Montag,
20190429
16:15 Uhr

Raum 404, ErnstZermeloStr. 1
Alexander Alexandrov (IBS Center for Geometry and Physics, Pohang):
Weighted Hurwitz numbers and topological recursion
In my talk I will discuss some elements of the proof of the
topological recursion for the weighted Hurwitz numbers. The main
ingredient is the taufunction  the all genera generating function,
which is a solution of the integrable KP or Toda hierarchy. My talk is
based on a series of joint papers with G. Chapuy, B. Eynard, and J.
Harnad. 
Montag,
20190506
16:15 Uhr

Raum 404, ErnstZermeloStr. 1
Yuhang Hou:
Elliptic Genera of ADE singularities
In a paper by Harvey, Lee and Murthy, the authers calculated the elliptic genera of ADE singularities as the partition of some gauged linear sigma models using the technique called supersymmetric localization. In this talk, I will give a free field construction of these elliptic genera and talk about the geometric interpretation. 
Montag,
20190513
16:1517:15 Uhr

Raum 404, ErnstZermeloStr. 1
Lothar Schiemanowski:
Introduction to the spinor flow
Geometric flows are a natural nonperturbative approach to the construction of special holonomy metrics. Several flows have been proposed in different settings, such as the KählerRicci flow and the Laplacian flow. The spinor flow is a unified approach for all Ricci flat special holonomy manifolds based on the spinorial characterization of such metrics. In this talk I will discuss its definition (due to Ammann, Weiß, Witt), its relationship to other flows and several recent results concerning its behavior. 
Montag,
20190520
16:1517:15 Uhr

Raum 404, ErnstZermeloStr. 1
Jonathan Glöckle (Regensburg):
On the space of initial value pairs satisfying the dominant energy condition strictly
The dominant energy condition implies an inequality for the induced initial value pair on a spacelike hypersurface of a Lorentzian manifold. In this talk, we want to study the
space of all initial value pairs that satisfy this inequality strictly. In order to do so, we introduce a Lorentzian alphainvariant for initial value pairs, and compare it to its classical counterpart. Recent nontriviality results for the latter will then imply that this space has nontrivial homotopy groups. 
Montag,
20190527
16:15 Uhr

Raum 404, ErnstZermeloStr. 1
José FigueroaO'Farrill (Edinburgh):
Generalised Spencer cohomology and supersymmetry
It is a fact of life that the Lie algebra of isometries of a riemannian manifold is a filtered Lie algebra whose associated graded Lie algebra is a subalgebra of the euclidean algebra: the Lie algebra of isometries of the flat model of riemannian geometry. It is also a fact of life, more recently understood, that the Lie superalgebras which arise as supersymmetries of supergravity backgrounds too are filtered Lie superalgebras whose associated graded Lie superalgebra is a subalgebra of the Poincaré superalgebra: the supersymmetry algebra of the flat supergravity background. The cohomology theory governing such filtered deformations is generalised Spencer cohomology. In this talk I will review these facts and describe some consequences of the calculations of generalised Spencer cohomology for Poincaré superalgebras in different dimensions: including what could be considered a cohomological derivation of elevendimensional supergravity and a determination of the possible lorentzian 4 and 6dimensional manifolds admitting rigid supersymmetry. This is based on collaborations with Andrea Santi and Paul de Medeiros. 
Montag,
20190603
16:1517:45 Uhr

Raum 404, ErnstZermeloStr. 1
Csaba Nagy (Melbourne):
Classifying 8dimensional Emanifolds
A manifold M is called an Emanifold if it has homology only
in even dimensions, ie. H_{2k+1}(M;Z) = 0 for all k. Examples include
complex projective spaces and complete intersections. We consider
8dimensional simplyconnected Emanifolds. Those that have Betti
numbers b_2 = r and b_4 = 0, and fixed second StiefelWhitney class
w_2 = w form a group \theta(r;w), which acts on the set of Emanifolds
with b_2 = r and w_2 = w. The classification of Emanifolds based on
this action consists of 3 steps: computing \theta(r;w), classifying
the set of orbits and finding the stabilizers. In this talk I will
present results in each of these steps, as well as an application, the
proof of a special case of Sullivan's conjecture about complete
intersections. 
Montag,
20190617
16:15 Uhr

