Ordered Basis for vector space groupoids
On vector spaces with an inner product, complex structure or symplectic form, it is possible to find ordered basis that adapted to those structures. It was not clear which basis one should choose for a vector space with a groupoid structure. In my work with Francesco Cattafi we choose some class of ordered basis, we proved this class is again a groupoid, the matrices changing two such ordered basis has also a groupoid structure and generalize it for vector bundle groupoids.
tba
Higher structures of embeddings of varieties
I explain a joint work in progress with Damien Calaque aimed at globalizing a local formality result by Calaque-Felder-Ferrario-Rossi, by means of which certain isomorphisms between Ext-algebras of embeddings of varieties can be derived from quasi-isomorphism of $A_\infty$-deformations.
E-symplectic and almost regular Poisson manifolds
When considering manifolds with boundary it is common to only consider vector fields tangent to the boundary. This set of vector fields is called the b-foliation and it coincides with sections of a vector bundle B. This choice of vector fields allows us to consider smooth sections on E*, which do not correspond to smooth forms but they give smooth functions when evaluated on elements of the b-foliation. A well studied class of singular symplectic manifolds are b-symplectic manifolds which are given by a symplectic B form, i.e. a non degenerate closed section on B*^B*. In this talk we will compare 2 objects. On the one hand, we will not restrict ourselves to study the b-foliation case, we will consider any set of vector fields described as sections of some vector bundle E, and symplectic forms on E, E-symplectic manifolds. On the other hand, we will consider a similar object, Poisson manifolds whose symplectic foliation is also controlled by a vector bundle E, almost regular Poisson manifolds. These two are surprisingly not the same object but they are related in a natural way.
Higher Coleman theory
VENUE: Endenicher Allee 60, Room 1.007, University of Bonn
https://people.mpim-bonn.mpg.de/scholze/ARGOS/ARGOS_SS25.pdf
An Annoyingly Simple Open Problem on Lattice Counting
In this talk, I will introduce an open problem and survey my failed attempts to solve it; as far as I know, it is new. The problem concerns Euclidean lattice counting, and its statement is rather elementary.
Arithmetic Applications of Hyperbolic Lattice Counting
The classical Gauss circle problem concerns estimating the number of lattice points inside a Euclidean disc of radius $R$. Equivalently, it asks for the average number of ways to write a positive integer $n<R^2$ as a sum of two squares. In this talk, we discuss various analogous situations in the hyperbolic space. Rather than focusing on the underlying geometric results themselves, we treat them as black boxes and concentrate on their arithmetic consequences. These include results on the distribution of sums of squares, norms of ideals in quadratic fields, and more.
A Hyperelliptic Statistics on Moduli Spaces of vector bundles
Reference: [1] Statistics of Moduli Space of Vector Bundles, Dey A., Dey S., and A. Mukhopadhyay, Bull.Sci.Math, Vol 151 (2019), 13-33.\\
https://doi.org/10.1016/j.bulsci.2018.12.003
[2] Statistics of Moduli Spaces of vector bundles over hyperelliptic curves\\
https://arxiv.org/pdf/2409.10558
tba
tba
tba
- 1
- 2
- 3
- 4
- 5
- 6
- 7
- 8
- 9
- …
- nächste Seite ›
- letzte Seite »
| © MPI f. Mathematik, Bonn | Impressum & Datenschutz |
English
Deutsch