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In mathematics, Diophantine geometry is the study of Diophantine equations by means of powerful methods in algebraic geometry. By the 20th century it became clear for some mathematicians that methods of algebraic geometry are ideal tools to study these equations. Diophantine geometry is part of the broader field of arithmetic geometry.
Lists of mathematics topics cover a variety of topics related to mathematics. Some of these lists link to hundreds of articles; some link only to a few. The template to the right includes links to alphabetical lists of all mathematical articles. This article brings together the same content organized in a manner better suited for browsing. Lists cover aspects of basic and advanced mathematics, methodology, mathematical statements, integrals, general concepts, mathematical objects, and reference tables. They also cover equations named after people, societies, mathematicians, journals, and meta-lists.
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Heiko Harborth is Professor of Mathematics at Braunschweig University of Technology, 1975–present, and author of more than 188 mathematical publications. His work is mostly in the areas of number theory, combinatorics and discrete geometry, including graph theory.
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Sheldon H. Katz is an American mathematician, specializing in algebraic geometry and its applications to string theory.
June E Huh is an American mathematician who is currently a professor at Princeton University. Previously, he was a professor at Stanford University. He was awarded the Fields Medal in 2022 and a MacArthur Fellowship in 2022. He has been noted for the linkages that he has found between algebraic geometry and combinatorics.
Jennifer Shyamala Sayaka Balakrishnan is an American mathematician known for leading a team that solved the problem of the "cursed curve", a Diophantine equation that was known for being "famously difficult". More generally, Balakrishnan specializes in algorithmic number theory and arithmetic geometry. She is the Clare Boothe Luce Associate Professor at Boston University.
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Melody Tung Chan is an American mathematician and violinist who works as Associate Professor of Mathematics at Brown University. She is a winner of the Alice T. Schafer Prize and of the AWM–Microsoft Research Prize in Algebra and Number Theory. Her research involves combinatorial commutative algebra, graph theory, and tropical geometry.
In arithmetic geometry, the uniform boundedness conjecture for rational points asserts that for a given number field and a positive integer that there exists a number depending only on and such that for any algebraic curve defined over having genus equal to has at most -rational points. This is a refinement of Faltings's theorem, which asserts that the set of -rational points is necessarily finite.
References
- ↑ Eric Katz (2005-07-15). "Formalism for Relative Gromov-Witten Invariants" . Retrieved May 24, 2019.
- ↑ "Combinatorics and more".
- ↑ "A Path Less Taken to the Peak of the Math World". Quanta Magazine . Retrieved 2017-07-01.
- ↑ "Hodge theory of matroids" (PDF), Notices of the AMS , retrieved 2017-07-03
- ↑ Baker, Matt. "Hodge Theory and Combinatorics" (PDF). 2017 AMS Current Events Bulletin. Retrieved 2017-07-04.
- ↑ Katz, Eric; Rabinoff, Joseph; Zureick-Brown, David (2016), Diophantine and tropical geometry, and uniformity of rational points on curves, arXiv: 1606.09618 , Bibcode:2016arXiv160609618K
- ↑ Eric Katz at the Mathematics Genealogy Project
