Zobrazeno 1 - 10
of 133
pro vyhledávání: '"Tillmann, Ulrike"'
The Harder-Narasimhan type of a quiver representation is a discrete invariant parameterised by a real-valued function (called a central charge) defined on the vertices of the quiver. In this paper, we investigate the strength and limitations of Harde
Externí odkaz:
http://arxiv.org/abs/2303.16075
Autor:
Palmer, Martin, Tillmann, Ulrike
Publikováno v:
Proc. R. Soc. A., vol. 479 (2023), article number 20230300
We prove homological stability for two different flavours of asymptotic monopole moduli spaces, namely moduli spaces of framed Dirac monopoles and moduli spaces of ideal monopoles. The former are Gibbons-Manton torus bundles over configuration spaces
Externí odkaz:
http://arxiv.org/abs/2212.11799
Autor:
Benjamin, Katherine, Bhandari, Aneesha, Shang, Zhouchun, Xing, Yanan, An, Yanru, Zhang, Nannan, Hou, Yong, Tillmann, Ulrike, Bull, Katherine R., Harrington, Heather A.
Spatial transcriptomics has the potential to transform our understanding of RNA expression in tissues. Classical array-based technologies produce multiple-cell-scale measurements requiring deconvolution to recover single cell information. However, ra
Externí odkaz:
http://arxiv.org/abs/2212.06505
We introduce a sheaf-theoretic stability condition for finite acyclic quivers. Our main result establishes that for representations of affine type $\widetilde{\mathbb{A}}$ quivers, there is a precise relationship between the associated Harder-Narasim
Externí odkaz:
http://arxiv.org/abs/2211.07553
Weighted digraphs are used to model a variety of natural systems and can exhibit interesting structure across a range of scales. In order to understand and compare these systems, we require stable, interpretable, multiscale descriptors. To this end,
Externí odkaz:
http://arxiv.org/abs/2210.11274
Autor:
Benjamin, Katherine, Mukta, Lamisah, Moryoussef, Gabriel, Uren, Christopher, Harrington, Heather A., Tillmann, Ulrike, Barbensi, Agnese
Quantification and classification of protein structures, such as knotted proteins, often requires noise-free and complete data. Here we develop a mathematical pipeline that systematically analyzes protein structures. We showcase this geometric framew
Externí odkaz:
http://arxiv.org/abs/2201.07709
The barcode of a persistence module serves as a complete combinatorial invariant of its isomorphism class. Barcodes are typically extracted by performing changes of basis on a persistence module until the constituent matrices have a special form. Her
Externí odkaz:
http://arxiv.org/abs/2111.03700
Publikováno v:
In Advances in Applied Mathematics February 2024 153
Autor:
Leygonie, Jacob, Tillmann, Ulrike
We study the inverse problem for persistent homology: For a fixed simplicial complex $K$, we analyse the fiber of the continuous map $\mathrm{PH}$ on the space of filters that assigns to a filter $f: K \to \mathbb R$ the total barcode of its associat
Externí odkaz:
http://arxiv.org/abs/2104.01372
Autor:
Palmer, Martin, Tillmann, Ulrike
Publikováno v:
Res. Math. Sci. 8, 38 (2021)
For a given bundle $\xi \colon E \to M$ over a manifold, configuration-section spaces on $\xi$ parametrise finite subsets $z \subseteq M$ equipped with a section of $\xi$ defined on $M \smallsetminus z$, with prescribed "charge" in a neighbourhood of
Externí odkaz:
http://arxiv.org/abs/2007.11607