A crucial task  in control applications is the design of a feedback operator allowing us to compute a control input which is able to stabilize a given dynamical system, being able to respond to small perturbations as well. Feedback inputs are given as a function of the state of the system, which is often not fully available in real world applications. Thus, another crucial task is the design of a dynamic Luenberger observer providing us with an estimate for the unknown state, by using the output of sensor measurements; here, the task is to find an operator that injects the output into the dynamics of the observer. In this talk, we discuss recent developments on the design of such feedback-input  and output-injection operators for models given by parabolic-like equations. The focus is put on the design of simple and explicit operators. Both theoretical and numerical aspects are discussed, including a comparison to more classical operators obtained through optimal control tools and involving the solution of Riccati or Hamilton-Jacobi-Bellman equations.

Room: 202 ed IV 
 
Abstract: Vectorial Boolean functions are used in cryptography, in particular in block ciphers. An important condition on these functions is a high resistance to the differential and linear cryptanalyses, which are the main mathematical attacks on block ciphers. The functions which possess the best resistance to the differential attack are called almost perfect nonlinear (APN). Almost bent (AB) functions are those mappings which oppose an optimum resistance to both linear and differential attacks. APN and AB functions are important not only for the purpose of constructing new block ciphers in cryptography, but for other areas of computer science and discrete mathematics (such as combinatorics, sequence design, coding theory, design theory) in which APN functions correspond to some optimal objects. In this talk we address some longstanding problems related to APN and AB monomials.

Abstract: In this talk I will give an overview of what is known about conjugacy growth and the formal series associated with it in infinite discrete groups. I will highlight how the rationality (or rather lack thereof) of these series is connected to both the algebraic and the geometric nature of groups such as (relatively) hyperbolic or nilpotent, and how tools from analytic combinatorics can be employed in this context. I will also mention results about the languages of conjugacy representatives in various groups.