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-features translates into a geometric duality that makes sense inside the geometric Langlands system and originates from the duality amongst electrical energy and magnetism. Physics and arithmetic turn out to be echoes of one another, in a way that echoes through the Langlands software.

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To take a toy illustration, think about you've got a triangle. Evaluate the size of each side, and you will generate a set of quantities that tells you how to write down down an L

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By building this link, and proficiently enlarging the scope of your Langlands software as it absolutely was at first conceived, The brand new paper offers an individual conceptual framework for the slew of mathematical connections.

The do the job has limits. In particular, the three mathematicians confirm the duality in between periods and L

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For months, Akshay Venkatesh carried close to a scrap of paper from the hopes that gazing it might support him decipher a mathematical enigma.

Online video: Rutgers University mathematician Alex Kontorovich can take us on a journey from the continents of arithmetic to study the awe-inspiring symmetries at the heart in the Langlands application.