The classical Toda lattice is a model for a one-dimensional crystal.
After a transformation in coordinates there is a Lax pair, for which the
operator L acts as a three-term recurrence operator. This gives a link
to orthogonal polynomials and other special functions related to
solutions of three-term recurrences. The time dependence of the
orthogonality measure involved is via a deformation using exponentials.
We consider the link to suitable Lie algebra representations, which we
keep very explicit. Some of the results extend to the nonabelian Toda
lattice which is briefly discussed.

In their classical formulation, systolic inequalities aim to study Riemannian metrics on a given compact surface by looking at the length of the shortest non-constant periodic geodesic, also known as the systole. One of the fundamental questions in the field is to find an upper bound, independent of the metric, for the systolic length when the metric has unit area.

After briefly discussing this question in general, we will concentrate on the case of the two-sphere. Here an interesting class of metrics pops up: Those for which all geodesics are systoles. Abbondandolo, Bramham, Hryniewicz and Salomao showed recently that these so-called Zoll metrics locally maximize the systolic length in the space of Riemannian metrics on the two-sphere.
Their proof uses symplectic techniques and will lead us, in the second talk, to consider an analogue of systoles and of Zoll metrics for contact hypersurfaces inside symplectic manifolds. In the contact world, global upper bounds for the systole do not hold but Zoll hypersurfaces still remain local maximizers for the systolic length.

These phenomena are related to the famous Viterbo conjecture in symplectic geometry about the capacity of convex domains in euclidean space, which will finally bring us to the frontier of current research.
  
Zoom details can be found in the website of the seminar: https://www.few.vu.nl/~trt800/ddtg.html  

The Workshop will consist of 3 minicourses ("Infinite dimensional geometry", "C^0 Symplectic Topology", "the Pontryagin maximum principle"), as well as ten talks given by junior participants.

Further details of the event can be found in http://utrechtgeometrycentre.nl/15iyrw/
The Zoom link will be sent to staff and students a few days before the event.

The Workshop will consist of 3 minicourses ("Infinite dimensional geometry", "C^0 Symplectic Topology", "the Pontryagin maximum principle"), as well as ten talks given by junior participants.

Further details of the event can be found in http://utrechtgeometrycentre.nl/15iyrw/
The Zoom link will be sent to staff and students a few days before the event.

The Workshop will consist of 3 minicourses ("Infinite dimensional geometry", "C^0 Symplectic Topology", "the Pontryagin maximum principle"), as well as ten talks given by junior participants.

Further details of the event can be found in http://utrechtgeometrycentre.nl/15iyrw/
The Zoom link will be sent to staff and students a few days before the event.

The Workshop will consist of 3 minicourses ("Infinite dimensional geometry", "C^0 Symplectic Topology", "the Pontryagin maximum principle"), as well as ten talks given by junior participants.

Further details of the event can be found in http://utrechtgeometrycentre.nl/15iyrw/
The Zoom link will be sent to staff and students a few days before the event.

The foundational stone of Fourier analysis is the statement that $\mathcal E(\Z)=\{e^{2\pi i n (\cdot)}\}_{n\in\Z}$ forms an orthonormal bases for the space of square integrable functions on the unit interval, $L^2[0,1]$. Simple scaling and translating arguments imply the couriosity that $\mathcal E(\Z)$ splits into $\mathcal E(2\Z)$ and $\mathcal E(2\Z+1)$, each forming an orthogonal bases for $L^2[0,1/2]$ and $L^2[1/2,1]$, respectively. We show for any partition of the unit interval into subintervals $I_k$ there exists a corresponding partition of the integers into sets $\Lambda_k$ so that all sets $\mathcal E(\Lambda_k)$ form a Riesz bases for $L^2(I_k)$. Consequences in the area of sampling theory are given to illustrate the relevance for applications. Joint work with Shauna Revay and David Walnut (George Mason University).

The Workshop will consist of 3 minicourses ("Infinite dimensional geometry", "C^0 Symplectic Topology", "the Pontryagin maximum principle"), as well as ten talks given by junior participants.

Further details of the event can be found in http://utrechtgeometrycentre.nl/15iyrw/
The Zoom link will be sent to staff and students a few days before the event.

TBA

Website of the seminar: http://utrechtgeometrycentre.nl/ugc-seminar/ 
Zoom details will be sent by email to the staff and student mailing lists a few days before the event.  

I will discuss the existence of hyperkähler structures on symplectic realizations of holomorphic Poisson manifolds, and show that they always exist when the Poisson manifold has complex dimension two. We obtain this structure by constructing a twistor space by lifting special deformations of the Poisson surface adapted from Hitchin's unobstructedness theorem. In the case of the zero Poisson structure, we recover the Feix-Kaledin hyperkähler structure on the cotangent bundle of a Kähler manifold. This talk is based on arXiv:2011.09282. 


Zoom details are sent in the weekly announcements. To join the mailing list you can drop us an email to fridayfishseminar[at]gmail.com.
Website of the seminar: http://utrechtgeometrycentre.nl/friday-fish-seminar-online-edition/