## Math Calendar

We will discuss first the history of polar degree and give several examples, e.g. the determinant hypersurface has polar degree 1. The hypersurfaces with polar degree are called homaloidal and are of extra interest because the gradient map is bi-rational.

Polar degree zero is related to the question of what happens if the Hessian of f is identically zero. This was solved by Gordan and Noether in 1876.

After a long period of algebraic studies, recently topological methods gave some interesting results. Dolgacev classified in 2000 all the projective homoloidal plane curves: a short list. Huh determined in 2014 all homoloidal hypersurfaces in P with at most isolated singularities.

In this talk we will reprove Huh's results with methods of singularity theory. Moreover we will prove the Huh's conjecture that his list of polar degree 2 surfaces with isolated singularities is complete!

Finally we say something more about hypersurfaces with the non-isolated singularities.

Website of the UGC seminar (and the pure side of the MI-alks):

__Practical details will be sent by email to the staff and student mailing lists a few days before the event.__

__http://utrechtgeometrycentre.nl/ugc-seminar/__Webpage of the AG seminar: https://webspace.science.uu.nl/~piero001/index_AG_seminar.html

**Title**: Phase retrieval with time-frequency structured measurements

**Abstract**: Phase retrieval is the non-convex inverse problem of signal reconstruction from intensity measurements with respect to a measurement frame. This problem is motivated by practical applications, such as diffraction imaging and audio processing. The nature of the measurements in a particular application determines the structure of the measurement frame. This makes the study of the phase retrieval with structured, application relevant frames especially interesting.

In the talk, we are going to focus on phase retrieval with Gabor frames, where the measurement vectors follow time-frequency structure that naturally appears in imaging and acoustics applications. We will discuss how to achieve stable and efficient reconstruction with such measurements and how prior information about the signal class can be used to regularize the phase retrieval problem and reduce the number of measurements required for reconstruction.

**Title:**Generation and analysis of sparse random graphs with a given degree sequence

**Abstract:**For a given graphical degree sequence, there is typically a large number of simple graphs that satisfy it. We will consider the problem of uniformly sampling a graph from this set. This can also be viewed as a model for a random graph, i.e. a graph-valued random variable. In general, algorithms that realise such sampling have exponential complexity, but there are special classes of graphs where the complexity is less severe and could even be linear. In this talk, we will discuss several of such classes called sparse graphs and show that their uniform generation can be achieved in linear time using the so called sequential construction — non-uniformly placing one edge at a time in the course of m steps while updating the probabilities after each step. In the second part of the talk we will discuss the underlying random graph model and show that it gives rise to solutions of interesting nonlinear partial differential equations and can even be regarded as a method for solving such equations formally

**Title:**Random graph models with spatial and degree constraints

**Abstract**:

In this talk we consider random graph models with both spatial information (random geometric graphs) and a prescribed degree sequence (configuration model). When these constraints are considered separately, the random graph models are well understood. However, when imposed together, conflicts arise.

In the first part of this talk, we will consider an algorithm for sampling random graphs with spatial and degree constraints. In particular, we will consider a target degree sequence d_{n} and edge-length distribution f_{n}. Provided that d_{n} is bounded uniformly and f_{n} is not too large compared to the empirical distribution of the available edge-lengths, we will show that our algorithm randomly produces a graph with degree sequence dn and empirical edge-length distribution close to f_{n}.

In the second part, we will look into the emergence of a giant component in these random graph models. We make a first step into this direction by considering a d-dimensional torus partitioned into compartments forming a cubic lattice. We distribute vertices equally over these compartments, and only allow local edges inside compartments and between neighbouring compartments. We assume the number of compartments diverges when the number of vertices grows. Using connections with multitype branching processes, we will prove that if the num- ber of vertices per compartment grows quickly enough, then a giant component emerges under similar conditions on the degree sequence as for the standard configuration model.

All is based on work together with Ivan Kryven. The first part is based on [KV22], while the second part is based on [KV21].

[KV21] Ivan Kryven and Rik Versendaal. “Giant component in the configu- ration model under geometric constraints”. In: ArXiv preprint (2021). url: https://arxiv.org/abs/2108.04112.

[KV22] Ivan Kryven and Rik Versendaal. “Sequential construction of spatial networks with arbitrary degree sequence and edge length distribution”. In: ArXiv preprint (2022). url: https : / / arxiv . org / abs / 2207 . 08527.

__Felix Wierstra (UvA)__

Tile: A recognition principle for iterated suspensions as coalgebras over the little cubes operad

Abstract: In this talk I will discuss and prove a recognition principle for iterated suspensions as coalgebras over the little disks operad. This is based on joint work with Oisín Flynn-Connolly and José Moreno-Fernández.

For general information on the seminar series, and to subscribe to the mailing list, please consult the seminar webpage: __https://sites.google.com/view/nialltaggartmath/seminars/topics__.

**Abstract:Bayesian Methods for Uncertainty Quantification **

This presentation discusses Bayesian theory andits applications in the field of reliability engineering. It addresses thebasic theory, philosophy, and simulation techniques to compute the posteriordistribution such as Markov Chain Monte Carlo and Particle Filtering methods.Application examples are the life prediction of Lithium-ion batteries, bladesin turbine engine, computer model calibration with uncertainty using real data,and crack growth prediction of aircraft structures.

__First lecture: A brief historical survey__

The talk will be followed by drinks in the HFG library.

More info on the Kan memorial lectures:

__https://utrechtgeometrycentre.nl/daniel-kan-memorial-lectures/__

More info on the Kan memorial lectures:

__https://utrechtgeometrycentre.nl/daniel-kan-memorial-lectures/__

**Title**: Modeling the impact of Corona measures

**Abstract**: In this talk, I will discuss a model we have developed for the ministry of Health, Welfare and Sports to estimate the impact of Corona ticket measures (QR-code) on the spread of SARS-CoV-2 in the Netherlands. I will discuss how the underlying assumptions lead to the model formulation and I will briefly discuss some results.

Website of the UGC seminar (and the pure side of the MI-alks):

__Practical details will be sent by email to the staff and student mailing lists a few days before the event.__

__http://utrechtgeometrycentre.nl/ugc-seminar/__Website of the UGC seminar (and the pure side of the MI-alks):

__Practical details will be sent by email to the staff and student mailing lists a few days before the event.__

__http://utrechtgeometrycentre.nl/ugc-seminar/__