| Private Homepage | https://www.uni-muenster.de/Arithm/hartl/index.html |
| Research Interests | Arithmetic algebraic geometry Arithmetic of function fields Algebraic Number Theory Structur theory of Shimura varieties and their function field analogs p-adic Hodge theory Model theory of valued fields |
| Topics in Mathematics Münster | T1: K-Groups and cohomology T2: Moduli spaces in arithmetic and geometry T4: Groups and actions |
| Current Publications | • Hartl, Urs; Viehmann, Eva The generic fiber of moduli spaces of bounded local G-shtukas. Journal of the Institute of Mathematics of Jussieu Vol. 22 (2), 2023, pp 1-80 online • E. Arasteh Rad, U. Hartl Category of C-Motives over Finite Fields. Journal of Number Theory Vol. 232, 2022, pp 283-316 online • Hartl, Urs; Singh, Rajineesh Kumar A short review on local shtukas and divisible local Anderson modules. Perfectoid SpacesInfosys Science Foundation Series in Mathematical Sciences, 2022 online • Arasteh Rad Esmail, Hartl Urs Uniformizing the Moduli Stacks of Global G-Shtukas. International Mathematics Research Notices Vol. 21, 2021, pp 16121-16192 online • U. Hartl, R. Singh Periods of Drinfeld modules and local shtukas with complex multiplication - Errata. Journal of the Institute of Mathematics of Jussieu Vol. 2021, 2021, pp 1-5 online • Hartl Urs, Kim Wansu Local Shtukas, Hodge-Pink Structures and Galois Representations. t-motives: Hodge structures, transcendence and other motivic aspects, 2020, pp 183-260 online • Hartl Urs, Hellmann Eugen The universal familly of semi-stable p-adic Galois representations. Algebra and Number Theory Vol. 14, 2020, pp 1055-1121 online • Hartl Urs, Singh Rajneesh Kumar Periods of Drinfeld modules and local shtukas with complex multiplication . Journal of the Institute of Mathematics of Jussieu Vol. 19, 2020, pp 175-208 online • Hartl Urs, Juschka Ann-Kristin Pink's Theory of Hodge Structures and the Hodge Conjecture over Function Fields. in t-motives: Hodge structures, transcendence and other motivic aspects, 2020, pp 31-182 online |
| Current Projects | • EXC 2044 - T01: K-Groups and cohomology K-groups and cohomology groups are important invariants in different areas of mathematics, from arithmetic geometry to geometric topology to operator algebras. The idea is to associate algebraic invariants to geometric objects, for example to schemes or stacks, C∗-algebras, stable ∞-categories or topological spaces. Originating as tools to differentiate topological spaces, these groups have since been generalized to address complex questions in different areas. online • EXC 2044 - T02: Moduli spaces in arithmetic and geometry The term “moduli space” was coined by Riemann for the space Mg parametrizing all one-dimensional complex manifolds of genus g. Variants of this appear in several mathematical disciplines. In arithmetic geometry, Shimura varieties or moduli spaces of shtukas play an important role in the realisation of Langlands correspondences. Diffeomorphism groups of high-dimensional manifolds and moduli spaces of manifolds and of metrics of positive scalar curvature are studied in differential topology. Moduli spaces are also one of the central topics in our research in mathematical physics, where we study moduli spaces of stable curves and of Strebel differentials. online • EXC 2044 - T04: Groups and actions The study of symmetry and space through the medium of groups and their actions has long been a central theme in modern mathematics, indeed one that cuts across a wide spectrum of research within the Cluster. There are two main constellations of activity in the Cluster that coalesce around groups and dynamics as basic objects of study. Much of this research focuses on aspects of groups and dynamics grounded in measure and topology in their most abstract sense, treating infinite discrete groups as geometric or combinatorial objects and employing tools from functional analysis, probability, and combinatorics. Other research examines, in contrast to abstract or discrete groups, groups with additional structure that naturally arise in algebraic and differential geometry. online | urs dot hartl at uni-muenster dot de |
| Phone | +49 251 83-33702 |
| FAX | +49 251 83-33786 |
| Room | 317 |
| Secretary | Sekretariat Harenbrock/Reckermann Frau Ina Reckermann Telefon +49 251 83-33700 Fax +49 251 83-33786 Zimmer 316 |
| Address | Prof. Dr. Urs Hartl Mathematisches Institut Fachbereich Mathematik und Informatik der Universität Münster Einsteinstrasse 62 48149 Münster Deutschland |
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