Raum 404, ErnstZermeloStr. 1
Jin Li:
G2 manifolds with isolated conical singularities and asymptotically conical G2 manifolds 
Montag,
20190624
16:15 Uhr

Raum 404, ErnstZermeloStr. 1
Nelvis Fornasin (Universität Freiburg):
The parametrix construction in the bcalculus: a case study
In this talk I will review the parametrix construction in the bcalculus by describing in detail a concrete example, the construction of the resolvent for the Laplacian on functions for an asymptotically Euclidean manifold.
I will mostly follow the two papers Resolvent at Low Energy and Riesz Transform for Schrödinger Operators on Asymptotically Conic Manifolds. I & II by C. Guillarmou and A. Hassell. 
Montag,
20190701
16:1517:15 Uhr

Raum 404, ErnstZermeloStr. 1
Alexander Grom:
Geometrische Multiplizität des zweiten SchrödingerEigenwerts auf geschlossenen zusammenhängenden Flächen
Ein SchrödingerOperator auf einer Fläche $S$ ist definiert als Summe aus dem LaplaceOperator mit einem Potential $V \in C_0(S)$. Wir interessieren uns hierbei speziell für die Multiplizität des zweiten Eigenwerts über geschlossenen zusammenhängenden Flächen. Y. Colin de Verdière hat die Vermutung aufgestellt, dass sich deren Supremum explizit über die Färbungszahl der Fläche ausdrücken lässt. Wir wollen dies mit einer Abschätzung über die Eulercharakterisik untermauern, in dem wir uns spezielle zweifache Überlagerungen für die Flächen betrachten und dafür eine verwandte Version des Borsuk Ulam Theorems zeigen. 
Montag,
20190708
16:1517:45 Uhr

Raum 404, ErnstZermeloStr. 1
Dr. Markus Upmeier (Oxford):
Orientation problems for PDEs and instanton moduli spaces
Moduli spaces of solutions to nonlinear elliptic PDE's such as instantons in
gauge theory are fundamental for the construction of counting invariants. Using
information about the solution space provided by the index theory of an
approximating family of linear differential operators, we explain our results
on orientations for moduli spaces, including new developments in G2holonomy. 
Montag,
20190715
16:15 Uhr

Raum 404, ErnstZermeloStr. 1
Fabian Lehmann (University College London):
Cohomogeneity one Spin(7)manifolds
Spin(7) is one of the exceptional holonomy groups. Spin(7)manifolds are in particular Ricci flat. The condition for a Spin(7)structure to be torsionfree gives rise to a complicated system of nonlinear differential equations. One of the most fundamental ways to solve differential equations is to use symmetries to reduce the number of variables and complexity. For exceptional holonomy manifolds this can only be used in the noncompact setting. I will explain the construction of Spin(7)manifolds with cohomogeneity one. Here the nonlinear PDE system is reduced to a nonlinear ODE system. I will give an overview over previous work and mention recent progress. 
Dienstag,
20190716
09:0010:00 Uhr

Raum 127, ErnstZermeloStr. 1
Jonas Schnitzer (Salerno):
Semilocal and global Properties of Jacobirelated Geometries
After a short introduction to Jacobi related geometries, such as Poisson,
symplectic, contact and generalized complex/contact manifolds, and their
appearance in mathematical physics, I want to present some results on their
(semi)local structure around transversal submanifolds, socalled "Normal
forms". They can be seen as generalization of the Weinstein splitting theorem
for Poisson manifolds and they induce in fact a very explicit local
description of Jacobirelated structures.
The second part of the talk is intended to focus on a special Jacobi related
geometry: generalized contact bundles, the odddimensional counterparts of
generalized complex manifolds. I want to show that their global existence is
cohomologically obstructed by means of a spectral sequence. At the end I want
to give some classes of examples of generalized contact structures. 
Dienstag,
20190716
11:0012:00 Uhr

