Mathematical Institute Calendar

Thursday, November 26, 2020

16:00-17:00

TEAMS

Applied Mathematics Seminar -- Erik Koelink (Radboud University Nijmegen) Toda lattice and special functions

see description

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.

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.

Friday, November 27, 2020

14:00-17:00

Dutch Differential Topology and Geometry Seminar

Gabriele Benedetti - First steps into the world of systolic inequalities. From Riemannian to Symplectic geometry

see description

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

Monday, November 30, 2020

14:30-19:00

On Zoom

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.

Tuesday, December 1, 2020

14:30-19:00

On Zoom

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.

Wednesday, December 2, 2020

14:30-19:00

On Zoom

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.

Thursday, December 3, 2020

14:30-19:00

On Zoom

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.

16:00-17:00

TEAMS

Applied Mathematics Seminar -- Götz Pfander (KU Eichstätt Ingolstadt) -- Exponential bases for partitions of intervals

see description

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).

Friday, December 4, 2020

14:30-18:00

On Zoom

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.

Tuesday, December 8, 2020

17:00-18:30

On Zoom

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.

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.

Thursday, December 10, 2020

Friday, December 11, 2020

11:00-12:00

online

Master thesis defense

Onno van Zomeren - Solving polynomial equations in power series using function fields

see description

Written under supervision by Prof. dr. G.L.M. Cornelissen with dr. V.Z.Karemaker as a second reader.

**Abstract:** A well-known theorem infinite automata theory is the following: a power series over a finite field isalgebraic if and only if its coefficient sequence is automatic. This result isknown as Christol's Theorem. In a recent paper, Bridy proved new bounds for thenumber of states for the automaton of an algebraic power series. Although thesebounds are sharp in some specific cases, there are many examples of algebraicpower series with automata which are far smaller than expected from the bounds.After introducing the theory of function fields and automata, we study Bridy'sbounds in more detail. We use an experimental approach to study the automata ofseveral families of algebraic power series. Lastly, we provide a MAGMAprocedure which for a given irreducible polynomial over a finite field computesall power series solutions and their automata.

My presentation will be held online via Microsoft Teams. You canjoin the team via the following link: https://teams.microsoft.com/l/team/19%3a411fef3f93f34df2b811f3c2986b464f%40thread.tacv2/conversations?groupId=1b15352a-1c37-4fdd-9529-80abaccd80c6&tenantId=d72758a0-a446-4e0f-a0aa-4bf95a4a10e7, or using the code **texxvti **. If any problems occur while trying tojoin, please notify me via e-mail: o.vanzomeren@students.uu.nl.

16:30-17:00

Zoom

Friday Fish Seminar

Maxence Mayrand - Hyperkähler realizations of holomorphic Poisson surfaces

see description

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/

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/

Thursday, December 17, 2020