# Research support for biostatistics and L-functions

Danish Council for Independent Research | Natural Sciences awards 51 DFF-Research Project Grants to researchers in Denmark to the sum of approximately DKK 159 million. Two of these projects are led by researchers from the Department of Mathematical Sciences.

Professor Helle Sørensen from the Section for Statistics and Probability Theory gets DKK two million for the project "Quantitative regression for longitudinal functional data". From the project description:

"Longitudinal functional data consists of curves (functions), which have been measured repeatedly for several individuals.

There is a well-established model framework to describe the relationship between the expected value of a measured response variable and functional predictors. We aim at developing a more flexible class of models, where we model the link between quantiles in the distribution of the response variable, yet taking into account the dependence between observations from the same individual.

As an illustration, we will analyze data from sows that feed their piglets, and investigate how curves over temperature and humidity affect the feed intake of the sows.

Models both with and without time-dependent effects of functional predictors will be developed and investigated, including statistical tests that examine if the effects are constant over time. In the specific example, this corresponds to determining whether the sows react differently to humidity or temperature throughout the suckling period.”

## New information about L-functions

Morten S. Risager from the research group Algebra and Number Theory has also received DKK two million for the project "L-functions". From the project description:

Infinite sums such as \[1+\frac{1}{2^x}+\frac{1}{3^x}+\frac{1}{4^x}+...\] or \[1-\frac{1}{2^x}+\frac{1}{3^x}-\frac{1}{4^x}+...,\] where \(x\) is a complex number, play a fundamental role in number theory. We have long understood many of the must fundamental properties of these sums, but they still keep some of their most profound secrets. If we could reveal these secrets we would gain new information about about primes and how they distribute themselve among the natural numbers. Primes play an key role in many parts of modern datasecurity.

This project aims to understand how the values of infinite families of infinite sums, like the ones described above, relate to one another. Is it possible to say something about parts of the family from information about the rest of the family? Or to what extend does the family change if one changes signs on parts of the family?

We have good conjectural answers to these questions, and the project aims to prove whether these conjectures are correct or wrong. If they are correct it may be used to better understand certain mathematical counting problems.

## Operator algebras

At the University of Southern Denmark, Professor Wojciech Szymanski is awarded DKK 5.5 million for the project "Automorphisms and Invariants of Operator Algebras".

Participants in the project include Søren Eilers, Ryszard Nest and Asger Törnquist from MATH/UCPH, who, among other things, have the opportunity to participate in international knowledge sharing.

Funds have been earmarked for a large conference held at MATH.

The project falls within the field of operator algebras - a mathematical discipline, located in the intersection between analysis, algebra and topology. The main focus of the project is on complex systems of linear transformations and the understanding of their symmetries and dynamic development.

The project resumes a tradition with a formalized operator network between UCPH, SDU and AU, founded in the 1980s.

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