Sam Raskin, a mathematician and professor at Yale University, has achieved a monumental accomplishment in mathematics by solving, alongside a team of experts, a crucial part of the Langlands Conjectures, a problem regarded as a true “Rosetta Stone” for mathematical study.
This work, done in collaboration with Dennis Gaitsgory and seven other mathematicians, has resulted in proving a geometric component of these conjectures, a breakthrough that has been hailed as a fundamental milestone for the mathematical understanding of deep connections between various areas that, for a long time, were thought to be unrelated.
The research spans five academic studies, totaling over 900 pages, which, after decades of collective effort, culminate in this demonstration of the Langlands Conjectures in their geometric form.
To grasp the magnitude of this work, it is essential to understand the proposition of Robert Langlands, a Canadian mathematician who suggested in the 1960s the possibility of hidden and complex connections between number theory, harmonic analysis, and geometry. These three traditionally independent areas might find a common language that would allow them to translate into one another, much like different languages.
Proving this hypothesis would represent a profound shift in how we understand certain mathematical structures, as it would open the doors to new ways of solving problems that have thus far remained enigmatic. Langlands, in essence, proposed a theoretical framework in which seemingly unrelated mathematical structures could be linked through deep symmetries and patterns.
The geometric part of this conjecture is what Raskin and his team have resolved. This breakthrough, known as the solution to the “geometric Langlands”, represents a monumental advancement not only for pure mathematics but also for other sciences such as theoretical physics. Physicists have shown interest in this work because one of the key elements of Langlands is a group of geometric symmetry that could help to understand natural phenomena, such as the interactions between electricity and magnetism.
Raskin, whose mathematical vision is based on the idea of discovering elements of nature through abstract structures, commented that he sees his work as a continuous exploration of a mathematical universe that never ceases to amaze with its complexity and depth.
The process that led to the final solution began to take shape in 2020, when Raskin, then a professor at the University of Texas at Austin, collaborated on a study addressing the harmonic analysis of the Langlands Conjectures, a concept that allows functions to be broken down into simpler “waves”. This analysis laid the groundwork for the geometric aspect of the project, and in 2022, Raskin and one of his students expanded these findings to apply them to the geometric Langlands. Solving this part of the problem required overcoming complex mathematical challenges, such as dealing with “irreducible representations”, a concept in representation theory.
Finally, this year, the team concluded their work in five detailed studies, thereby consolidating a general solution for all the group structures involved in the geometric Langlands. Raskin expressed satisfaction in stating that they achieved a robust and verifiable proof. As he himself pointed out, in mathematics, there is the privilege of saying with certainty that something is true or false; and in this case, they can affirm that all prior intuition and theories have been confirmed.
This achievement by Sam Raskin and his team marks a turning point in the field of mathematics, not only for solving a long-standing theoretical problem but also for the future implications of their work. The solution to the geometric Langlands could open new avenues in understanding physical phenomena and in creating mathematical tools to solve problems that have not yet been addressed.
SOURCES
D. Arinkin, D. Beraldo, J. Campbell, L. Chen, J. Faergeman, D. Gaitsgory, K. Lin, S. Raskin and N. Rozenblyum, Proof of the Geometric Langlands Conjecture.
- Share on:
Discover more from LBV Magazine English Edition
Subscribe to get the latest posts sent to your email.
The Newly Formed Earth Was a Dry and Hot Place: A Theory Explains How Water Arrived Here and on Other Planets of the Solar System
A group of scientists from the Paris Observatory has proposed a new theory about how water arrived on Earth, a key question for understanding the emergence of life on our…
Analysis of Mesopotamian Texts in Akkadian Reveals How Emotions Were Experienced: Love Was Felt in the Knees
Love and emotions have been universal themes throughout human history, expressed in diverse ways but with commonalities across different cultures and eras. A fascinating recent study reveals that people in…
Veritable Records of the Joseon Dynasty, the chronicles of the Korean kingdom spanning five centuries, are the longest uninterrupted ones of a single dynasty in history
In 2006, the Seoul government announced that the Guksa Pyeonchan Wiwonhoe (National Institute of Korean History) had undertaken the digitization of the Joseon Wangjo Sillok, that is, the “Veritable Records…
Tsakonian Is the Only Current Greek Language That Derives from the One Spoken by the Spartans
Although it is officially considered a dialect, Tsakonian is a divergent variety of Greek frequently classified as a separate language, as it is not intelligible to speakers of standard Modern…
Structures Found in Iraq Reveal the Deliberate Collapse of One of the First Centralized Governments Over 5,000 Years Ago
At the archaeological site of Shakhi Kora, located in the Iraqi Kurdistan region, excavations have provided new insights into the origin and evolution of the earliest state institutions, dated to…
The “Cella Vinaria” and Grounds of a Villa Where Famous 2nd Century Saguntine Wine Mentioned by Roman Writers Was Produced, discovered in Spain
Excavations conducted at the Sant Gregori site, located in the town of Burriana (Castellón, Spain), have brought to light significant remnants of a maritime villa from the Roman era that…
Spectacular Bronze Statues and Thousands of Coins Found in the Etruscan-Roman Sanctuary of San Casciano dei Bagni
In the picturesque municipality of San Casciano dei Bagni, located in the Italian province of Siena, archaeological discoveries continue to shed light on the rich history of the Etruscan-Roman sanctuary…
Why Inuit Culture Survived in Greenland While the Norse Disappeared: Children’s Toys Made the Difference
During the Little Ice Age, a period marked by freezing temperatures and extreme climatic conditions, two cultures coexisted in Greenland: the Inuit and the Norse. Although both groups faced the…
Deutsche Physik: The Germanized and Aryan Physics Some Nazi Scientists Opposed to Einstein’s Relativity
What does physics have to do with politics? Or racism? The answer is nothing… unless we are talking about Germany in the first half of the 20th century. In that…
Tiny Black Holes Created at the Beginning of the Universe Could Be Hiding in Hollow Planets, Rocks, and Ancient Buildings on Earth
Black holes result from the collapse of massive stars after they exhaust their fuel, creating regions of spacetime where not even light can escape. However, new research suggests that the…
Something went wrong. Please refresh the page and/or try again.
