Monday, June 12 |
07:00 - 08:45 |
Breakfast ↓ Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building. (Vistas Dining Room) |
08:45 - 09:00 |
Introduction and Welcome by BIRS Staff ↓ A brief introduction to BIRS with important logistical information, technology instruction, and opportunity for participants to ask questions. (TCPL 201) |
09:00 - 10:00 |
Tryphon Georgiou: Geometry and Applications of Optimal Mass Transport and Schrödinger Bridges (Part I) ↓ Optimal mass transport (OMT) was posed as a problem in 1781 by Gaspar Monge. It provides
a natural geometry for the space of probability distributions. As such it has been the cornerstone
of many recent developments in physics, probability theory, image processing, and so on.
The Schrödinger bridge problem (SBP) was posed by Erwin Schrödinger in 1931, in an attempt
to provide a classical interpretation of quantum mechanics. It is rooted in statistical mechanics
and large deviations theory, and provides an alternative model for flows of distributions (entropic
interpolation). In Part I, we will explain the close relation between the two problems, their
relevance in modeling and control, computational aspects, and their various extensions.
In Part II, we will focus on the relevance of the topic in stochastic thermodynamics. (TCPL 201) |
10:00 - 10:30 |
Coffee Break (TCPL Foyer) |
10:30 - 11:30 |
Tryphon Georgiou: Geometry and Applications of Optimal Mass Transport and Schrödinger Bridges (Part II) ↓ Optimal mass transport (OMT) was posed as a problem in 1781 by Gaspar Monge. It provides
a natural geometry for the space of probability distributions. As such it has been the cornerstone
of many recent developments in physics, probability theory, image processing, and so on.
The Schrödinger bridge problem (SBP) was posed by Erwin Schrödinger in 1931, in an attempt
to provide a classical interpretation of quantum mechanics. It is rooted in statistical mechanics
and large deviations theory, and provides an alternative model for flows of distributions (entropic
interpolation). In Part I, we will explain the close relation between the two problems, their
relevance in modeling and control, computational aspects, and their various extensions.
In Part II, we will focus on the relevance of the topic in stochastic thermodynamics. (TCPL 201) |
11:30 - 13:00 |
Lunch ↓ Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building. (Vistas Dining Room) |
13:00 - 14:00 |
Guided Tour of The Banff Centre ↓ Meet in the PDC front desk for a guided tour of The Banff Centre campus. (PDC Front Desk) |
14:00 - 14:20 |
Group Photo ↓ Meet in foyer of TCPL to participate in the BIRS group photo. The photograph will be taken outdoors, so dress appropriately for the weather. Please don't be late, or you might not be in the official group photo! (TCPL Foyer) |
14:30 - 15:00 |
Andrew Lewis: Composition, superposition, and regularity properties for ordinary differential equations ↓ The operation of pull-back of functions induces two sorts of operators, one where the mapping
is fixed and the function varies (the composition operator) and another where the function is
fixed and the mapping varies (the superposition operator). We overview a few classical results
regarding these operators, indicate a new one, and show how these operators show up in
chronological calculus and in classical Picard iteration. We then show how continuity of the
superposition operator can be used to prove regularity results for a very general setting of
time-varying, parameter-dependent ordinary differential equations. (TCPL 201) |
15:00 - 15:30 |
Coffee Break (TCPL Foyer) |
15:30 - 16:00 |
Rafal Goebel: How regular-enough set-valued dynamics allow for the usual asymptotic stability theory, and more. ↓ For differential inclusions, hybrid systems, and other natural generalizations of classical dynamics, continuous dependence of solutions on initial conditions may be too much to ask for. Concepts of set convergence and (semi)continuity of set-valued mappings come to the rescue. The talk will present the foundations of these ideas; highlight how, under natural (semi)continuity assumptions on the data of a differential inclusion or a hybrid system, classical results on invariance, smooth Lyapunov functions, uniformity and robustness of asymptotic stability, etc., extend to these settings; and perhaps connect these extensions, in the hybrid setting, to a result from topological theory of dynamical systems called the Conley's decomposition. The talk will be low on technical details. (TCPL 201) |
16:00 - 16:30 |
Jacob Carruth: Optimal agnostic control ↓ Consider a particle whose position q is governed by the dynamics
dq = (aq + u)dt + dW,
where W is Brownian motion, a is a real number, and u is a control
variable. We would like to choose u to minimize a given cost function.
If the parameter a is known, then it is a classical result that the
optimal u is the linear-quadratic regulator. Suppose, however, that a
is completely unknown; we refer to this as agnostic control. In this
case it is not even clear what it means to choose u optimally. In this
talk, I will introduce the notion of regret to characterize optimal
strategies for agnostic control—-a strategy is optimal if it minimizes
the regret. Given any ε>0, I will then exhibit an agnostic control
strategy that minimizes the regret to within a factor of (1+ε).
This is joint work with M. Eggl, C. Fefferman, C. Rowley. (TCPL 201) |
16:30 - 17:30 |
Vakhtang Putkaradze: Integrability, Chaos and Control of a Figure Skater ↓ Figure skating is a beautiful sport combining elegance, precision, and athleticism. To understand some of the mechanics and complexity involved in this sport, we derive and analyze a model of a figure skater in continuous contact with the ice (i.e., no jumps). In the first part of the talk, we analyze the dynamics of a model figure skater and show that the behavior of the skater can either be regular (solvable) or chaotic, depending on the mass distribution. For regular dynamics, we show that there are constants of motion, one coming from symmetry (conservation of angular momentum) and one of a mysterious origin with no clear physical explanation. We then explain how a skater may control the trajectory on ice in a compulsory figures competition. For simplicity, we consider the model of a skater with no lean, with a controlled moving mass. We derive a control procedure by approximating the trajectories using circular arcs. We show that there is a control procedure of a 'lazy' (or 'efficient') figure skater, minimizing the 'relative kinetic energy' of the control mass, which leads to well-posed equations for the control masses. We demonstrate examples of our system tracing actual compulsory figure skating trajectories. We also discuss further extensions of the model and applications to real-life figure skating.
Joint work with M. Rhodes and V. Gzenda (TCPL 201) |
17:30 - 19:30 |
Dinner ↓ A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building. (Vistas Dining Room) |