Postdoc at Institut des Hautes Études Scientifiques
Lukas Nakamura received his doctoral degree in mathematics from Uppsala University in 2024
Thanks to a grant from the Knut and Alice Wallenberg Foundation
he will hold a postdoctoral position with Professor Maxim Kontsevich
Institut des Hautes Études Scientifiques (IHES)
the topic of this project was created in the nineteenth century
neither quantum mechanics nor Einstein’s general theory of relativity
let alone the string theory of modern physics
Geometry grew from the need to replace Newton’s complicated differential equations with simpler methods of describing motion
the trajectory of a moving object is determined by its position and velocity – by a pair of quantities that together form a two-dimensional surface: the basic structure of symplectic geometry.
symplectic geometry has experienced a renaissance
The twentieth century saw the development of two new pillars of physics: quantum mechanics
which describes the smallest parts of the universe
and Albert Einstein’s general theory of relativity
and one promising theory for this reconciliation is called string theory
This builds our world in eleven dimensions rather than Einstein’s four
and its smallest components are tiny strings instead of quantum particles.
Modern symplectic geometry is further developed in interaction with string theory and quantum field theory
Nowadays it not only tackles two-dimensional spaces
but all abstract spaces with an even number of dimensions
Spaces with odd dimensions are treated by contact geometry
which is closely related to symplectic geometry
The interaction between these two geometries and mathematical operations inside and in between different geometric spaces are the subjects of the current project.
Knut and Alice Wallenberg Foundation has since its establishment in 1917 awarded over SEK 39 billion in grants
In 2024 the yearly grants to excellent basic research and education in Sweden was in total almost SEK 2.4 billion
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‘Dutch-style’ roundabouts are becoming increasingly common in France
and are designed to enable vehicle drivers and cyclists to better ‘co-exist’
The roundabouts are so-called because they are inspired by the Netherlands where cycling is very popular
They are designed to make it safer for cyclists to use and reduce the risk of blind spots and dangerous vehicle-bike collisions
They have a ‘second’ roundabout - which is a cycle lane - around the main one used by motorised vehicles
They are designed to offer everyone the best possible visibility at every junction
Cyclists have priority when entering and exiting the roundabout
Read also: Nice trials video software to fine drivers who block cycle routesRead more: New type of traffic light aims to improve cyclist safety in France
Some were recently built in the Paris region
notably in the towns of Bures-sur-Yvette (Essonne) and in Créteil (Val-de-Marne).
Another was put in place in Clermont-Ferrand (Puy-de-Dôme) last year
after they were also introduced in Rennes (Ille-et-Vilaine) and Brest (Finistère)
They appear to be well-used and well-received by cyclists and may become even more popular and widespread as a result
cycling associations have said that there is still work to be done to convince motorists of the new system.
For example, the group Mieux se déplacer à bicyclette (‘Getting around better by bike’) have been campaigning for better awareness and increased adoption of this type of roundabout in a bid to win over more drivers, reports Capital
The roundabouts come after a report published in 2022 showed a sharp rise in the number of cyclist deaths - up 30% compared to 2019
This was blamed partly on the reported increase in cyclists on the roads since the Covid pandemic
In early 2023, a serious crash - in which a drunk driver ran into the back of a group of young bike riders in Brittany, seriously injuring two of them - prompted renewed debates on how to make cycling safer in France
Read also: France to spend €43m to improve cycling paths
safety campaigner Teodoro Bartuccio - an Olympic cycling trainer
who founded the Mon vélo est une vie association (‘My bike is a life’) - called for an in-depth debate on transport to decide how to make cycling safer
“We have worked hard in Paris and other cities on cycle lanes and it is starting to have an effect
because there are more and more cyclists,” he told The Connexion.