Raum 127, ErnstZermeloStr. 1
Dr. Hemanth Saratchandran (Augsburg):
Essential selfadjointness of powers of first order differential operators on noncompact manifolds with low regularity metrics
The problem of determining the essential selfadjointness of a
differential operator on a smooth manifold, and its powers, is an
important and well studied topic. One of the primary motivations for studying
the essential selfadjointness of a differential operator $D$,
comes from the fact that it allows one to build a functional calculus (of Borel
functions) for the closure of that operator. Such a
functional calculus is then used to solve partial differential equations on a
manifold, defined through the operator.
In this talk, I will present joint work with L. Bandara where we consider the
question of essential selfadjointness of first order differential operators,
and their
powers, in the context of nonsmooth metrics on noncompact manifolds. Using
methods from geometry and operator theory we are able to show
that essential selfadjointness, at its heart, is an operator theoretic
condition which requires minimal assumptions on the geometry
of the manifold. Applications to Dirac type operators on Dirac bundles will be
discussed. 
Dienstag,
20190716
14:15 Uhr

Raum 318, ErnstZermeloStr. 1
Bin Xu:
Removable singularities of Kähler metrics of constant holomorphic sectional curvature
Let n>1 be an integer, and B^n be the unit ball in C^n. K\subset B^n is a compact subset or {z_1=0=z_2}. By using developing map and Hartogs' extension theorem, we show that a Kaehler metric on B^n\K with constant holomorphic sectional curvature uniquely extends to the ball. This is a
joint work with Sien Gong and Hongyi Liu. 
Freitag,
20190719
14:15 Uhr

Raum 318, ErnstZermeloStr. 1
Bin Xu:
Singular hyperbolic metrics on Riemann surfaces
J. Nitsche showed that an isolated singularity of a hyperbolic metric is either a cone singularity or a cusp one. M. Heins proved on compact Riemann surfaces a classical existence theorem about singular hyperbolic metrics where the GaussBonnet formula is the necessary and sufficient condition. We prove that a developing map of a singular hyperbolic metric on a compact Riemann surface has a Zariski dense monodromy group in PSL(2;R). Moreover, we also provide
some evidences to the conjecture that it be also the case on a noncompact Riemann surface which admits no nontrivial negative subharmonic function. This is a joint work with Yu Feng, Yiqian Shi, Jijian Song. 
Montag,
20190722
16:15 Uhr

Raum 404, ErnstZermeloStr. 1
Ana RosCamacho (Utrecht):
Computational aspects of orbifold equivalence
LandauGinzburg models are a family of quantum field theories characterized by a polynomial (satisfying some conditions) usually called ‘potential’. Often appearing in mirrorsymmetric phenomena, they can be collected in categories with nice properties that allow direct computations. In this context, it is possible to introduce an equivalence relation between two different potentials called `orbifold equivalence’. We will present some recent examples of this equivalence, and discuss the computational challenges posed by the search of new ones. Joint work with Timo Kluck. 
Dienstag,
20190723
09:0010:00 Uhr

Raum 127, ErnstZermeloStr. 1
Siarhei Finski (Paris):
RiemannRochGrothendieck theorem for families of curves with hyperbolic cusps and its applications to the moduli space of curves
We’ll present a refinement of RiemannRochGrothendieck theorem on
the level of differential forms for families of curves with hyperbolic cusps.
The study of spectral properties of the Kodaira Laplacian on a Riemann surface,
and more precisely of its determinant, lies in the heart of our approach.
When our result is applied directly to the moduli space of punctured stable
curves, it expresses the extension of the WeilPetersson form (as a current) to
the boundary of the moduli space in terms of the first Chern form of a
Hermitian line bundle, which provides a generalisation of a result of
TakhtajanZograf.
If time permits, we will explain how our result implies some bounds on the
growth of the WeilPetersson form near the compactifying divisor of the moduli
space of punctured stable curves. This would permit us to give a new approach
to some wellknown results of Wolpert on the WeilPetersson geometry of the
moduli space of curves. 
Montag,
20190729
16:15 Uhr

Raum 404, ErnstZermeloStr. 1
Benoit Charbonneau:
Monopoles with arbitrary symmetry breaking
Monopoles are pairs formed of a connection and an endomorphism of the bundle that satisfy the Bogomolny equation. There is ample literature on the study of monopoles on R3 under the constraint that the eigenvalues of the endomorphism on the sphere at infinity are distinct, the socalled maximal symmetry breaking case. In joint work with Ákos Nagy, we are exploring monopoles with arbitrary symmetry breaking on R3, and in particular their Nahm transform. 
Mittwoch,
20190807
13:4514:45 Uhr

Raum 404, ErnstZermeloStr. 1
Gaetan Leclerc (Rennes):
Scalar Curvature Deformation
We will present the main result of an article by Corvino on
scalar curvature deformation. 