# apl. Prof. Dr. Jörg Schürmann, Mathematisches Institut

Member of CRC 1442 Geometry: Deformations and RigidityMember of Mathematics Münster

Investigator in Mathematics Münster

Member of Mathematics Münster

Investigator in Mathematics Münster

Sprechstunde Mo: 14:00-15:00 Uhr und nach Vereinbarung.

Private Homepage | https://www.uni-muenster.de/Arithm/schuermann/index.html |

Project membershipMathematics Münster | A: Arithmetic and GroupsC: Models and ApproximationsA1: Arithmetic, geometry and representations C4: Geometry-based modelling, approximation, and reduction |

Current Publications | • Aluffi, Paolo; Mihalcea, Leonardo; Schürmann, Jörg; Su, Changjian
Motivic Chern classes of Schubert cells, Hecke algebras, and applications to Casselman's problem. Annales Scientifiques de l'École Normale Supérieure Vol. 57 (1), 2024 online• Schürmann, Jörg; Wulkenhaar, Raimar An algebraic approach to a quartic analogue of the Kontsevich model. Mathematical Proceedings Vol. 174 (3), 2023 online• Aluffi, Paolo; Mihalcea, Leonardo; Schürmann, Jörg; Su, Changjian Shadows of characteristic cycles, Verma modules, and positivity of Chern–Schwartz–MacPherson classes of Schubert cells. Duke Mathematical Journal Vol. 172 (17), 2023 online• Aluffi, P., Mihalcea, L., Schürmann, J., Su C. Positivity of Segre–MacPherson Classes. Facets of Algebraic Geometry: A Collection in Honor of William Fulton's 80th Birthday, 2022, pp 1-28 online• Maxim, Laurentiu; Schürmann, Jörg Constructible Sheaf Complexes in Complex Geometry and Applications. Handbook of Geometry and Topology of Singularities IIIHandbook of Geometry and Topology of Singularities, 2022 online• Maxim Laurentiu, Saito Morihiko, Schürmann Jörg Spectral Hirzebruch–Milnor classes of singular hypersurfaces. Mathematische Annalen Vol. 377 (1-2), 2020 online• Maxim Laurentiu, Saito Morihiko, Schürmann Jörg Thom–Sebastiani Theorems for Filtered D-Modules and for Multiplier Ideals. International Mathematics Research Notices Vol. 2020 (1), 2020 online• Maxim Laurentiu, Schürmann Jörg Plethysm and cohomology representations of external and symmetric products. Advances in Mathematics Vol. 375, 2020, pp 107373 online• Schürmann Jörg, Woolf Jon Witt groups of abelian categories and perverse sheaves. Annals of K-theory Vol. 2019 (4), 2019 online |

Current Projects | • CRC 1442: Geometry: Deformation and Rigidity - D03: Integrability We investigate blobbed topological recursion for the general Kontsevich matrix model, as well as the behaviour of Baker–Akhiezer spinor kernels for deformations of the spectral curve and for the quartic Kontsevich model. We study relations between spin structures and square roots of Strebel differentials, respectively between topological recursion and free probability. We examine factorisation super-line bundles on infinite-dimensional Grassmannians and motivic characteristic classes for intersection cohomology sheaves of Schubert varieties. • EXC 2044 - A1: Arithmetic, geometry and representations The Langlands programme relates representations of (the adele valued points of) reductive groups G over Q - so-called automorphic representations - with certain representations of the absolute Galois group of Q. This programme includes the study of these objects over general global fields (finite extension of Q or Fp (t)) and local fields as well. In its local form the classical programme onlyconsidered l-adic Galois representations of p-adic fields for unequal primes l neq p. In order to allow for a p-adic variation of the objects, it is absolutely crucial to extend it to the case l = p. In the global situation, the automorphic representations in question can often be realised in (or studied via) the cohomology of a tower of Shimura varieties (or related moduli spaces) attached to the group G. We will focus on the following directions within this programme: The p-adic and mod p Langlands programme asks for an extension of such a correspondence involving certain continuous representations with p-adic respectively mod p coefficients. Broadening the perspective to p-adic automorphic forms should, for example, enable us to capture all Galois representations, not just those having a particular Hodge theoretic behaviour at primes dividing p. This extended programme requires the introduction of derived categories. We will study differential graded Hecke algebras and their derived categories on the reductive group side. On the Galois side, we hope to use derived versions of the moduli spaces of p-adic Galois representations introduced by Emerton and Gee. The geometric Langlands programme is a categorification of the Langlands programme. We plan to unify the different approaches using motivic methods. In another direction, we study the geometry and arithmetic of moduli stacks of global G-shtukas over function fields. Their cohomology has been the crucial tool to establish large parts of the local and global Langlands programme over function fields. Variants of G-shtukas are also used to construct and investigate families of p-adic Galois representations.Cohomology theories are a universal tool pervading large parts of algebraic and arithmetic geometry. We will develop and study cohomology theories, especially in mixed characteristic, that generalise and unify étale cohomology, crystalline cohomology and de Rham cohomology as well as Hochschild cohomology in the non-commutative setting. Developing (topological) cyclic homology in new contexts is an important aim. A main goal is to construct a cohomology theory that can serve the same purposes for arithmetic schemes as the l-adic or crystalline cohomology with their Frobenius actions for varieties over finite fields. Ideas from algebraic geometry, algebraic topology, operator algebras and analysis blend in these investigations. online • EXC 2044 - C4: Geometry-based modelling, approximation, and reduction In mathematical modelling and its application to the sciences, the notion of geometry enters in multiple related but different flavours: the geometry of the underlying space (in which e.g. data may be given), the geometry of patterns (as observed in experiments or solutions of corresponding mathematical models), or the geometry of domains (on which PDEs and their approximations act). We will develop analytical and numerical tools to understand, utilise and control geometry, also touching upon dynamically changing geometries and structural connections between different mathematical concepts, such as PDE solution manifolds, analysis of pattern formation, and geometry. online |

E-Mail | jschuerm at uni-muenster dot de |

Phone | +49 251 83-32734 |

FAX | +49 251 83-32774 |

Room | 514 |

Secretary | Sekretariat Dierkes Frau Gabi Dierkes Telefon +49 251 83-33730 Zimmer 414 |

Address | apl. Prof. Dr. Jörg Schürmann Mathematisches Institut Fachbereich Mathematik und Informatik der Universität Münster Einsteinstrasse 62 48149 Münster Deutschland |

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