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Arab News
6 days ago
- Politics
- Arab News
COP30 must make good on past climate pledges
In 2015, the landmark Paris climate agreement set the ambitious but necessary goal of limiting global warming to 1.5 degrees Celsius above pre-industrial levels, and ensuring that the increase stays 'well below' 2 C. With the average global surface temperature having already reached 1.1 C above the 20th-century baseline, time is running out to reach this goal. Yet governments so far have failed to agree on a strategy for doing so. At the 62nd session of the UN Climate Change Subsidiary Bodies (SB62) in Bonn last month — the negotiations intended to lay the groundwork for November's UN Climate Change Conference in Brazil — countries got so hung up on the details of the agenda that little progress was made. Such delays have long characterized the UN Framework Convention on Climate Change, but they are at odds with scientific reality, which demands rapid and unified action. Building consensus is, thus, a key challenge facing Brazil's COP30 presidency. The task ahead is formidable not only because of the challenges inherent in the UNFCCC process, but also because four interconnected global developments are undermining trust and impeding multilateral cooperation. First, the global-governance architecture, with the UN at its core, is showing signs of disarray. Institutions that were designed to nurture and facilitate cooperation are increasingly hamstrung by bureaucratic inertia and outdated organizational structures. With reform efforts gridlocked, the UN system risks losing its relevance, and multilateralism its credibility. Second, the rise of transactional diplomacy has meant countries prioritize their own short-term interests over collective long-term needs. This approach, based on a narrow conception of national interest, effectively precludes broad-based cooperation, as it erodes the norms that have traditionally underpinned international engagement. Brazil's COP30 presidency must eschew flashy results in favor of pragmatic pathways to deliver on past commitments. Jacinda Ardern, Carlos Lopes, and Laurence Tubiana Third, compromise is increasingly being rejected in favor of 'realism,' leading to extreme polarization and entrenched negotiating positions. Multilateral negotiations frequently come down to the wire, and the results are often disappointing, further encouraging transactional engagement at the expense of cooperation and compromise. Finally, climate change is increasingly taking a back seat to other challenges, with armed conflicts, a global trade slowdown, intensifying growth headwinds, and record debt levels consuming countries' political attention, diplomatic space, and financial resources. Brazil clearly has its work cut out. Above all, it must resist the tendency for COP presidencies to emphasize fresh agreements and ambitious commitments — the kind that grab headlines and make the negotiations look like a smashing success, but often fall short when the hard work of implementation begins. Brazil's COP30 presidency must eschew flashy results in favor of pragmatic pathways to deliver on past commitments. Fortunately, Brazil recognizes this. Its fourth letter to the international community outlines an action agenda aimed at making progress on what the world has 'already collectively agreed' during previous COPs and in the Paris climate agreement. Specifically, the agenda seeks to leverage existing initiatives to complete the implementation of the first 'global stocktake' under the Paris agreement, which was concluded at COP28. This focus on previously agreed outcomes is well-suited to the current geopolitical context, in which any agreement can be difficult to reach. Representatives at the SB62 in Bonn did not achieve a consensus, and last month's G7 summit failed to deliver a joint communique. Rather than perpetuating stalemates, the action agenda invites stakeholders to make progress where agreement already exists. The agenda also charts the way forward. It is organized into six thematic 'axes,' including stewarding forests, oceans, and biodiversity; transforming agriculture and food systems; and building resilience for cities, infrastructure, and water. 'Unleashing enablers and accelerators' in finance, technology, and capacity-building — the final, cross-cutting axis — will accelerate implementation at scale. Since responsibility for the implementation and governance of climate policy is distributed among many actors — which must have some level of trust that others are doing their part — the agenda also establishes 'transparency, monitoring, and accountability' as top priorities. To this end, Brazil's COP30 presidency should seek to deliver a set of shared principles and supportive mechanisms. As COP30 special envoys, we extend our full support to the action agenda. By emphasizing consolidation, rather than spectacle, Brazil is setting the stage for a highly productive COP30 — one focused on bridging divides, building trust, and delivering genuine progress. The task ahead is daunting, but the chance to rebuild momentum is real. Copyright: Project Syndicate.
