Researching intricate geometric and arithmetic objects
is the goal of the new Collaborative Research Centre Transregio 326 (TRR 326),
coordinated by Goethe University. On 25th May, the German Research
Foundation (DFG) announced that the TRR 326 would be funded with 9.2 million
euros for the next four years. The CRC 1039 “Signalling by fatty acid
derivatives and sphingolipids in health and disease", for which Goethe
University is spokesperson, will be continued and receive 9.6 million euros for
the third funding period. Two other TRRs in which Goethe University is involved
will also be funded by the DFG: In the TRR 211 “Strongly interacting matter under
extreme conditions", the spokesperson will switch from Goethe University to the
Technical University of Darmstadt (9.2 million euros). Finally, scientists from
Goethe University are also significantly involved in TRR 301 "The tropopause region in a changing atmosphere" (spokesperson:
Johannes Gutenberg University Mainz, €12.3 million).
FRANKFURT. Professor
Enrico Schleiff, President of Goethe University Frankfurt, congratulates the
scientists on their success: "Goethe University's commitment, particularly
in the Transregio Collaborative Research Centres, demonstrates our excellent
scientific networking in the region, especially in the natural sciences and
medicine. The association of the Rhine-Main universities of Frankfurt, Mainz
and Darmstadt, have given this regional cooperation a framework: There are now
more than 30 research associations and networks in this strategic alliance, and
last year we established the RMU degree programme so that talented students can
also benefit from RMU."
The mathematical exploration of
complicated geometric and arithmetic spaces with the help of uniformization is
the research topic of TRR 326
"Geometry and arithmetic of uniformized structures - GAUS".
Together with coordinator Goethe University Frankfurt, the Technical University
of Darmstadt and Heidelberg University successfully applied for TRR 326;
associated institutions are the Johannes Gutenberg University Mainz and the
Technical University of Munich. The concept of uniformization goes back to
ideas of Felix Klein and Henri Poincaré from the 19th century and seeks a
uniform description of certain geometric objects. A very simple example uniformization
can be illustrated with the slinky, a metal spiral toy which is able to
"run" down a staircase doing "somersaults". When pressed
together, it has - seen from above - the geometry of a circle. This circle can
be uniformized by pulling the metal spiral apart. It becomes particularly simple
when the spiral is completely unwound and, geometrically, is only a simple
wire. In order to preserve the information of the slinky, each spiral turn on
the wire is marked with a colour dot, which gives the wire a shifting symmetry
(you change levels in the spiral). A globally complicated geometric space (in our
example, the circle of the slinky) is replaced by a much simpler space (here a
straight line) without changing the local structure. The original complexity is
described by internal symmetries (illustrated in the example by periodic
markings) of the simpler space.
In TRR 326 GAUS, mathematicians deal with uniformization
of very complicated geometric spaces - this includes modern geometric concepts,
in particular tropical and p-adic geometries - and with analogous applications
of the uniformization technique to arithmetic (number-theoretic) questions.
Here, the researchers try to identify fundamental connections, for example to
moduli spaces, automorphic forms, Galois representations, and cohomological
structures. Professor Jakob Stix, mathematician at Goethe University and GAUS
spokesman, says: "With the SFB Transregio GAUS, we are building on the
extremely successful collaboration between TU Darmstadt and Goethe University
in the LOEWE priority 'Uniformed Structures in Arithmetic and Geometry' and the
DFG research group 'Symmetry, Geometry and Arithmetic' at TU Darmstadt and Heidelberg
University. I am very much looking forward to doing joint research with so many
outstanding colleagues."
The Collaborative
Research Centre 1039 "Signalling by fatty acid derivatives and
sphingolipids in health and disease," which Goethe University is now
continuing together with the Max Planck Institute for Heart and Lung Research
in Bad Nauheim, is entering its third funding period. The scientists are
studying a group of poorly water-soluble biomolecules, the lipids. As lipid
bilayers, they prominently form the membranes that surround our cells and also
divide the interior of the cells. As fats, they serve as energy storage for our
bodies.
However, CRC 1039 is investigating a
function that is still comparatively under-researched: Lipids are part of many
signalling pathways through which cells regulate growth and metabolism and
communicate with their environment. Dysregulated lipids are apparently
decisively involved in the development and progression of diseases such as diabetes,
cancer, inflammation, and neurodegenerative diseases. After fundamental work in
the first two funding periods, the third funding period focuses on
understanding the whole organism. Professor Josef Pfeilschifter, pharmacologist
at Goethe University and spokesman of SFB 1039, explains: "We want to
understand the lipid signalling network as a whole and thus develop innovative
ways to diagnose and treat a wide variety of diseases related to dysregulated
lipids. In doing so, we can rely on a long-standing and broad expertise in
'lipid signalling', which is also founded on the establishment of sophisticated
analytical methods based on mass spectrometry."
Scientists from Goethe University are
significantly involved in two other CRC Transregios:
How matter behaves under conditions of
extreme pressure and temperature, in which atoms overlap and fuse with each
other is being investigated by TRR 211
"Strongly interacting matter under extreme conditions", which is
entering its second funding period. For extremely short periods of time, such
states of matter can be created in particle accelerators, revealing something
about the strong interaction that holds atomic nuclei together. In the cosmos,
such extreme states of matter occur when, for example, neutron stars collide
with each other. BesidesGoethe University, the Technical University of
Darmstadt, which is the new host university, and Bielefeld University are also
involved in this collaborative research centre.
In the new TRR 301 "The tropopause region in a changing atmosphere",
atmospheric scientists will study the tropopause region: the zone in the
atmosphere that separates the lower "weather layer" (troposphere)
from the stratosphere above. The research focus is on the physical and chemical
processes of this region and their influence on planetary circulation and
climate. The main locations are the Johannes Gutenberg University Mainz (spokesperson)
and Goethe University Frankfurt. Also involved are the Technical University of
Darmstadt, the Ludwig Maximilian University of Munich, the Max Planck Institute
for Chemistry in Mainz, the Jülich Research Centre and the German Aerospace
Centre (DLR) in Oberpfaffenhofen.
Image for download:
http://www.uni-frankfurt.de/101626857
Caption:
Using the mathematical technique of uniformization,
complicated geometric spaces (here: the j-invariant as an automorphic function
on the uniformization of the moduli space of elliptic curves) can be represented
as highly symmetric geometric patterns. Credit: Michaelis Neururer
Further
information:
Professor Jakob Stix
Spokesman
TRR 326 „GAUS“
Institute for Mathematics
Goethe University Frankfurt
Tel: +49 69 798-28998
https://crc326gaus.de
stix@math.uni-frankfurt.de
Professor Josef Pfeilschifter
Spokesman
SFB 1039 “Signalling by fatty acid derivatives and sphingolipids in health and
disease"
Institute for General Pharmacology and Toxicology
Goethe University Frankfurt
Tel. +49 69
6301-6950
pfeilschifter@em.uni-frankfurt.de
https://www.lipidsignalling.de/de/home/index.php
TRR 211 „Strongly
interacting matter under extreme conditions“
https://crc-tr211.org/
TRR
301 „The tropopause region in a changing atmosphere“
https://tpchange.de/