t.b.a.
Montag, 2.5.16, 16:15-17:15, Raum 404, Eckerstr. 1
Existence of minimizing Willmore Klein bottles in euclidean four-space
Dienstag, 3.5.16, 16:15-17:15, Raum 404, Eckerstr. 1
We consider immersed Klein bottles in euclidean four-space with low Willmore energy. It turns out that there are three distinct homotopy classes of immersions that are regularly homotopic to an embedding. One is characterized by the property that the immersions have Euler normal number zero. This class contains embedded Klein bottles with Willmore energy strictly less than \(8\bpi\). We prove that the infimum of the Willmore energy among all immersed Klein bottles in euclidean four-space is attained by a smooth embedding that is in this first homotopy class. In the other two homotopy classes we have that the Willmore energy is bounded from below by \(8\bpi\). We classify all immersed Klein bottles with Willmore energy \(8\bpi\) and Euler normal number \(+4\) or \(-4\). These surfaces are minimizers of the second or the third homotopy class.
Uncountable trees and pure decision, part II
Mittwoch, 4.5.16, 16:30-17:30, Raum 404, Eckerstr. 1
Discretisation-Invariant Swap Contracts and Higher-Moment Risk Premia.
Mittwoch, 4.5.16, 17:00-18:00, Hörsaal Weismann-Haus, Albertstr. 21a
Realised pay-offs for discretisation-invariant swaps are those which satisfy a restricted `aggregation property' of Neuberger (2012) for twice continuously differentiable deterministic functions of a multivariate martingale. They are initially characterised as solutions to a second-order system of PDEs, then those pay-offs based on martingale and log-martingale processes alone form a vector space. Interestingly, these DI swaps are aggregating according to both Neuberger's definition and the aggregation property introduced by Bondarenko (2014). \n\nThere exists an infinite variety of variance and higher-moment risk premia that are less prone to bias than standard variance swaps, because their option replication portfolios have no discrete-monitoring or jump errors. Their fair values are also independent of the monitoring partition. A sub-class consists of pay-offs with fair values that are further free from numerical integration errors over option strikes. Here exact pricing and hedging is possible via dynamic trading strategies on a few vanilla puts and calls. \n\nAn empirical study on the determinants of higher-moment risk premia in the S&P 500 index concludes.\n\n(Gast von Prof. T. Schmidt)
Donnerstag, 5.5.16, 17:00-18:00, Hörsaal II, Albertstr. 23b
Competing selective sweeps
Freitag, 6.5.16, 12:00-13:00, Raum 404, Eckerstr. 1
In population genetics, mathematical models are used to study the distributions and changes of allele frequencies. Main evolutionary factors influencing these frequencies are (among others) mutation, selection and recombination. Maynard Smith and Haigh (1974) analysed in a pioneering theoretical framework the process when a new, strongly selected advantageous mutation becomes fixed in a population. They identified that such an evolution, called selective sweep, leads to the reduction of diversity around the selective locus. In the following years other scientists faced the question to what extent this characteristic still holds, when certain assumptions are modified. \n\nIn this talk a situation is presented where two selective sweeps within a narrow genomic region overlap in a sexually evolving population. For such a competing sweeps situation the probability of a fixation of both beneficial alleles, in cases where these alleles are not initially linked, is examined. To handle this question a graphical tool, the ancestral selection recombination graph, is utilized, which is based on a genealogical view on the population. This approach provides a limit result (for large selection coefficients) for the probability that both beneficial mutations will eventually fix. The analytical examination is complemented by simulation results.
Competing selective sweeps
Freitag, 6.5.16, 12:00-13:00, Raum 404, Eckerstr. 1
In population genetics, mathematical models are used to study the distributions and changes of allele frequencies. Main evolutionary factors influencing these frequencies are (among others) mutation, selection and recombination. Maynard Smith and Haigh (1974) analysed in a pioneering theoretical framework the process when a new, strongly selected advantageous mutation becomes fixed in a population. They identified that such an evolution, called selective sweep, leads to the reduction of diversity around the selective locus. In the following years other scientists faced the question to what extent this characteristic still holds, when certain assumptions are modified. \n\nIn this talk a situation is presented where two selective sweeps within a narrow genomic region overlap in a sexually evolving population. For such a competing sweeps situation the probability of a fixation of both beneficial alleles, in cases where these alleles are not initially linked, is examined. To handle this question a graphical tool, the ancestral selection recombination graph, is utilized, which is based on a genealogical view on the population. This approach provides a limit result (for large selection coefficients) for the probability that both beneficial mutations will eventually fix. The analytical examination is complemented by simulation results.
Adiabatic Limits of Eta Invariants
Montag, 9.5.16, 16:15-17:15, Raum 404, Eckerstr. 1
We will introduce eta invariants, which are spectral invariants of Dirac operators, and the notion of adiabatic limits. Then we present some known results by Bismut, Cheeger and Dai before we give a partial answer in a more general setting.
The Centre of the distribution algebra in positive characteristic
Dienstag, 10.5.16, 15:15-16:15, Raum 119, Eckerstr. 1
Min-Max theory and the Willmore conjecture, Fernando C. Marques, André Neves
Dienstag, 10.5.16, 16:00-17:00, Raum 404, Eckerstr. 1
Large Monochromatic Subtrees
Mittwoch, 11.5.16, 16:30-17:30, Raum 404, Eckerstr. 1
Donnerstag, 12.5.16, 17:00-18:00, Hörsaal II, Albertstr. 23b
Donnerstag, 19.5.16, 17:00-18:00, Hörsaal II, Albertstr. 23b
Surgery stability of the space of metrics with invertible Dirac operator
Montag, 23.5.16, 16:15-17:15, Raum 404, Eckerstr. 1
Surgery stability of the space of metrics with invertible Dirac operator
Montag, 23.5.16, 16:15-17:15, Raum 404, Eckerstr. 1
Min-Max theory and the Willmore conjecture, Fernando C. Marques, André Neves
Dienstag, 24.5.16, 16:15-17:15, Raum 404, Eckerstr. 1
Donnerstag, 26.5.16, 17:00-18:00, Hörsaal II, Albertstr. 23b
The p-canonical basis of Hecke algebras
Freitag, 27.5.16, 10:15-11:15, Raum 404, Eckerstr. 1
The first Steklov eigenvalue
Dienstag, 31.5.16, 16:15-17:15, Raum 404, Eckerstr. 1