Our aim is to provide ample space for discussion. To this end, talks will be limited to an hour (for invited speakers) or 45 minutes (contributed talks), leaving the rest of the slot for questions and discussion.
You can also see abstracts.
6WFTop sessions will be in LG rooms of the Old Gym near the centre of Birmingham University main (Edgbaston) campus, building Y1 on the campus map. It is 5 minutes or less from the Computer Science building Y9 and University Station, and around 10 minutes from Edgbaston Park Hotel, building G23.
The Sambin/Vickers Saturday will take place in room UG06 in a different building, the Murray Learning Centre building R28, which is directly opposite Computer Science.
###Monday 8 April 2019
LG12, Old Gym
Tutorial day What is a space?
Benedikt Ahrens (Birmingham): Univalent type theory
Mathieu Anel (Carnegie Mellon): Toposes
09:00 coffee
09:30 Ahrens
11:00 break
11:30 Ahrens
12:30 lunch
14:30 Anel
16:00 break
16:30 Anel
17:30 end of the day
###Tuesday 9 April
LG06, Old Gym
09:00 coffee
09:30 Giovanni Sambin (Padova) invited speaker “Half way to Grothendieck’s aim”
11:00 break
11:30 Samuele Maschio (Padova) “Factorizing the Top-Loc adjunction through positive topologies”
12:30 lunch
14:30 Peter Johnstone (Cambridge) invited speaker “Betweenness reals”
16:00 break
16:30 Sina Hazratpour (Birmingham) “Fibrations of toposes”
17:30 end of the day
###Wednesday 10 April
LG12, Old Gym
09:00 coffee
09:30 Olivia Caramello (Como) invited speaker “Denseness conditions and equivalences of toposes”
11:00 break
11:30 Steve Vickers “Toposes via arithmetic universes”
12:30 lunch
The afternoon is free.
###Thursday 11 April
LG12, Old Gym
09:00 coffee
09:30 Ingo Blechschmidt (Verona) invited speaker “A general Nullstellensatz for generalized spaces”
11:00 break
11:30 Graham Manuell (Edinburgh) “The spectrum of a localic semiring”
12:30 lunch
14:30 Milly Maietti (Padova) “On the constructivity of the notion of formal space”
15:30 break
16:00 Auke Booij (Birmingham) “Extensional constructive analysis via locators”
17:00 Eric Finster (Birmingham) “Spectra as Infinitesimal Homotopy Types”
18:00 end of the day
19:00 Banquet - Pasta di Piazza. If you are expecting to go to the banquet, please check that your name is on the list on the banquet page. If it isn’t, please tell Steve Vickers by the end of Tuesday.
###Friday 12 April
LG12, Old Gym
09:00 coffee
09:30 Maria Manuel Clementino (Coimbra) invited speaker “Revisiting generalised enriched categories”
11:00 break
11:30 Paige North (Ohio) “Constructing models of homotopy type theory with abstract real numbers”
12:30 lunch
14:30 Thierry Coquand “Constructive mathematics and higher topos theory”
15:30 break
16:00 General discussion to bring together the different threads of the workshop.
We’ll start from a quote from Bourbaki “Introduction to the Theory of Sets”, archived as R154_nbr_055
“… nowadays it is known to be possible, logically speaking, to derive practically the whole of known mathematics from a single source, the Theory of Sets. … By so doing we do not claim to legislate for all time. It may happen at some future date that mathematicians will agree to use modes of reasoning which cannot be formalized in the language described here; according to some, the recent evolution of axiomatic homology theory would be a sign that this date is not so far. It would then be necessary, if not to change the language completely, at least to enlarge its rules of syntax. But this is for the future to decide.”
Now we are the future, what might we decide?
17:30 end
###Saturday 13 April {#sambinvickers}
Talks to celebrate the 70th birthday of Giovanni Sambin, and the 65th of Steve Vickers, in a one-day event organized by:
The event will take place in UG06, Murray Learning Centre, building R28, which is directly opposite the Computer Science building.
Breaks will be in the Computer Science atrium opposite.
09:30 Thierry Coquand (Chalmers) “Regular entailment relations”
10:00 break
10:10 Francesco Ciraulo (Padova) “Weak closure, Strong density: an overtview”
10:40 break (CS atrium)
11:10 Hajime Ishihara (JAIST) “Equivalents of the finitary non-deterministic inductive definitions”
11:40 break
11.50 Claudio Sacerdoti Coen (Bologna) TBA
12.20-14.10 lunch (CS atrium)
14.10 Erik Palmgren (Stockholm) “Localic completions in constructive analysis”
14:40 break
14:50 Pedro Resende (IST Lisbon) The observational logic of quantum mechanics
15:20 break
15.30 Christopher Townsend History of the double power locale
16:00 break (CS atrium)
16.30 Martin Escardo (Birmingham) TBA
17:00 wine and food (CS atrium)
For those wishing to gather afterwards for dinner, we have a table reserved at Jimmy Spices for 20:00. The price there is £15 for as much as you can eat from a diverse international buffet.