Andrew Sutherland (mathematician)

Andrew Sutherland
Andrew Sutherland at MIT in 2016
NationalityAmerican
Alma materMIT
Awards
Scientific career
FieldsMathematics
InstitutionsMIT
ThesisOrder computations in generic groups (2007)
Websitemath.mit.edu/~drew

Andrew Victor Sutherland is an American mathematician and Principal Research Scientist at the Massachusetts Institute of Technology.[1] His research focuses on computational aspects of number theory and arithmetic geometry.[1] He is known for his contributions to several projects involving large scale computations, including the Polymath project on bounded gaps between primes,[2][3][4][5][6] the L-functions and Modular Forms Database,[7][8] the sums of three cubes project,[9][10][11] and the computation and classification of Sato-Tate distributions.[12][13][14][15]

Education and career

Sutherland earned a bachelor's degree in mathematics from MIT in 1990.[1] Following an entrepreneurial career in the software industry he returned to MIT and completed his doctoral degree in mathematics in 2007 under the supervision of Michael Sipser and Ronald Rivest, winning the George M. Sprowls prize for this thesis.[1][16] He joined the MIT mathematics department as a Research Scientist in 2009, and was promoted to Principal Research Scientist in 2011.[1]

He is one of the principal investigators in the Simons Collaboration on Arithmetic Geometry, Number Theory, and Computation, a large multi-university collaboration involving Boston University, Brown, Harvard, MIT, and Dartmouth College,[17] and he currently serves as an Associate Editor of Mathematics of Computation, Editor in Chief of Research in Number Theory,[18] Managing Editor of the L-functions and Modular Forms Database,[19] and President of the Number Theory Foundation.[20]

Contributions

Sutherland has developed or improved several methods for counting points on elliptic curves and hyperelliptic curves, that have applications to elliptic curve cryptography, hyperelliptic curve cryptography, elliptic curve primality proving, and the computation of L-functions.[21][22][23][24] These include improvements to the Schoof–Elkies–Atkin algorithm[25][26] that led to new point-counting records[27], and average polynomial-time algorithms for computing zeta functions of hyperelliptic curves over finite fields, developed jointly with David Harvey.[28][29][30]

Much of Sutherland's research involves the application of fast point-counting algorithms to numerically investigate generalizations of the Sato-Tate conjecture regarding the distribution of point counts for a curve (or abelian variety) defined over the rational numbers (or a number field) when reduced modulo prime numbers of increasing size.[21][31][32][33]. It is conjectured that these distributions can be described by random matrix models using a "Sato-Tate group" associated to the curve by a construction of Serre.[34][35] In 2012 Francesc Fite, Kiran Kedlaya, Victor Rotger and Sutherland classified the Sato-Tate groups that arise for genus 2 curves and abelian varieties of dimension 2,[14] and in 2019 Fite, Kedlaya, and Sutherland announced a similar classification to abelian varieties of dimension 3.[36]

In the process of studying these classifications, Sutherland compiled several large data sets of curves and then worked with Andrew Booker and others to compute their L-functions and incorporate them into the L-functions and Modular Forms Database.[12][37][38] More recently, Booker and Sutherland resolved Mordell's question regarding the representation of 3 as a sum of three cubes.[39][40][41]

Recognition

Sutherland was named to the 2021 class of fellows of the American Mathematical Society "for contributions to number theory, both on the theoretical and computational aspects of the subject".[42] He was selected to deliver the Arf Lecture in 2022.[43]