Yahoo
21-07-2025
- Science
- Yahoo
Landmark Langlands Proof Advances Grand Unified Theory of Math
The Langlands program has inspired and befuddled mathematicians for more than 50 years. A major advance has now opened up new worlds for them to explore One of the biggest stories in science is quietly playing out in the world of abstract mathematics. Over the course of last year, researchers fulfilled a decades-old dream when they unveiled a proof of the geometric Langlands conjecture — a key piece of a group of interconnected problems called the Langlands programme. The proof — a gargantuan effort — validates the intricate and far-reaching Langlands programme, which is often hailed as the grand unified theory of mathematics but remains largely unproven. Yet the work's true impact might lie not in what it settles, but in the new avenues of inquiry it reveals. 'It's a huge triumph. But rather than closing a door, this proof throws open a dozen others,' says David Ben-Zvi at the University of Texas at Austin, who was not involved with the work. Proving the geometric Langlands conjecture has long been considered one of the deepest and most enigmatic pursuits in modern mathematics. Ultimately, it took a team of nine mathematicians to crack the problem, in a series of five papers spanning almost 1,000 pages. The group was led by Dennis Gaitsgory at the Max Planck Institute for Mathematics in Bonn, Germany, and Sam Raskin at Yale University in New Haven, Connecticut, who completed his PhD with Gaitsgory in 2014. [Sign up for Today in Science, a free daily newsletter] The magnitude of their accomplishment was quickly recognized by the mathematical community: in April, Gaitsgory received the US$3-million Breakthrough Prize in Mathematics, and Raskin was awarded a New Horizons prize for promising early-career mathematicians. Like many landmark results in mathematics, the proof promises to forge bridges between different areas, allowing the tools of one domain to tackle intractable problems in another. All told, it's a heady time for researchers in these fields. 'It gives us the strongest evidence yet that something we've believed in for decades is true,' says Ben-Zvi. 'Now we can finally ask: what does it really mean?' The hole story The Langlands programme traces its origins back 60 years, to the work of a young Canadian mathematician named Robert Langlands, who set out his vision in a handwritten letter to the leading mathematician André Weil. Over the decades, the programme attracted increasing attention from mathematicians, who marvelled at how all-encompassing it was. It was that feature that led Edward Frenkel at the University of California, Berkeley, who has made key contributions to the geometric side, to call it the grand unified theory of mathematics. Langlands' aim was to connect two very separate major branches of mathematics — number theory (the study of integers) and harmonic analysis (the study of how complicated signals or functions break down into simple waves). A special case of the Langlands programme is the epic proof that Andrew Wiles published, in 1995, of Fermat's last theorem — that no three positive integers a, b and c satisfy the equation an + bn = cn if n is an integer greater than 2. The geometric Langlands conjecture was first developed in the 1980s by Vladimir Drinfeld, then at the B. Verkin Institute for Low Temperature Physics and Engineering in Kharkiv, Ukraine. Like the original or arithmetic form of the Langlands conjecture, the geometric conjecture also makes a type of connection: it suggests a correspondence between two different sets of mathematical objects. Although the fields linked by the arithmetic form of Langlands are separate mathematical 'worlds', the differences between the two sides of the geometric conjecture are not so pronounced. Both concern properties of Riemann surfaces, which are 'complex manifolds' — structures with coordinates that are complex numbers (with real and imaginary parts). These manifolds can take the form of spheres, doughnuts or pretzel-like shapes with two or more holes. Many mathematicians strongly suspect that the 'closeness' of the two sides means the proof of the geometric Langlands conjecture could eventually offer some traction for furthering the arithmetic version, in which the relationships are more mysterious. 'To truly understand the Langlands correspondence, we have to realize that the 'two worlds' in it are not that different — rather, they are two facets of one and the same world,' says Frenkel. 'Seeing this unity requires a new vision, a new understanding. We are still far from it in the original formulation. But the fact that, for Riemann surfaces, the two worlds sort of coalesce means that we are getting closer to finding this secret unity underlying the whole programme,' he adds. One side of the geometric Langlands conjecture concerns a characteristic called a fundamental group. In basic terms, the fundamental group of a Riemann surface describes all the distinct ways in which loops can be tied around it. With a doughnut, for example, a loop can run horizontally around the outer edge or vertically through the hole and around the outside. The geometric Langlands deals with the 'representation' of a surface's fundamental group, which expresses the group's properties as matrices (grids of numbers). The other side of the geometric Langlands programme has to do with special kinds of 'sheaves'. These