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Elliptic Integrable Systems and Related Topics: Advanced Seminars |  |
Dates: September 18 - September 30, 2024 (Arrival: Sep 18, Departure: Sep 30)
Venue: Shanghai University, Shanghai, China
Organizers: Wei Fu (East China Normal University), Frank Nijhoff (University of Leeds, Shanghai University), Cheng Zhang (Shanghai University), Da-jun Zhang (Shanghai University)
Contact: Da-jun Zhang (djzhang@staff.shu.edu.cn )
Sponsors: NSFC Tianyuan Grant
Link: https://math.shu.edu.cn/info/1043/20891.htm
Objectives:
This is a programme of Tianyuan Advanced Seminars, focusing on elliptic integrable systems, elliptic solutions and related topics. There are two ways that elliptic curves can play a role in integrable systems: either as elliptic type solutions (i.e., solutions expressible in terms of elliptic functions) or as elliptic deformation of the equations themselves (namely, elliptic integrable systems, which contain the modular parameters of an elliptic curve). In either way, the study of the elliptic case is richer than the trigonometric/hyperbolic and rational case, and reveals many new features of the models in question, thus leading to new insights into the true nature of those integrable systems.
The main focuses of the Advanced Seminars are the following:
(1) The discrete Krichever-Novikov equation and the related novel structure.
(2) Algebra representation of the vertex operators involved with elliptic functions.
(3) Finite gap solutions.
(4) Integrable systems associated with elliptic curves.
(5) Ultra-discrete integrable systems and related topics.
(6) Discretization of elliptic curves and applications.
(7) Elliptic Lax pairs and isomonodromic deformation problems.
(8) Elliptic orthogonal polynomials and corresponding integrable systems.
(9) QRT maps and generalizations.
Invited speakers:
Name | Institute | Visiting dates |
James Atkinson | UK | 18 Sep – 30 Sep |
Anton Dzhamay | BIMSA | 14 Sep – 21 Sep |
Andrew N. W. Hone | University of Kent | 13 Sep – 29 Sep |
Nalini Joshi | University of Sydney | 19 Sep – 03 Oct |
Yuji Kodama | The Ohio State Univ | 18 Sep – 29 Sep, |
Kenichi Maruno | Waseda Univ | 18 Sep – 29 Sep |
Yasuhiro Ohta | Kobe Univ | 18 Sep – 27 Sep |
Linyu Peng | Keio Univ | 23 Sep – 02 Oct |
Pieter Roffelsen | University of Sydney | 18 Sep – 30 Sep |
Alexander Stokes | Waseda Univ | 18 Sep – 30 Sep |
Daisuke Takahashi | Waseda Univ | 18 Sep – 21 Sep |
Peter van der Kamp | La Trobe Univ | 18 Sep – 30 Sep |
Programme:
18 Sep: 14:00pm-20:00pm, registration, LeHu Hotel
19 Sep: 09:30am-10:00pm, registration, GJ-303
Lunch: 11:30-13:00, LeHu Hotel
Seminars (Lecture Room GJ-303)
Date | 10:00-11:00 | 11:00-11:30 | 14:00-15:00 | 15:00-15:40 | 15:40-16:40 |
19 Sep Thu | S1 Nijhoff | Tea break | S2 Takahashi | Tea break | S3 Dzhamay |
20 Sep Fri | S4 Takahashi | Tea break | S5 Dzhamay | Tea break | S6 Stokes |
21 Sep Sat | S7 Dzhamay | Tea break | S8 Stokes | Tea break | S9 Stokes |
22 Sep | Free discussion |
23 Sep Mon | S10 Kodama | Tea break | S11 Maruno | Tea break | S12 Ohta |
24 Sep Tue | S13 Kodama | Tea break | S14 Ohta | Tea break | S15 Maruno |
25 Sep Wed | S16 Kodama | Tea break | S17 Hone | Tea break | S18 van der Kamp |
26 Sep Thu | S19 van der Kamp | Tea break | S20 Hone | Tea break | S21 Joshi(public talk for students) |
27 Sep Fri | S22 Hone | Tea break | S23 Nijhoff | Tea break | S24 Atkinson |
28 Sep Sat | S25 Joshi | Tea break | S26 Roffelsen | Tea break | S27 Atkinson |
29 Sep Sun | S28 Joshi | Tea break | S29 Roffelsen | Tea break | S30 Peng |
Titles:
1. James Atkinson: [S24, S27] Extended lattices of integrable equations: towards unification
2. Anton Dzhamay: [S3, S5, S7] Geometric deautonomization from a QRT map to a discrete Painlevé equation
3. Andrew N. W. Hone: [S17, S20, S22] Elliptic & hyperelliptic analogues of Chebyshev polynomials, and related discrete integrable systems
4. Nalini Joshi: [S25, S28] Dynamics on and out of elliptic curves: from Newton to Okamoto
5. Yuji Kodama: [S10, S13, S16] KP solitons, the Riemann theta functions and the vertex operators
6. Kenichi Maruno: [S11, S15] Constructions of integrable self-adaptive moving mesh schemes and delay soliton equations
7. Frank Nijhoff: Topic (1): [S1] Elliptic integrable lattice equations: an overview and open problems.
Topic (2): [S23] The elliptic lattice KdV revisited: challenges and redeeming features
8. Yasuhiro Ohta: [S12, S14] Special function type solutions for soliton equations and bilinear method
9. Linyu Peng: [S30] Discrete moving frames and the invariant discrete Noether's theorem
10. Pieter Roffelsen: [S26, S29] On connection problems and algebraic equations over fields of elliptic functions
11. Alexander Stokes: [S6, S8, S9] Deautonomisation of integrable mappings and degree growth
12. Daisuke Takahashi: [S2, S4] On equations defined by max operators.
13. Peter van der Kamp: Topic (1): [S18] A proof of the Cayley-Bacharach theorem and some of its consequences;
Topic (2): [S19] QRT maps and generalizations
Participants: