Monday,
20230424
16:00

Raum 125, ErnstZermeloStr. 1
Ryszard Nest:
Automorphisms of the Boutet de Monvel algebra
In a remarkable work, Duistermaat and Singer in 1976 studied the algebras of all classical pseudodifferential operators on smooth (boundaryless) manifolds. They gave a description of order preserving algebra isomorphism between the algebras of classical pseudodifferential operators of two manifolds. The subject of this talk is the generalisation of their results to manifolds with boundary. The role of the algebra of pseudodifferential operators that we are interested in is the Boutet de Monvel algebra.
The main fact of life about manifold with boundary is that vector fields do not define global flows and the "boundary conditions" are a way of dealing with this problem. The Boutet de Monvel algebra corresponds to the choice of local boundary conditions and is, effectively, a noncommutative completion of the manifold. One can think of it as a parametrised version of the classical Toeplitz algebra as a completion of the halfspace.
What appears in the study of automorphisms are Fourier integral operators and we will try to explain their appearance  both in boundaryless and boundary case. as it turns out, the nontrivial boundary case introduces both some complications but also some simplifications of the analysis involved, Once this is done, the analysis that we need reduces to a high degree to relatively classical results about automorphisms and homology of the Toeplitz algebra and some basic facts from Ktheory.
This is a joint work in progress with Elmar Schrohe. 
Tuesday,
20230502
16:00

Raum 404, ErnstZermeloStr. 1
Miquel Cueca Tan:
Shifted Lagrangian structures in Poisson geometry
It is well known that BG carries a 2shifted symplectic structure. In this talk, I will study the shifted lagrangian groupoids of BG. I will show how many constructions on Poisson geometry unify using the language of shifted symplectic groupoids. This is work in progress with Daniel Alvarez and Henrique Bursztyn. 
Monday,
20230508
16:1517:45

Raum 125, ErnstZermeloStr. 1
Dr. Lukas Braun (Freiburg):
ODD Riemannian metrics
We describe a generalization of Riemannian metrics motivated from
Kähler geometry of singular complex varieties. These generalizations
are semipositive symmetric 2tensors, but degenerate in such way, that
e.g. they still induce a metric space structure on the underlying
manifold.
In this talk, we will mostly use instructive examples to sketch how far
Riemannian Geometry can (hopefully) be pursued for these ODD metrics. 
Monday,
20230515
16:00

Raum 125, ErnstZermeloStr. 1
Ksenia Fedosova:
Shifted convolution sums
In talk I will evaluate shifted convolution sums of divisor functions of the form $\displaystyle\sum_{n_1,n_2\in\mathbb{Z}\setminus{0}, n_1+n_2=n}
Q_{d}^{(r_1,r_2)}\Big(\frac{n_2n_1}{n_1+n_2}\Big)\sigma_{r_1}(n_1)\sigma_{r_2}(n_2)$ where $\sigma_{r}(n) = \sum_{d \mid n} d^ r$ and $Q_{d}^{(r_1,r_2)}(x)$ is the Jacobi function of the second kind. These sums can be considered as a shifted version of the Ramanujan sum $\sum_{n_1 \in \mathbb{Z}} \sigma_{r_1}(n_1) \sigma_{r_2}(n_1) n_1^s$.
Key words that appear in the proof and the final result: nonholomorphic Eisenstein series, cusp forms, values of $L$functions, Mellin transform and Whittaker's functions. 
Monday,
20230522
16:15

