Gong Show: What I found on the arXiv
Montag, 23.4.18, 16:15-17:15, Raum 404, Ernst-Zermelo-Str. 1
Gong Show: What I found on the arXiv
Montag, 30.4.18, 16:15-17:15, Raum 404, Ernst-Zermelo-Str. 1
T.B.A.
Donnerstag, 3.5.18, 16:15-17:15, Raum 404, Ernst-Zermelo-Str. 1
Topological field theory on r-spin surfaces and the Arf invariant
Montag, 7.5.18, 16:15-17:15, Raum 404, Ernst-Zermelo-Str. 1
We present a state-sum construction of TFTs on r-spin surfaces which uses a combinatorial model of r-spin structures. We give an example of such a TFT which computes the Arf invariant for r even. We use the combinatorial model and this TFT to calculate diffeomorphism classes of r-spin surfaces with parametrized boundary.
Hodge Numbers from Differential Equations
Montag, 7.5.18, 17:15-18:15, Raum 404, Ernst-Zermelo-Str. 1
A natural way of constructing Calabi-Yau manifolds is to build them as fibrations whose fibers are Calabi-Yau manifolds of lower dimension. For example, elliptic curves can be thought of as fibrations over the projective line by pairs of points, and K3 surfaces fibered over the projective line by elliptic curves form a large class of interesting K3 surfaces. In higher dimensions, the question of computing the Hodge numbers of such Calabi-Yau manifolds becomes a non-trivial one. I’ll talk about a method of computing Hodge numbers starting from the Picard-Fuchs differential equation of a family of Calabi-Yau manifolds. Applying this to families of lattice-polarized K3 surfaces provides a key ingredient in the classification of fibered Calabi-Yau threefolds.
Gong Show: What I found on the arXiv
Montag, 14.5.18, 16:15-17:15, Raum 404, Ernst-Zermelo-Str. 1
On stable, closed geodesics on a K3
Montag, 28.5.18, 16:15-17:15, Raum 404, Ernst-Zermelo-Str. 1
I will report on the search for stable, closed geodesics on a K3 surface. In particular, I will sketch the Bourguignon-Yau proof of why the Riemann tensor vanishes along such geodesics, and I will explain how to find totally geodesic tori in highly symmetric Kummer K3s.
A general mirror symmetry construction
Montag, 4.6.18, 16:15-17:15, Raum 404, Ernst-Zermelo-Str. 1
I will talk about joint work with Bernd Siebert, which aims to give a general construction of mirrors to either log Calabi-Yau manifolds or maximal degenerations of Calabi-Yau manifolds. The construction goes by way of building the coordinate ring of the mirror as an abstract ring whose multiplication law is governed by counting curves on the original (log) Calabi-Yau.
Moduli Spaces of Nonnegatively Curved Riemannian Metrics
Montag, 11.6.18, 16:15-17:15, Raum 404, Ernst-Zermelo-Str. 1
I will report on general results and questions about spaces and moduli spaces of Riemannian metrics \nwith non-negative Ricci or non-negative sectional curvature on closed and open manifolds,\nand present recent joint work with Michael Wiemeler. In particular, \nwe construct the first classes of manifolds for which these spaces \nhave non-trivial rational homotopy, homology and cohomology groups.
Wave equations with initial data on compact Cauchy horizons
Montag, 18.6.18, 16:15-17:15, Raum 404, Ernst-Zermelo-Str. 1
Wave equations are usually studied in globally hyperbolic regions of \nspacetimes. However, to approach the famous strong cosmic censorship \nconjecture, this is not sufficient. One needs to understand the behavior \nof waves close to the boundary of the globally hyperbolic region, the \nCauchy horizon. The purpose of this talk is to discuss the \ncharacteristic Cauchy problem with initial data on a compact Cauchy \nhorizon. We prove an energy estimate close to compact non-degenerate \nCauchy horizons which implies existence and uniqueness results for wave \nequations. In particular, we overcome the essential remaining difficulty \nin proving the Moncrief-Isenberg conjecture in the non-degenerate case. \nThis can be seen as a special case of the strong cosmic censorship \nconjecture.
Equivalence of field theories in the BV-BFV formalism. Insights from General Relativity
Montag, 25.6.18, 16:15-17:15, Raum 404, Ernst-Zermelo-Str. 1
The standard notion of equivalence of field theories roughly requires the Euler-Lagrange loci of the two associated variational problems to be diffeomorphic, possibly modulo the action of the respective symmetry distributions, in some appropriate framework.\nThis can be made stated more precisely in the Batalin-Fradkin-Vilkovisky setting, where some cohomological presentation of said locus is constructed.\nI will discuss a series of examples, all related to General Relativity in different space-time dimensions, that suggest that higher codimension data should play a role in defining (and refining) equivalence between classical theories, and raise the question of whether (and how) this picture carries over to quantisation.
Introduction to contact dynamics
Montag, 2.7.18, 16:15-17:15, Raum 404, Ernst-Zermelo-Str. 1
This talk will be an introduction to contact geometry and dynamics.\nIn particular, I will explain the relation between Hamiltonian systems and contact dynamics.\nThe main examples are level sets of Hamiltonians from classical mechanics and contact manifolds, ob which the Reeb flow induces an S^1-action with reasonably nice quotients.
Vector-valued automorphic functions and their Fourier series
Montag, 9.7.18, 16:15-17:15, Raum 404, Ernst-Zermelo-Str. 1
The Weyl Denominator Identity in light of the structure of root systems
Montag, 16.7.18, 16:15-17:15, Raum 404, Ernst-Zermelo-Str. 1
The Weyl Denominator Identity arises usually as a special case of the Weyl Character Formula of a complex semisimple Lie algebra. Even though it prominently features the roots of the Lie algebra, the original proof provides limited insight into the structure of the root system.\nI will therefore present a direct proof of the Denominator Identity. This alternative approach explicitly uses connections between the roots and the Weyl Group and might provide a different perspective on the Denominator Identity as well as the structure of the root system.