he called for more to be done in the countryside and warned that many cyclists had even experienced “deliberate violence from motorists”
an SUV driver in Paris was charged with murder and is accused of deliberately running over a cyclist in a road rage incident
The incident sparked protests calling for a crackdown on road rage and improved cyclist safety in France
We recap the rules on safety and bike condition
New lights have been authorised and cyclists can now (legally) ride side by side in certain circumstances
With 8 Fields Medallists since its creation
the Institut des Hautes Études Scientifiques (IHES) in Bures-sur-Yvette is one of the most recognized global institutions in mathematics
We visit the institution with its director
who has served as a permanent Professor at the Institut des Hautes Études Scientifiques (IHES) since 2016
has just been awarded the prestigious Fields Medal
It is one more medallist for the IHES
which is among the world's institutions that can boast the most Fields Medals
The IHES also has a highly developed visitors programme
hosting 200 international scientists per year for average stays of two and a half months
with housing and offices available for their entire stay
and we expect nothing in return from our invitees
The goal is to attract those who produce new and original science
so that they can directly discuss with their peers and explain their approach
a method that is much more effective than reading publications
U. : There are no calls for applications for permanent professor positions
The Institute's Scientific Council continually works to identify the most promising researchers in mathematics and theoretical physics
and conducts a rigorous examination process before extending a definitive offer
the salary remains our primary difficulty in the face of international competition
that they would be spared administrative constraints
and that they could surround themselves with a team
These advantages are familiar to the community
The living environment offered by our magnificent institute amid a wooded estate
along with the proximity of the Université Paris-Saclay ecosystem
are also obviously beneficial factors.
We also receive applications from visitors and postdoctoral fellows
with the Scientific Council making selections twice per year
and even more so in the fields in which our scientists work
which is very characteristic of the institute
The IHES is a founding member of the new Université Paris-Saclay
U. : It is highly advantageous on numerous levels
it gives us international visibility: the ARWU
or the famous "Shanghai ranking," ranked l'Université Paris-Saclay number one worldwide in mathematics two years in a row
The collaboration also offers more possibilities for professors to supervise theses in collaboration with doctoral schools such as the Jacques Hadamard Doctoral School of Mathematics
or the Ile-de-France Doctoral School of Physics
We have also emphasized partnerships by organising events such as the Lectures series
which have become anticipated and prestigious meetings
in addition to seminars and the start of the school year for masters students and doctoral schools.
How is the IHES positioned within the international community
U. : The institute is distinctive in this regard
It was modelled after the Institute for Advanced Study at Princeton
although that institute includes more disciplines than us
this interdisciplinary dimension is not absent from the IHES
where there is true interaction between mathematicians and physicists
Only a small number of other institutes abroad
such as the Korea Institute for Advanced Study in Seoul
You have been directing the institute for 9 years
U. : We have developed a number of initiatives that are already at the contract stage
Postdoctoral fellows were considered visitors
and as such were not employees of the institute
We also offer new types of tenure-track professorships over five years
The leading Chinese probabilist Yilin Wang joined the IHES this year thanks to such a contract
we emphasized our interactions with l'Université Paris-Saclay
in which a scientific committee of experts meets one hundred researchers at IHES to present the state of research in a particular field
This model is very popular with both the organisers and participants
for instance through the adoption of an Ethics Charter by our Scientific Council
the Scientific Council expanded with the arrival of three excellent women mathematicians at the institute (Fanny Cassel
CNRS Senior Researcher; Laure Saint-Raymond
the first permanent female professor at the IHES; and Yilin Wang). We also have many projects for the future
notably with a view to recruiting new permanent professors
What is your view of the role of French mathematics in the world
U. : French academic mathematics continues to do well
in 2021 l'université Paris-Saclay and Sorbonne Université came in first and third respectively in the Shanghai ranking
There is a tremendous concentration of high-level mathematics in France
with great wealth within laboratories in the provinces as well
We are one of the nations with the most Fields Medallists
This demonstrates a genuine tradition of mathematics at the highest level
It is nevertheless important to underscore the dichotomy between excellent academic mathematics and scholastic mathematics
Perhaps there is a lack of scientists in the circles around political decision makers to stress these concerns
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Alain Connes (born April 1, 1947, Draguignan, France) is a French mathematician who won the Fields Medal in 1982 for his work in operator theory
Connes’s publications included Géométrie non commutative (1990; Noncommutative Geometry)
He served as editor for the Journal of Functional Analysis
and the Journal of Noncommutative Geometry
By David Shiga
