Views 2042 Votes 0 Comment 0
?

Shortcut

PrevPrev Article

NextNext Article

Larger Font Smaller Font Up Down Go comment Print
?

Shortcut

PrevPrev Article

NextNext Article

Larger Font Smaller Font Up Down Go comment Print
Extra Form
일정시작 2022-07-21
일정종료 2022-07-21
배경색상 #77CC00

Speaker : 이경용 (University of Alabama) 

Place : 129동406호

Schedule :  7월21일(목) 10:00 ~ 11:00

TiTle : Finding ALL solutions 

Abstract : 

We introduce two famous (or notorious) open problems from Smale's list and Millennium problems: the Jacobian conjecture and the Birch--Swinnerton-Dyer conjecture. 

 

The Jacobian conjecture states that if the Jacobian of a polynomial map is a nonzero constant, then the map is bijective. The condition of the Jacobian being equal to a constant can be translated to a system of (too many) polynomial equations. An elementary but promising approach is to find ALL solutions systematically. This is based on joint work with Jacob Gliedwell, William Hurst, Li Li, and George Nasr.

 

 A special case of the weak BSD conjecture can be translated to counting integer solutions of certain Diophantine equations. Again an elementary but promising approach is to find ALL solutions systematically. This is based on joint work with Ty Clements, Zach Socha, and Vishak Vikranth.

 

This talk will be completely elementary and accessible to non-experts, as all my collaborators including myself are non-experts.

 

 

 


List of Articles
No. Subject Author Date Views
Notice QSMS Mailing List Registration qsms 2021.09.09 4626
85 [QSMS Seminar 2022-08-24] Vector bundles and representation theory on a curve qsms 2022.08.13 1452
84 [SNU Number Theory Seminar 2022-08-11] The dual Lagrangian fibration of hyper-Kähler manifolds qsms 2022.08.04 1500
83 [SNU Number Theory Seminar 2022-08-08] Geometry of the $B_{dR}^+$-Grassmannian qsms 2022.08.04 1483
82 [SNU Number Theory Seminar 2022-06-21] Arithmetic local systems over the moduli space of curves qsms 2022.07.21 1458
» [QSMS Seminar 20220721] Finding ALL solutions qsms 2022.07.14 2042
80 [QSMS Mini-course] Pablo Portilla cuadrado (University of Lille) qsms 2022.07.04 1454
79 [QSMS Monthly Seminar] Yokonuma Hecke algebras and invariants of framed links qsms 2022.05.27 1439
78 [SNU Number Theory Seminar 2022-06-03] The Coleman conjecture on circular distributions and the equivariant Tamagawa Number conjecture qsms 2022.05.18 1717
77 [SNU Number Theory Seminar 2022-05-20] Distribution of Hecke eigenvalues of GL_2 automorphic representations qsms 2022.05.18 1377
76 [QSMS Geometry Seminar 2022-05-17, 19] Symplectic Criteria on Stratified Uniruledness of Affine Varieties and Applications qsms 2022.05.09 1584
75 [QSMS Geometry Seminar 2022-05-12] Tropical Lagrangian multi-sections and tropical locally free sheaves qsms 2022.05.07 1503
74 [2022 KMS Spring Meeting] Related talks qsms 2022.04.28 1623
73 [QSMS Monthly Seminar] Quantization of integrable differential difference equations qsms 2022.04.22 1452
72 [SNU Number Theory Seminar 2022-05-06] On an upper bound of the average analytic rank of a family of elliptic curves qsms 2022.04.19 1580
71 [SNU Number Theory Seminar 2022-05-13] A singular function containing all Lagrange numbers less than three qsms 2022.04.12 1483
70 [SNU Number Theory Seminar 2022-04-15] A note on non-ordinary primes for some genus-zero arithmetic groups qsms 2022.04.12 1396
69 [QSMS-BK21 Toric Geometry Seminar] Moduli Space of Special Lagrangians in the Complement of an Anticanonical Divisor qsms 2022.04.12 1554
68 [QSMS Seminar 2022.04.19] Universal objects in vertex algebra theory qsms 2022.04.07 1428
67 [SNU Number Theory Seminar 20220401] Randomness and structure for sums of cubes qsms 2022.03.28 1597
66 [QSMS Monthly Seminar] The dimension of the kernel of an Eisenstein ideal qsms 2022.03.25 1441
Board Pagination Prev 1 2 3 4 5 6 7 8 Next
/ 8