tools of algebraic geometry are rules that allot 'vector spaces' (where vectors — arrows — can be added and multiplied) to points on a manifold in much the same way as a function describing a gravitational field, say, can assign numbers for the strength of the field to points in standard 3D space. Bridgework in progress Work on bridging this divide began back in the 1990s. Using earlier work on Kac–Moody algebras, which 'translate' between representations and sheaves, Drinfeld and Alexander Beilinson, both now at the University of Chicago, Illinois, described how to build the right kind of sheaves to make the connection. Their paper (see nearly 400 pages long, has never been formally published. Gaitsgory, together with Dima Arinkin at the University of Wisconsin–Madison, made this relationship more precise in 2012; then, working alone, Gaitsgory followed up with a step-by-step outline of how the geometric Langlands might be proved. 'The conjecture as such sounds pretty baroque — and not just to outsiders,' says Ben-Zvi. 'I think people are much more excited about the proof of geometric Langlands now than they would have been a decade ago, because we understand better why it's the right kind of question to ask, and why it might be useful for things in number theory.' One of the most immediate consequences of the new proof is the boost it provides to research on 'local' versions of the different Langlands conjectures, which 'zoom in' on particular objects in the 'global' settings. In the case of the geometric Langlands programme, for example, the local version is concerned with the properties of objects associated with discs around points on a Riemann surface — rather than the whole manifold, which is the domain of the 'global' version. Peter Scholze, at the Max Planck Institute for Mathematics, has been instrumental in forging connections between the local and global Langlands programmes. But initially, even he was daunted by the geometric side. 'To tell the truth,' Scholze says, 'until around 2014, the geometric Langlands programme looked incomprehensible to me.' That changed when Laurent Fargues at the Institute of Mathematics of Jussieu in Paris proposed a reimagining of the local arithmetic Langlands conjectures in geometrical terms. Working together, Scholze and Fargues spent seven years showing that this strategy could help to make progress on proving a version of the local arithmetic Langlands conjecture concerning the p-adic numbers, which involve the primes and their powers. They connected it to the global geometric version that the team led by Gaitsgory and Raskin later proved. The papers by Scholze and Fargues built what Scholze describes as a 'wormhole' between the two areas, allowing methods and structures from the global geometric Langlands programme to be imported into the local arithmetic context. 'So I'm really happy about the proof,' Scholze says. 'I think it's a tremendous achievement and am mining it for parts.' Quantum connection According to some researchers, one of the most surprising bridges that the geometric Langlands programme has built is to theoretical physics. Since the 1970s, physicists have explored a quantum analogue of a classical symmetry: that swapping electric and magnetic fields in Maxwell's equations, which describe how the two fields interact, leaves the equations unchanged. This elegant symmetry underpins a broader idea in quantum field theory, known as S-duality. In 2007, Edward Witten at the Institute for Advanced Study (IAS) in Princeton, New Jersey, and Anton Kapustin at the California Institute of Technology in Pasadena were able to show that S-duality in certain four-dimensional gauge theories — a class of theories that includes the standard model of particle physics — possesses the same symmetry that appears in the geometric Langlands correspondence. 'Seemingly esoteric notions of the geometric Langlands program,' the pair wrote, 'arise naturally from the physics.' Although their theories include hypothetical particles, called superpartners, that have never been observed, their insight suggests that geometric Langlands is not just a rarefied idea in pure mathematics; instead, it can be seen as a shadow of a deep symmetry in quantum physics. 'I do think it is fascinating that the Langlands programme has this counterpart in quantum field theory,' says Witten. 'And I think this might eventually be important in the mathematical development of the Langlands programme.' Among the first to take that possibility seriously was Minhyong Kim, director of the International Centre for Mathematical Sciences in Edinburgh, UK. 'Even simple-sounding problems in number theory — like Fermat's last theorem — are hard,' he says. One way to make headway is by using ideas from physics, like those in Witten and Kapustin's work, as a sort of metaphor for number-theoretic problems, such as the arithmetic Langlands conjecture. Kim is working on making these metaphors more rigorous. 'I take various constructions in quantum field theory and try to cook up precise number-theoretic analogues,' he says. Ben-Zvi, together with Yiannis Sakellaridis at Johns Hopkins University in Baltimore, Maryland, and Akshay Venkatesh at the IAS, is similarly seeking inspiration from theoretical physics, with a sweeping project that seeks to reimagine the whole Langlands programme from the perspective of gauge theory. Witten and Kapustin studied two gauge theories connected by S-duality, meaning that, although they look very different mathematically, the theories are equivalent descriptions of reality. Building on this, Ben-Zvi and his colleagues are investigating how charged materials behave in each theory, translating their dual descriptions into a network of interlinked mathematical conjectures. 