Jacob Fox
Jacob Fox (born Jacob Licht April 7, 1984 ) is an American mathematician who studies combinatorics .
Fox, who won prizes as a student, studied at the Massachusetts Institute of Technology (MIT) from 2002 , where he received his bachelor's degree in 2006 and the Morgan Prize as an undergraduate in 2006 for a series of publications , and was at Princeton University in 2010 PhD with Benjamin Sudakov (Benny Sudakov) ( Ramsey Numbers ). He then returned to MIT, where he became Assistant Professor in 2010 and Associate Professor (with tenure ) in 2014 , and has been a professor at Stanford University since 2015 .
He deals with combinatorial number theory, Ramsey theory , extremal graph theory and other areas of graph theory, algebraic and probabilistic methods in combinatorics, combinatorial geometry and applications of combinatorics in computer science. He received the Dénes-Kőnig-Preis in 2010 for his progress (partly with Benny Sudakov and David Conlon ) in determining Ramsey numbers , an area known to be particularly difficult.
In addition to his work with Sudakov on improved bounds for hypergraph Ramsey numbers, he received the Oberwolfach Prize, in particular for his contributions to the understanding of regularity theorems such as Endre Szemerédi's regularity lemma , which apart from graph theory has many applications in combinatorics and computer science and says that graphs that are large enough can be broken down into subgraphs of roughly the same size, so that the edges between the parts behave almost randomly. A consequence of the regularity lemma is the “Graph Removal Lemma”: every graph with n nodes and at most copies of a fixed graph H on h edges can be made free of H by removing edges. The lemma has applications in additive combinatorics, discrete geometry and computer science. Fox gave a new proof of the Graph Removal Lemma without using Szemeredi's regularity lemma and with improved quantitative estimates.
In addition, he gave with David Conlon and Yufei Zhao a simple proof of a tightening of the relative Szemeredi theorem, which is an important part of the proof of the theorem of Ben Green and Terence Tao about prime numbers in arithmetic progressions of any length. The simplified the proof of the theorem of Green-Tao and the compression technique (used Densification ) was beyond application and was created by Tao and Tamar Ziegler used to prove the existence of primes in polynomial progressions.
In 2016 he received the Oberwolfach Prize and in 2010 the Dénes-Kőnig Prize of the SIAM . In 2012 he received the Edmund F. Kelly Research Award from MIT. From 2013 to 2015 he was a “Sloan Fellow”, 2010 to 2013 MIT “Simons Fellow” and from 2013 a “Packard Fellow”. In 2014 he received a Career Award from the National Science Foundation. In 2002, he won second prize in the Intel Science Talent Search and first prize at the International Science and Engineering Fair. He gave the Ahlfors Lectures at Harvard and the Marston Morse Lectures at the Institute for Advanced Study .
In 2014 he was invited speaker at the International Congress of Mathematicians in Seoul ( The graph regularity method: variants, applications, and alternative methods ).
In 2010 he became editor of the Journal of Graph Theory and 2014 of the Journal of Combinatorial Theory A .
Fonts
- A new proof of the graph removal lemma , Annals of Mathematics, Volume 174, 2011, pp. 561-579, Arxiv
- with David Conlon : Graph removal lemmas , Surveys in Combinatorics, 2013, pp. 1–50 ( Preprint, Arxive, 2012 )
- with B. Sudakov: Density theorems for bipartite graphs and related Ramsey-type results , Combinatorica, Volume 29, 2009, pp. 153-196, Arxiv
- with Mikhail Gromov , Vincent Lafforgue , Assaf Naor , Janos Pach : Overlap properties of geometric expanders, Journal for pure and applied mathematics, Volume 671, 2012, pp. 49–83, Arxiv
- with D. Conlon, B. Sudakov: Hypergraph ramsey numbers , Journal of the American Mathematical Society, Volume 23, 2010, pp. 247-266, Arxiv
- with B. Sudakov: Dependent random choice , Random Structures & Algorithms, Volume 38, 2011, pp. 68-99, Arxiv
- with D. Conlon: Bounds for graph regularity and removal lemmas , Geometric and Functional Analysis, Volume 22, 2012, pp. 1191–1256, Arxiv
- with D. Conlon, B. Sudakov: An approximate version of Sidorenko's conjecture , Geometric and Functional Analysis, Volume 20, 2010, pp. 1354-1366, Arxiv
- with D. Conlon, Yufei Zhao: A relative Szemeredi Theorem , Geom. Funct. Anal., Vol. 25, 2015, pp. 733-762, Arxiv
- with Conlon, Sudakov: Recent developments in Graph Ramsey Theory , 2015, Arxiv
Web links
Individual evidence
- ↑ Date of birth according to VIAF, Princeton University Archives given as the source
- ↑ Notices AMS, 2006, No. 4, Acknowledgment for the Morgan Prize
- ↑ Notices AMS, 2006, No. 4 (PDF), with appreciation, photo and biography. As an undergraduate he has already published 11 scientific papers.
- ↑ Jacob Fox in the Mathematics Genealogy Project (English)
- ^ Alumnus Jacob Fox Wins the Konig Prize , Society for Science and the Public, 2010
- ↑ Appreciation for the Oberwolfach Prize , PDF
| personal data | |
|---|---|
| SURNAME | Fox, Jacob |
| ALTERNATIVE NAMES | Light, Jacob |
| BRIEF DESCRIPTION | American mathematician |
| DATE OF BIRTH | April 7, 1984 |