Organizers: Ivan Corwin and Jeffrey Kuan
All times below are Central Standard Time (CST)
Zoom link here Meeting ID: 970 5689 9453 Passcode: 2718281828
Date and Time 
Speaker 
Title and Abstract 
Wednesday, June 2, 10am CST 
Cristian Giardinà 
Exact solution of a boundarydriven integrable particle system. I present the results of a joint (ongoing) work with Rouven Frassek. We consider the boundarydriven interacting particle systems introduced in [1], related to the open noncompact Heisenberg model in one dimension. We show that a finite chain of N sites connected at its ends to two reservoirs can be solved exactly, i.e. the nonequilibrium steadystate has a closedform expression for each N. The solution relies on probabilistic arguments and techniques inspired by integrable systems. It is obtained in two steps: i) the introduction of a dual absorbing process reducing the problem to a finite number of particles; ii) the solution of the dual dynamics exploiting a nonlocal symmetry obtained from the Quantum Inverse Scattering Method. The exact solution allows to prove by direct computation that, in the thermodynamic limit, the system approaches local equilibrium, whereas microscopically there are longranged correlations. A byproduct of the solution is the algebraic construction of a direct mapping (a conjugation) between the generator of the nonequilibrium process and the generator of the associated reversible equilibrium process. Macroscopically, this mapping was previously observed by Tailleur, Kurchan and Lecomte in the context of Macroscopic Fluctuation Theory. [1] R. Frassek, C. Giardinà, J. Kurchan, Noncompact quantum spin chains as integrable stochastic particle processes, Journal of Statistical Physics 180, 366397 (2020).

Wednesday, June 2, 11am CST 
Wolter Groenevelt 
Orthogonal duality functions from Lie algebra representations In this talk I explain how, for certain symmetric interacting particle processes associated to Lie algebras, orthogonal duality functions can be obtained from unitary intertwining operators for certain Lie algebra representations. This gives, for example, an algebraic explanation for the occurrence of Krawtchouk polynomials as selfduality functions for the symmetric exclusion process.

Thursday, June 3, 5pm CST 
Michael Wheeler 
qdeformed KnizhnikZamolodchikov equations, vertex models and duality I will discuss certain solutions of the qdeformed KnizhnikZamolodchikov (qKZ) equations, which may be expressed via partition functions in stochastic vertex models. After recasting the qKZ equations in terms of generators of the Hecke algebra, one may interpret the resulting relations as a duality between two multispecies ASEPs. This leads to a kind of factory for producing duality observables, as partition functions within the vertex model in question. Several examples will be discussed.

Friday, June 4, 10am CST 
Alexey Bufetov 
Colorposition symmetry in interacting particle systems Multispecies versions of several interacting particle systems, including ASEP, qTAZRP, and kexclusion processes, can be interpreted as random walks on Hecke algebras. An involution in Hecke algebra leads to an interesting symmetry of these processes which we refer to as the colorposition symmetry. In the talk I will describe this symmetry and several applications to asymptotic questions. Based on joint works with A. Borodin and with P. Nejjar.

Friday, June 4, 11am CST 
Yier Lin 
Markov duality for stochastic six vertex model We prove that Schütz’s ASEP Markov duality functional is also a Markov duality functional for the stochastic six vertex model. We introduce a new method that uses induction on the number of particles to prove the Markov duality. If time permits, I will also talk about some application of this duality.

Monday, June 7, 10am CST 
Gunter Schütz 
Integrability, supersymmetry and duality for vicious walkers with pair creation

Monday, June 7, 11am CST 
Florian Völlering 
Markov process representation of semigroups whose generators include negative rates Generators of Markov processes on a countable state space can be represented as finite or infinite matrices. One key property is that the offdiagonal entries corresponding to jump rates of the Markov process are nonnegative. I will present stochastic characterizations of the semigroup generated by a generator with possibly negative rates. This is done by considering a larger state space with one or more particles and antiparticles, with antiparticles being particles carrying a negative sign.

Tuesday, June 8, 10am CST 
Frank Redig 
Selfduality in the continuum We generalize classical and orthogonal dualities beyond the framework of lattice systems, including e.g. random walks on general state spaces and interacting Brownian motions. Using some natural concepts from point process theory together with the notion of consistency, we introduce two intertwining relations which in the case of lattice systems give the known ``classical’’ and orthogonal dualities for exclusion and inclusion processes. We provide several examples including the inclusion process in the continuum. Based on joint work with S. Floreani (Delft), S. Jansen (Munich), S. Wagner (Munich).

Tuesday, June 8, 11am CST 
Chiara Franceschini 
Selfduality for particle systems via (q)orthogonal polynomials In this talk I will present some results regarding selfduality for two families of symmetric and asymmetric interacting particle systems. The method relies on their algebraic description and give rise to selfduality functions which are families of orthogonal polynomials in case of symmetric processes and qorthogonal polynomials in case of asymmetric processes.
