Schedule for: 23w5055 - A Convergence of Computable Structure Theory, Analysis, and Randomness

Beginning on Sunday, March 19 and ending Friday March 24, 2023

All times in Banff, Alberta time, MDT (UTC-6).

Sunday, March 19
16:00 - 16:01 Check-in begins (BIRS Juniper Hotel)
17:30 - 18:30 Dinner Seating 1 (Juniper Bistro)
18:30 - 19:30 Dinner Seating 2 (Juniper Bistro)
19:30 - 20:30 Dinner Seating 3 (Juniper Bistro)
Monday, March 20
07:30 - 08:30 Breakfast Buffet (Juniper Hotel)
08:45 - 09:00 Introduction from BIRS Staff (Kiguli Room)
09:00 - 09:30 Introductions
We'll introduce ourselves, describe our work, and say what we're hoping to get out of the workshop
(Kiguli Room)
09:30 - 10:45 Isaac Goldbring: A primer in continuous model theory
In this talk, we give an introduction to modern continuous model theory. We use the metric ultraproduct construction to motivate the notion of a continuous language and the appropriate notion of structure for such languages. We give some examples of metric structures of interest in this workshop, such as Banach spaces, Hilbert spaces, and C*-algebras. We then move on to discuss compactness and completeness for continuous logic. Time permitting, we discuss some of the more nuanced aspects of continuous model theory, such as generalized formulas, definable sets, and the metric on type spaces.
(Kiguli Room)
10:45 - 12:00 Wesley Calvert: How to think about computable structures
In the very early days of computable structure theory there were only specific algebraic questions about specific structures that were presumed to be well known (e.g. does every explicitly given field have a unique computable algebraic closure). Later, this line of thought was abstracted into computable model theory, which could perhaps have looked something like model theory --- except that, as Millar famously remarked, there were "too many counterexamples." Over time what took hold was the study of a new category, taking the putative pathologies (e.g. distinctions between classically isomorphic structures) as features of a new and interesting mathematical realm. Apparently niche interests like infinitary logics, admissible set theory, and alpha-jump priority constructions found a natural home in this discipline. This talk will outline the kinds of questions asked in computable structure theory, and the style of arguments used.
(Kiguli Room)
12:00 - 13:30 Lunch Buffet (Juniper Bistro)
13:30 - 14:00 Group Photo (Meet at Bistro Patio (Weather Permitting))
14:00 - 15:15 Dan Turetsky: Broad Swathes of Randomness
I will give an overview of algorithmic randomness; this will cover definitions, central and illustrative results, and applications of randomness to other areas of computability theory. My intention is to give a picture of the field and show some of its potential for crossover with other areas.
(Kiguli Room)
15:15 - 15:45 Coffee break (Kiguli Room)
15:45 - 17:00 Alexander Melnikov: Computable dualities
I will talk about several recent results that explicitly relate computable algebra with computable topology via various sorts of effective dualities.
(Kiguli Room)
17:30 - 18:30 Dinner Seating 1 (Juniper Bistro)
18:30 - 19:30 Dinner Seating 2 (Juniper Bistro)
19:30 - 20:30 Dinner Seating 3 (Juniper Bistro)
Tuesday, March 21
07:30 - 08:30 Breakfast Buffet (Juniper Hotel)
09:00 - 10:00 Open problem session (Kiguli Room)
10:00 - 10:30 Coffee break (Kiguli Room)
10:30 - 11:00 Open problem selection
Division into groups to work on open problems.
(Kiguli Room)
11:00 - 12:00 Group 1 Discussion
Working on open problems.
(Kiguli Room)
12:00 - 13:30 Lunch Buffet (Juniper Bistro)
13:30 - 15:00 Group 1 Discussion
Working on open problems.
(Kiguli Room)
15:00 - 15:30 Coffee break (Kiguli Room)
15:30 - 17:00 Group 1 Discussion
Working on open problems.
(Kiguli Room)
17:30 - 18:30 Dinner Seating 1 (Juniper Bistro)
18:30 - 19:30 Dinner Seating 2 (Juniper Bistro)
19:30 - 20:30 Dinner Seating 3 (Juniper Bistro)
Wednesday, March 22
07:30 - 08:30 Breakfast Buffet (Juniper Hotel)
09:00 - 09:30 Open problem discussion
Discussion of progress from the previous day and group reformation (if desired).
(Kiguli Room)
09:30 - 10:30 Group 1 Discussion
Working on open problems.
(Kiguli Room)
10:30 - 11:00 Coffee break (Kiguli Room)
11:00 - 12:00 Group 1 Discussion
Working on open problems.
(Kiguli Room)
12:00 - 13:30 Lunch Buffet (Juniper Bistro)
13:30 - 17:30 Free Afternoon - Shuttle Service to Banff town (Banff National Park)
17:30 - 18:30 Dinner Seating 1 (Juniper Bistro)
18:30 - 19:30 Dinner Seating 2 (Juniper Bistro)
19:30 - 20:30 Dinner Seating 3 (Juniper Bistro)
Thursday, March 23
07:30 - 08:30 Breakfast Buffet (Juniper Hotel)
09:00 - 09:30 Open problem discussion
Discussion of progress from the previous day and group reformation (if desired).
(Kiguli Room)
09:30 - 10:30 Group 1 Discussion
Working on open problems.
(Kiguli Room)
10:30 - 11:00 Coffee break (Kiguli Room)
11:00 - 12:00 Group 1 Discussion
Working on open problems.
(Kiguli Room)
12:00 - 13:30 Lunch Buffet (Juniper Bistro)
13:30 - 14:00 Open problem discussion
Discussion of progress from the morning and group reformation (if desired).
(Kiguli Room)
14:00 - 15:00 Group 1 Discussion
Working on open problems.
(Kiguli Room)
15:00 - 15:30 Coffee break (Kiguli Room)
15:30 - 17:00 Group 1 Discussion
Working on open problems.
(Kiguli Room)
17:30 - 18:30 Dinner Seating 1 (Juniper Bistro)
18:30 - 19:30 Dinner Seating 2 (Juniper Bistro)
19:30 - 20:30 Dinner Seating 3 (Juniper Bistro)
Friday, March 24
07:30 - 08:30 Breakfast Buffet (Juniper Hotel)
09:00 - 10:15 Group 1 Discussion
Working on open problems.
(Kiguli Room)
10:15 - 10:45 Coffee break (Kiguli Room)
10:45 - 12:00 Workshop Conclusion Meeting
Wrapping up, discussing the progress that has been made, and planning for the future.
(Kiguli Room)
11:00 - 11:01 Check out by 11 (Juniper Front Desk)
12:00 - 13:30 Lunch Buffet (Juniper Bistro)