'Their work really stimulated a lot of research, especially in the number-theory world,' says Raskin. 'There's a lot of people who are working in that circle of ideas now.' One of their most striking results concerns a two-way relationship between quite different mathematical objects called periods and L-functions. (The Riemann hypothesis, considered perhaps the most important unsolved problem in mathematics, is focused on the behaviour of a type of L-function.) Periods are a part of harmonic analysis, whereas L-functions are from the realm of number theory — the two sides of Langlands' original conjectures. However, through the lens of physics, Ben-Zvi and his colleagues showed that the relationship between periods and L-functions also mirrors that of the geometric programme. Hunting deeper truth Many mathematicians are confident that the proof of the geometric conjecture will stand, but it will take years to peer review the papers setting it out, which have all been submitted to journals. Gaitsgory, however, is already pushing forward on several fronts. For instance, the existing proof addresses the 'unramified' case, in which the terrain around points on the Riemann surface is well behaved. Gaitsgory and his collaborators are now hoping to extend their results to the more intricate, ramified case by accounting for more-complex behaviour around points as well as for singularities or 'punctures' in the surface. To that end, they are extending their work to the local geometric Langlands conjecture to understand in more detail what happens around a single point — and collaborating with, among others, Jessica Fintzen at the University of Bonn. 'This result opens the door to a whole new range of investigations — and that's where our interests start to converge, even though we come from very different worlds,' she says. 'Now they're looking to generalize the proof, and that's what's drawing me deeper into the geometric Langlands. Somehow, the proof's the beginning and not the end.' Fintzen studies the representations of p-adic groups — groups of matrices where the entries are p-adic numbers. She constructs the matrices explicitly — essentially, deriving a recipe for writing them down — and this seems to be the kind of local information that must be incorporated into the global geometric case to ramify it, Gaitsgory says. What began as a set of deep conjectures linking abstract branches of mathematics has evolved into a thriving, multidisciplinary effort that stretches from the foundations of number theory to the edges of quantum physics. The Langlands correspondence might not yet be the grand unified theory of mathematics, but the proof of its geometric arm is a nexus of ideas that will probably shape the field for years to come. 'The Langlands correspondence points to much deeper structures in mathematics that we're only scratching the surface of,' says Frenkel. 'We don't really understand what they are. They're still behind the curtains.' This article is reproduced with permission and was first published on July 16, 2025. Solve the daily Crossword
Arab News
21-07-2025
- Politics
- Arab News
Taliban sends envoys to Germany to coordinate deportations
BERLIN: The German government said Monday that two new envoys had been sent by Afghanistan's Taliban administration to help coordinate deportations, days after 81 convicted Afghans were sent back to their homeland. The flight on Friday was the second from Germany since expulsions to Afghanistan resumed last year. Germany does not recognize the Taliban leaders in Afghanistan but does have 'technical contacts' on the deportations, which have been facilitated by Qatar. Government spokesman Stefan Kornelius said that during the exchanges 'it has been agreed that two representatives of the Afghan administration will be incorporated' into Afghanistan's missions in Germany. A foreign ministry source later confirmed to AFP that the two envoys had arrived in Germany over the weekend. 'They are currently going through the normal registration process before they begin their work,' the source said. According to the Frankfurter Allgemeine Zeitung (FAZ) daily, the two envoys will work at the Afghan embassy in Berlin and at the country's consulate in the western city of Bonn. The Taliban authorities demanded this step in return for making last Friday's flight possible, the paper reported. The FAZ said that the envoys had already worked in consular services and were not considered extremists. Germany stopped deportations to Afghanistan and closed its embassy in Kabul following the Taliban movement's return to power in 2021. However last year the last German government resumed expulsions with a flight in August carrying 28 Afghans. Current chancellor Friedrich Merz has vowed to continue deportations, having made a tougher line on immigration a key campaign theme in February's general election. Kornelius said that further flights were in the offing. 'The government has committed to systematic expulsions of those convicted of crimes and this will not be accomplished with just one flight,' he said.