Wormholes could provide portals to other worlds (Illustration: NASA/Les Bossinas)
The objects scientists think are black holes could instead be wormholes leading to other universes
it would help resolve a quantum conundrum known as the black hole information paradox
but critics say it would also raise new problems
such as how the wormholes would form in the first place
A black hole is an object with such a powerful gravitational field that nothing
can escape it if it strays within a boundary known as the event horizon
Einstein’s theory of general relativity says black holes should form whenever matter is squeezed into a small enough space
astronomers have identified many objects that appear to be black holes based on observations of how matter swirls around them
But physicists Thibault Damour of the Institut des Hautes Etudes Scientifiques in Bures-sur-Yvette
and Sergey Solodukhin of International University Bremen in Germany now say that these objects could be structures called wormholes instead
Wormholes are warps in the fabric of space-time that connect one place to another
If you imagine the universe as a two-dimensional sheet
you can picture a wormhole as a “throat” connecting our sheet to another one
the other sheet could be a universe of its own
Damour and Solodukhin studied what such a wormhole might look like
and were surprised to discover that it would mimic a black hole so well that it would be virtually impossible to tell the difference
Matter would swirl around a wormhole in the same way as for a black hole
since both objects distort the space around them in the same way
One might hope to distinguish the two by something called Hawking radiation
an emission of particles and light which should only come from black holes and would have a characteristic energy spectrum
But this radiation is so weak that it would be completely swamped by other sources
such as the background glow of microwaves left over from the big bang
Another difference one might hope to exploit is that unlike black holes
This means that things could go in a wormhole and come back out again
theorists say one variety of wormhole wraps back onto itself
But this does not provide a foolproof test either
Depending on the detailed shape of the wormhole
it could take billions of years or more for things to pop back out after falling in
even the oldest wormholes in our universe would not have had time to spit anything back out yet
It seems the only way to decide the issue for sure with astronomical black holes is to make a daring plunge inside
the incredibly strong gravitational field inside would tear apart every atom in your body
you might find yourself in another universe on the other side
the wormhole would tend to suck you back in and carry you back to the opening in your universe
“The spaceship would do this yo-yo motion,” Damour told New Scientist
then you can escape from the attracting power of the wormhole and explore” the space on the other side
But a friend in either universe might have to wait billions of years to hear back from you
since the transit time could be excruciatingly long
Such a delay would make meaningful communication with anyone on the other side impossible
But the delay gets smaller with smaller wormholes
If a microscopic wormhole could be found or constructed
the delay across it could be as short as a few seconds
potentially making two-way communication possible
Stephen Hsu of the University of Oregon in Eugene
who has studied the formation of black holes and the properties of wormholes
says he agrees that distinguishing between the two types of object with observations is practically impossible
“The most important property of a black hole – that there is a ‘point of no return’ for an object falling in – is not something we can test at the moment,” he told New Scientist
he says the objects out there suspected to be black holes probably really are black holes rather than wormholes
There are plausible scenarios for forming black holes
but it is not clear how you would form a wormhole
“Wormholes that might be confused with a macroscopic black hole require some kind of exotic matter to stabilise them
and it is not known whether such exotic matter exists,” he says
Solodukhin says that a wormhole might form in much the same way that black holes form
Physicists normally expect in these situations that a black hole would be produced
but Solodukhin says that quantum effects may stop the collapse just short of producing a black hole
He says this mechanism might be inevitable in a more complete picture of physics that unites gravity and quantum mechanics – a longstanding goal of physics
then wherever we used to expect black holes to form
And there might be a way to test the conjecture. Some physicists say that future particle accelerator experiments could produce microscopic black holes (see Atom smasher may give birth to ‘Black Saturns’)
Such tiny black holes would emit measurable amounts of Hawking radiation
proving that they are black holes rather than wormholes
and microscopic wormholes are formed instead
you would actually see if it is a black hole or a wormhole,” he says
An added benefit of wormholes is that they could resolve the so-called black hole information paradox. The only way anything can exit a black hole is in the form of Hawking radiation, but it is not clear how the radiation carries information about the original object that was swallowed. This scrambling effect conflicts with quantum mechanics, which forbids such erasing of information (see Black holes: The ultimate quantum computers?)
wormholes are much better than black holes because all these problems with information loss don’t exist in this case,” Solodukhin says
things are free to leave without first being converted into Hawking radiation
so there is no problem with lost information
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