조회 수 15589 추천 수 0 댓글 0
?

단축키

Prev이전 문서

Next다음 문서

크게 작게 위로 아래로 댓글로 가기 인쇄
?

단축키

Prev이전 문서

Next다음 문서

크게 작게 위로 아래로 댓글로 가기 인쇄
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
번호 제목 글쓴이 날짜 조회 수
공지 QSMS Mailing List Registration qsms 2021.09.09 33971
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 17345
71 [SNU Number Theory Seminar 2022-05-13] A singular function containing all Lagrange numbers less than three qsms 2022.04.12 18130
70 [SNU Number Theory Seminar 2022-04-15] A note on non-ordinary primes for some genus-zero arithmetic groups qsms 2022.04.12 18074
69 [QSMS-BK21 Toric Geometry Seminar] Moduli Space of Special Lagrangians in the Complement of an Anticanonical Divisor qsms 2022.04.12 15230
68 [QSMS Seminar 2022.04.19] Universal objects in vertex algebra theory qsms 2022.04.07 16940
67 [SNU Number Theory Seminar 20220401] Randomness and structure for sums of cubes qsms 2022.03.28 15695
66 [QSMS Monthly Seminar] The dimension of the kernel of an Eisenstein ideal qsms 2022.03.25 15321
65 [SNU Number Theory Seminar 20220321, 0322, 0324] Three lectures on the Eisenstein ideal qsms 2022.03.19 15639
64 [SNU Number Theory Seminar 2022.03.18] On p-rationality of $\mathbb{Q}(\zeta_{2l+1})^{+}$ for Sophie Germain primes $l$ qsms 2022.03.19 15746
63 [BK21-QSMS Toric Geometry Seminar] The Fredholm regularity of discs qsms 2022.03.14 15606
62 [QSMS Seminar 2022.04.05] Trialities of W-algebras qsms 2022.02.15 15837
61 [QSMS Seminar 2022.03.04 (시간변경)] Introduction to Supersymmetric Field Theories qsms 2022.02.15 15804
60 [BK21-QSMS Toric Geometry Seminar] Moment Polytope qsms 2022.01.03 15808
59 [QSMS Monthly Seminar] Introduction to finite-dimensional representations of quantum affine algebras qsms 2021.12.03 15413
58 [QSMS Seminar 14,16 Dec] A brief introduction to differential graded Lie algebras I, II qsms 2021.11.29 15552
57 [SNU Number Theory Seminar 2021.12.03] Algebraization theorems in complex and non-archimedean geometry qsms 2021.11.19 15772
56 [QSMS 위상기하 세미나 2021.11.25] Exotic families of Weinstein manifolds with Milnor fibers of ADE types qsms 2021.11.19 15188
55 [SNU Number Theory Seminiar 2021.11.12] Moduli of Fontaine-Laffailles and mod-p local-global compatibility file qsms 2021.10.29 16607
54 [QSMS Monthly Seminar] Quantum entanglement entropy in abelian arithmetic Chern-Simons theory qsms 2021.10.29 15511
53 [SNU Number Theory Seminiar 2021.11.05] Bianchi modular symbols and p-adic L-functions qsms 2021.10.20 16413
Board Pagination Prev 1 2 3 4 5 6 7 8 Next
/ 8