The Guardian
09-07-2025
- Politics
- The Guardian
John le Carré: the constant researcher
I can testify to the accuracy of John le Carré's research, which you note with reference to a new exhibition at Oxford's Bodleian libraries (8 July). When researching British foreign policy, I spent a day in the embassy in Bonn in 1973. It struck me as so much like its portrayal in A Small Town in Germany that I remarked that if someone came pushing the registry trolley I would not be surprised to hear it squeak, as he had described it. 'It's a pity you weren't here two or three years ago,' came the reply, 'you would have recognised several of the characters as well.'William WallaceLiberal Democrat, House of Lords I was never a fan of Norman Tebbit (Obituaries, 8 July) but an ex briefly worked security at Conservative HQ and had nothing but praise for him as the only person who said hello and goodbye to everyone by name every KimberPlymouth Just as John Smith is considered by many to have been the greatest Labour prime minister we never had, perhaps the same could be said of Norman Tebbit for the FullerAmpthill, Bedfordshire I was intrigued by the quoted advice that 'men should think about shortening their penis' as a method to strengthen the pelvic floor (Don't 'power pee' – but do grab a mirror: 13 easy, effective ways to protect your pelvic floor, 8 July). Disappointingly, it was not explained how we might achieve this YoungsDrinkstone, Suffolk Re (Whatever the truth of The Salt Path, I know why people wanted to believe it, 8 July): is it The Pinch of Salt Path?Sarah HannDorridge, West Midlands Have an opinion on anything you've read in the Guardian today? Please email us your letter and it will be considered for publication in our letters section.
The Sun
08-07-2025
- Entertainment
- The Sun
Mystery as huge UK band cancel two gigs just hours before they're due on stage blaming ‘unforeseen circumstances'
MASSIVE Attack fans have been left heartbroken after the band cancelled two gigs just hours before being due on stage. Blaming "unforeseen circumstances", the trip hop collective announced the first cancellation on Monday night, ahead of their KUNST!RASEN gig in Bonn, Germany. 3 According to local reports from the General-Anzeiger, fans received word of the concert being called off just two hours before doors were set to open. A brief statement from organisers, emailed to local news outlet General-Anzeiger, read: 'Due to unforeseen circumstances, the Massive Attack concert has been canceled today. Tickets can be returned where they were purchased.' No further reason was provided, and follow-up requests for clarification were met with silence - fuelling frustration among ticketholders, some of whom had already travelled long distances for the show. One fan wrote on Reddit: 'My girlfriend is currently in the airport and she just saw the news. She's in tears. I don't know how to calm her.' Another simply said: 'Totally disappointing.' The Bonn concert wasn't the only one scrapped at the last minute. A second show — scheduled for Vienna the following night — was also pulled, again with no detailed explanation. Speculation online has quickly mounted, with some fans suggesting political reasons could be behind the decision. In recent gigs, Massive Attack have openly shown support for Palestine, screening pro-Palestinian documentaries and waving Palestinian flags on stage. Some Reddit users have speculated that this stance may have clashed with Germany's strict new regulations around political expression, particularly rules that have controversially redefined some support for Palestine as antisemitic. Massive Attack performs Angel at Wireless Festival One suggested: 'Playing a pro Palestine documentary & waving the flag would be against the law.' It comes less than a week after Massive Attack headlined Poland's Open'er Festival with a politically-charged set that included footage of a devastated Gaza, a dedication to the Palestinian people and chants of 'Free Palestine' from the crowd. Frontman Robert Del Naja told fans: 'Never again must mean never again for everybody.' So far, the band have not addressed the cancellations publicly - and they do not have any further dates lined up. Representatives for Massive Attack have been contacted for comment. 3 3