References

1. Andrew Sutherland, MIT, retrieved February 13, 2020
2. ^ Klarreich, Erica (November 19, 2013), "Together and Alone, Closing the Prime Gap", Quanta Magazine
3. ^ Grolle, Johann (March 17, 2014), "Atome der Zahlenwelt", Der Spiegel
4. ^
5. ^ Castryck, Wouter; Fouvry, Étienne; Harcos, Gergely; Kowalski, Emmanuel; Michel, Philippe; Nelson, Paul; Paldi, Eytan; Pintz, János; Sutherland, Andrew V.; Tao, Terence; Xie, Xiao-Feng (2014). "New equidistribution results of Zhang type". Algebra and Number Theory. 8: 2067–2199. doi:10.2140/ant.2014.8.2067. MR 3294387.
6. ^ Polymath, D.H.J. (2014). "Variants of the Selberg sieve". Research in the Mathematical Sciences. 1 (12). doi:10.1186/s40687-014-0012-7.
7. ^ "International team launches vast atlas of mathematical objects", MIT News, Massachusetts Institute of Technology, May 10, 2016
8. ^ Grolle, Johann (May 14, 2016), "Befreundete Kurven", Der Spiegel
9. ^ Miller, Sandi (September 10, 2019), "The answer to life, the universe, and everything: Mathematics researcher Drew Sutherland helps solve decades-old sum-of-three-cubes puzzle, with help from "The Hitchhiker's Guide to the Galaxy."", MIT News, Massachusetts Institute of Technology
10. ^ Lu, Donna (September 6, 2019), "Mathematicians crack elusive puzzle involving the number 42", New Scientist
11. ^ Linkletter, Dave (December 27, 2019), "The 10 Biggest Math Breakthroughs of 2019", Popular Mechanics
12. ^ a b Barrett, Alex (April 20, 2017), "220,000 cores and counting: Mathematician breaks record for largest ever Compute Engine job", Google Cloud Platform
13. ^ Sutherland, Andrew V. (2019). "Sato-Tate distributions". Analytic methods in arithmetic geometry. Contemporary Mathematics. Vol. 740. American Mathematical Society. pp. 197–258. arXiv:1604.01256. doi:10.1090/conm/740/14904. MR 4033732.
14. ^ a b Fité, Francesc; Kedlaya, Kiran; Sutherland, Andrew V; Rotger, Victor (2012). "Sato-Tate distributions and Galois endomorphism modules in genus 2". Compositio Mathematica. 149 (5): 1390–1442. doi:10.1112/S0010437X12000279. MR 2982436.
15. ^ Sutherland, Andrew V., Sato-Tate distributions in genus 2, MIT, retrieved February 13, 2020
16. ^ Andrew Victor Sutherland, Mathematics Genealogy Project, retrieved February 13, 2020
17. ^ "Principal Investigators", Simons Collaboration on Arithmetic Geometry, Number Theory, and Computation, Brown University, retrieved February 14, 2020
18. ^ Research in Number Theory Editors, Springer, retrieved February 13, 2020
19. ^ LMFDB Editorial Board, The L-functions and Modular Forms Database, retrieved February 13, 2020
20. ^ Number Theory Foundation home page, Number Theory Foundation, retrieved February 13, 2020
21. ^ a b Kedlaya, Kiran S.; Sutherland, Andrew V. (2008). "Computing L-series of hyperelliptic curves". Algorithmic Number Theory 8th International Symposium (ANTS VIII). Lecture Notes in Computer Science. Vol. 5011. Springer. pp. 312–326. arXiv:0801.2778. doi:10.1007/978-3-540-79456-1_21.
22. ^ Sutherland, Andrew V. (2011). "Structure computation and discrete logarithms in finite abelian p-groups". Mathematics of Computation. 80 (273): 477–500. doi:10.1090/S0025-5718-10-02356-2.
23. ^ Sutherland, Andrew V. (2011). "Computing Hilbert class polynomials with the Chinese remainder theorem". Mathematics of Computation. 80 (273): 501–538. doi:10.1090/S0025-5718-2010-02373-7.
24. ^ Sutherland, Andrew V. (2012). "Accelerating the CM method". LMS Journal of Computation and Mathematics. 15: 317–325. doi:10.1112/S1461157012001015.
