2025 CMS Winter Meeting
Toronto, Dec 5 - 8, 2025
Org: Stephen Anco (Brock University) and Konstantin Druzhkov (University of Saskatchewan)
[PDF]
- STEPHEN ANCO, Brock University
- EVANS BOADI, University at Buffalo
- KOSTYA DRUZHKOV, University of Saskatchewan
- JORDAN FAZIO, Brock University
- JAMES HORNICK, McMaster University
- SERHII KOVAL, Memorial University
- MAHDIEH GOL BASHMANI MOGHADAM, Brock University
- ALEXANDER ODESSKI, Brock University
p-Determinants and monodromy of differential operators [PDF]
- EVANS BOADI, University at Buffalo
-
We review interrelations between arithmetic properties (so-called p-determinants) and analytic properties (eigenvalues of monodromy operators) for differential operators of certain type. This is a joint project with Maxim Kontsevich.
- BARBARA PRINARI, University at Buffalo
Breather interactions in the integrable discrete Manakov system [PDF]
-
In this talk we will consider a vector generalization of the Ablowitz-Ladik model referred to as the integrable discrete Manakov system. In the focusing regime, this system admits a variety of discrete vector soliton solutions, referred to as fundamental solitons, fundamental breathers, and composite breathers. We will give a full characterization of the interactions of these solitons and breathers, including the explicit forms of their polarization vectors before and after the interaction. Additionally, the results will be interpreted in terms of a Yang-Baxter refactorization property for the transmission coefficients associated with the interacting solitons.
- ARCHISHMAN SAHA, University of Ottawa
- ALIREZA SHARIFI, University of Manitoba
Integrability and KAM Non–Ergodicity in the Thermostated Hamiltonian Systems [PDF]
- ALIREZA SHARIFI, University of Manitoba
-
In this talk I will discuss Hamiltonian systems that are thermostated using the Jellinek--Berry (JB) thermostat (J.\ Phys.\ Chem.\ 1988; Phys.\ Rev.\ A\ 1988). Jellinek and Berry proposed this model as a functional extension of Nos\'e's thermostat (J.\ Chem.\ Phys.\ 1984), introducing several functional parameters that generalize the coupling between the physical system and the thermal reservoir. In molecular dynamics, the JB family aims to generate the canonical ensemble of a Hamiltonian \(H\) by coupling \(H\) to a one--dimensional heat reservoir with potential energy \(v(s)\) and kinetic energy \(\tfrac{1}{2Q}(p_s/u(s))^2\); i.e.,
\[
G(x,s,p_s) := \underbrace{H(a(s)\!\cdot\! x)}_{\text{Physical system}} + \underbrace{\frac{p_s^2}{2Q\,u(s)^2} + gkT\,v(s)}_{\text{Thermostat}}.
\]
I will describe when the JB--thermostated periodic ideal gas is Liouville completely integrable and satisfies a KAM twist condition known as R\"ussmann non--degeneracy. This property ensures that the system admits action--angle variables and a nondegenerate frequency map. Using these results, one can show that a thermostated, collisionless, non--ideal gas---that is, a smooth perturbation of the ideal case---possesses a positive--measure set of invariant tori at sufficiently high reservoir temperatures. Consequently, the thermostated dynamics remain non--ergodic in this regime.
The talk will emphasize the geometric structure underlying these results, including the role of symplectic transformations, the existence and persistence of invariant tori, highlighting the connection between thermostat design and classical problems of integrability and ergodicity in Hamiltonian systems.
- JACEK SZMIGIELSKI, University of Saskatchewan