 05 | external |

Shehu, Elima | Elima.Shehu | 756 | F3 04 | external |

Stegemeyer, Maximilian | Maximilian.Stegemeyer | 576 | B3 09 | |

Teich, Marie | Marie.Teich | 539 | A3 10 |

## Alumni

Name | Advisor | Graduation | Topic |

Renan Assimos Martins | Jürgen Jost | 2019 | The geometry of maximum principles and a Bernstein theorem in codimension 2 (see more) |

David Bauer | Matthias Schwarz | 2013 | Towards discretization by piecewise pseudoholomorphic curves (see more) |

Philipp Benner | Jürgen Jost | 2016 | Combining prior information for the prediction of transcription factor binding sites (see more) |

Guy Buss | Jürgen Jost | 2009 | On the construction and the behaviour of automorphic forms on completions of Teichmüller spaces and higher Bers maps |

Brian Clarke | Jürgen Jost | 2009 | The completion of the manifold of Riemannian metrics with respect to its L2 metric (see more) |

Masud Ehsani | Jürgen Jost | 2021 | Self-organized criticality in neural networks by inhibitory and excitatory synaptic plasticity |

Marzieh Eidi | Jürgen Jost | 2022 | Topological and geometric methods with a view towards data analysis |

Paul Görlach | Bernd Sturmfels, Mateusz Michalek | 2020 | Projective geometry, toric algebra and tropical computations (see more) |

Jiao Gu | Jürgen Jost, Peter Stadler | 2014 | The spectral distance based on the normalized Laplacian and applications to large networks |

Vishal Gupta | Tobias Finis | 2018 | Limit multiplicity problem (see more) |

Julian Hofrichter | Jürgen Jost | 2014 | On the diffusion approximation of Wright-Fisher models with several Alleles and Loci and its geometry (see more) |

Danijela Horak | Jürgen Jost | 2012 | Combinatorial Laplace operators on simplicial complexes |

Leonhard Horstmeyer | Jürgen Jost | 2017 | Towards a geometric theory of exact lumpability (see more) |

Nidhi Kaihnsa | Bernd Sturmfels | 2019 | Algebraic methods for dynamical systems and optimisation (see more) |

Martin Kell | Jürgen Jost | 2014 | On curvature conditions using Wasserstein spaces : with an application to the q-Laplace heat equation (see more) |

Enno Keßler | Jürgen Jost | 2017 | The super conformal action functional on super Riemann surfaces (see more) |

Ilona Kosiuk | Jürgen Jost | 2012 | Relaxation oscillations in slow-fast systems beyond the standard form (see more) |

Alexei Lebedev | Jürgen Jost | 2008 | Simple modular Lie superalgebras |

Shiping Liu | Jürgen Jost | 2012 | Synthetic notions of curvature and applications in graph theory (see more) |

Yangjing Long | Jürgen Jost, Peter Stadler | 2014 | Graph relations and constrained homomorphism partial orders (see more) |

Arun Maiti | Hans-Bert Rademacher | 2017 | On the Goresky-Hingston product (see more) |

Orlando Marigliano | Bernd Sturmfels | 2020 | The algebraic statistics of sampling, likelihood, and regression (see more) |

Raffaella Mulas | Jürgen Jost | 2020 | Spectra of normalized Laplace operators for graphs and hypergraphs (see more) |

Wiktor Młynarski | Jürgen Jost | 2015 | Functional sensory representations of natural stimuli : the case of spatial hearing (see more) |

Niccolò Pederzani | Nadine Große | 2018 | On the spin cobordism invariance oft he homotopy type of the space $R^{inv}(M)$ (see more) |

Paolo Perrone | Jürgen Jost | 2018 | Categorical probability and stochastic dominance in metric spaces (see more) |

Stephan Poppe | Jürgen Jost | 2017 | Foundational aspects of coherent predictive and statistical inference for exchangeable categorical sequences |

Sharwin Rezagholi | Jürgen Jost | 2020 | Hyperspace-type monads on top and the entropy theory of cynamical systems |

Christoph Sachse | Jürgen Jost | 2007 | Global analytic approach to super Teichmüller spaces (see PDF) |

Murat Sağlam | Matthias Schwarz | 2017 | A search for finer topological information by holomorphic curves in symplectizations : the case of lens spaces and their unit cotangent bundles |

Camilo Eduardo Sarmiento Cortés | Jürgen Jost | 2014 | Concerning triangulations of products of simplices (see more) |

Mahsa Sayyary Namin | Bernd Sturmfels | 2021 | Real algebraic geometry of the sextic curves (see more) |

Matti Schneider | Matthias Schwarz | 2013 | The Leray-Serre spectral sequence in Morse homology on Hilbert manifolds and in Floer homology on cotangent bundles (see more) |

Tim Seynnaeve | Mateusz Michalek, Bernd Sturmfels | 2020 | Algebraic geometry for tensor networks, matrix multiplication, and flag matroids (see more) |

Gerardo Sosa Garciamarín | Jürgen Jost | 2017 | On symmetric transformations in metric measure geometry (see more) |

Linlin Sun | Jürgen Jost | 2015 | Dirac equations, Dirac-harmonic maps and their heat flows |

Tat Dat Tran | Jürgen Jost | 2012 | Information geometry and the Wright-Fisher model of mathematical population genetics (see more) |

José Javier Vasquez | Hans-Bert Rademacher | 2017 | Isospectral nearly Kähler manifolds (see more) |

Ying Wang | Jürgen Jost | 2010 | Branching processes : optimization, variational characterization, and continuous approximation (see more) |

Anatol Wegner | Jürgen Jost | 2015 | Subgraph covers : an information theoretic approach to motif analysis in networks (see more) |

Ruijun Wu | Jürgen Jost | 2017 | Analysis of a two-dimensional nonlinear sigma model with gravitino (see more) |

Marius Emar Yamakou | Jürgen Jost | 2018 | Weak-noise-induced phenomena in a slow-fast dynamical system |

Odette Sylvia Yaptieu Djeungue | Jürgen Jost | 2018 | Generalizations of discrete Morse theory (see more) |

Tinggui Zhang | Jürgen Jost | 2014 | Separability and local unitary equivalence of quantum states |

Miaomiao Zhu | Jürgen Jost | 2008 | Harmonic maps and Dirac-Harmonic maps from degenerating surfaces |