25. ^ Bröker, Reinier; Lauter, Kristin; Sutherland, Andrew V. (2012). "Modular polynomials via isogeny volcanoes". Mathematics of Computation. 81 (278): 1201–1231. doi:10.1090/S0025-5718-2011-02508-1.
26. ^ Sutherland, Andrew V. (2013). "On the evaluation of modular polynomials". Algorithmic Number Theory 10th International Symposium (ANTS X). Open Book Series. Vol. 1. Mathematical Sciences Publishers. pp. 312–326. doi:10.2140/obs.2013.1.531.
27. ^ Sutherland, Andrew V., Genus 1 point counting records over prime fields, retrieved February 14, 2020
28. ^ Harvey, David; Sutherland, Andrew V. (2014). "Computing Hasse-Witt matrices of hyperelliptic curves in average polynomial time". LMS Journal of Computation and Mathematics. 17: 257–273. doi:10.1112/S1461157014000187.
29. ^ Harvey, David; Sutherland, Andrew V. (2016). "Computing Hasse-Witt matrices of hyperelliptic curves in average polynomial time, II". Frobenius distributions: Lang-Trotter and Sato-Tate conjectures. Contemporary Mathematics. Vol. 663. pp. 127–148. arXiv:1410.5222. doi:10.1090/conm/663/13352.
30. ^ Harvey, David; Massierer, Maike; Sutherland, Andrew V. (2016). "Computing L-series of geometrically hyperelliptic curves of genus three". LMS Journal of Computation and Mathematics. 19: 220–234. arXiv:1605.04708. doi:10.1112/S1461157016000383.
31. ^ Kedlaya, Kiran S.; Sutherland, Andrew V. (2009). "Hyperelliptic curves, L-polynomials, and random matrices". Arithmetic, Geometry, Cryptography and Coding Theory. Contemporary Mathematics. Vol. 487. American Mathematical Society. pp. 119–162. doi:10.1090/conm/487/09529.
32. ^ Fité, Francesc; Sutherland, Andrew V. (2014). "Sato-Tate distributions of twists of ${\displaystyle y^{2}=x^{5}-x}$ and ${\displaystyle y^{2}=x^{6}+1}$". Algebra and Number Theory. 8: 543–585. doi:10.2140/ant.2014.8.543.
33. ^ Fité, Francesc; Lorenzo Garcia, Elisa; Sutherland, Andrew V. (2018). "Sato-Tate distributions of twists of the Fermat and the Klein quartics". Research in the Mathematical Sciences. 5 (41). doi:10.1007/s40687-018-0162-0.
34. ^ Katz, Nicholas M.; Sarnak, Peter (1999). Random matrices, Frobenius eigenvalues, and monodromy. American Mathematical Society.
35. ^ Serre, Jean-Pierre (2012). Lectures on ${\displaystyle N_{X}(p)}$. Research Notes in Mathematics. CRC Press.
36. ^ Fité, Francesc; Kedlaya, Kiran S.; Sutherand, Andrew V. (2021). "Sato–Tate groups of abelian threefolds: A preview of the classification". Arithmetic, Geometry, Cryptography and Coding Theory. Contemporary Mathematics. Vol. 770. pp. 103–129. arXiv:1911.02071. doi:10.1090/conm/770/15432. ISBN 978-1-4704-6426-4. S2CID 207772885.
37. ^ Booker, Andrew R; Sisjling, Jeroen; Sutherland, Andrew V.; Voight, John; Yasaki, Dan (2016). "A database of genus 2 curves over the rational numbers". LMS Journal of Computation and Mathematics. 19: 235–254. doi:10.1112/S146115701600019X.
38. ^ Sutherland, Andrew V. (2019). "A database of nonhyperelliptic genus-3 curves over ${\displaystyle \mathbb {Q} }$". Thirteenth Algorithmic Number Theory Symposium (ANTS XIII). Open Book Series. Vol. 2. Mathematical Sciences Publishers. doi:10.2140/obs.2019.2.443.
39. ^ Honner, Patrick (November 5, 2019), "Why the Sum of Three Cubes Is a Hard Math Problem", Quanta Magazine
40. ^ Dunne, Edward (18 September 2019), "3", AMS Blogs, American Mathematical Society
41. ^ Lu, Donna (September 18, 2019), "Mathematicians find a completely new way to write the number 3", New Scientist
42. ^ 2021 Class of Fellows of the AMS, American Mathematical Society, retrieved 2020-11-02
43. ^ Arf Lectures, Middle East Technical University, retrieved 2020-11-17