Raum 125, ErnstZermeloStr. 1
Simone Cecchini:
Metric inequalities with positive scalar curvature
We will discuss various situations where a certain perturbation of the Dirac operator on spin manifolds can be used to obtain distance estimates from lower scalar curvature bounds.
A first situation consists in an area nondecreasing map from a Riemannian spin manifold with boundary $X$ into the round sphere under the condition that the map is locally constant near the boundary and has nonzero degree. Here a positive lower bound of the scalar curvature is quantitatively related to the distance from the support of the differential of f and the boundary of $X$.
A second situation consists in estimating the distance between the boundary components of Riemannian “bands” $M×[−1,1]$ where $M$ is a closed manifold that does not carry positive scalar curvature. Both situations originated from questions asked by Gromov.
In the final part, I will compare the Dirac method with the minimal hypersurface method and show that if $N$ is a closed manifold such that the cylinder $N \times \mathbb{R}$ carries a complete metric of positive scalar curvature, then $N$ also carries a metric of positive scalar curvature. This answers a question asked by Rosenberg and Stolz. Based on joint work with Daniel Raede and Rudolf Zeidler. 
Monday,
20230605
16:00

Raum 125, ErnstZermeloStr. 1
Jonas Schnitzer:
Deformations of Lagrangian Qsubmanifolds
Positively graded symplectic Qmanifolds encompass a lot of wellknown mathematical structures, such as Poisson manifolds, Courant algebroids, etc. Lagrangian submanifolds of them are of special interest, since they simultaniously generalize coisotropic submanifolds, Diracstructures and many more. In this talk we set up their deformation theory inside a symplectic Qmanifold via strong homotopy Lie algebras. 
Monday,
20230612
16:15

Raum 125, ErnstZermeloStr. 1
Christian Ketterer:
Gluing spaces with BakryEmery Ricci curvature bounded from below
In this talk I will explain the BakryEmery Ricci tensor and the metric gluing construction between two (weighted) Riemannian manifolds along isometric parts of their boundary. When the (weighted) Riemannian manifolds admit a lower bound for the (BakryEmery) Ricci curvature, I will present a necessary and sufficient condition such that the metric glued space has synthetic Ricci curvature bounded from below. 
Monday,
20230626
16:1517:45

Raum 125, ErnstZermeloStr. 1
Thorsten Hertl:
On Line Bundle Twists for Unitary Bordisms
Classical theorems of ConnerFloyd and HopkinsHovey say that complex $K$theory is completely determined by unitary bordism and $\mathrm{Spin}^c$ bordism respectively. The isomorphisms appearing in these theorems are induced by the maps that send a bordism class to its orientationclass in complex $K$theory. Despite this geometric description, the proofs that they are indeed isomorphism are rather abstract and homotpytheoretical.
Motivated by theoretical physics, Baum, Joachim, Khorami and Schick extend Hopkins and Hovey’s result in a forthcoming paper to twisted $\mathrm{Spin}^c$ bordism and twisted $K$theory. Here, the twists are given by (representatives of) elements in third integral cohomology.
Since every almost complex structure induces a $\mathrm{Spin}^c$ structure and since the classical ConnerFloyd orientation factors through the HopkinsHovey orientation, one may wonder whether there is a twisted unitary bordism theory and a twisted ConnerFloyd orientation that extends the result of Baum, Joachim, Khorami and Schick ‘to the left’.
In this talk, I answer this question in the negative. 
Monday,
20230717
16:15

Raum 125, ErnstZermeloStr. 1
Markus Upmeier:
Spinoren, kalibrierte Untermannigfaltigkeit und Instantonen
Tee und Kekse werden 30 Minuten vor dem Vortrag im Gemeinschaftsraum bereitgestellt.
In der Modulraumtheorie gibt es eine tiefe, weitgehend unverstandene Dualität zwischen den InstantonZusammenhängen auf Hauptfaserbündeln über einer Mannigfaltigkeit und den kalibrierten Untermannigfaltigkeiten, welche als Modelle für „singuläre“ Instantonen auftreten. Während des Vortrags werde ich mithilfe von DiracOperatoren und Spinoren eine entsprechende Dualität (im adiabatischen Limes) der linearisierten Deformationstheorien dieser Modulräume herstellen. Das Hauptergebnis hat Anwendungen auf die Konstruktion von Orientierungsdaten in der DonaldsonThomas Theorie. 