Log24

Introduction

In the present article, the research work of many years is summarized in an interim report concerning the connection between logic, space, time and matter. The author always had in mind two things, namely 1. The discovery/construction of an interface between matter and mind, and 2. some entry points for the topos view that concern graphs, grade rotations and contravariant involutions in geometric Boolean lattices. In this part of the MiTopos theme I follow the historic approach to mathematical physics and remain with the Clifford algebra of the Minkowski space. It turns out that this interface is a basic morphogenetic structure inherent in both matter and thought. It resides in both oriented spaces and logic, and most surprisingly is closely linked to the symmetries of elementary particle physics.

— "MiTopos: Space Logic I," 
      by Bernd Schmeikal,
      23rd of January 2023

27th Friday

9:00 – 10:00 Andrés Villaveces (Univ. Nacional de Colombia):
Galoisian model theory:
the role(s) of Grothendieck (à son insu! )

10:00 – 11:00 Olivia Caramello (Univ. of Insubria; by Zoom):
The “unifying notion” of topos 1

1:00 – 11:15 Coffee Break

1:15 – 12:15 Mike Shulman (Univ. of San Diego):
Lifting Grothendieck universes to Grothendieck toposes 

12:15 – 1:15 José Gil-Ferez (Chapman Univ.)
The Isomorphism Theorem of Algebraic Logic:
a Categorical  Perspective

1:15 – 2:30 Lunch

2:30 – 3:30 Oumar Wone (Chapman) :
Vector bundles on Riemann surfaces according to
Grothendieck and his followers

3:30 – 4:30 Claudio Bartocci (Univ. of Genova):
The inception of the theory of moduli spaces:
Grothendieck's Quot scheme

4:30 – 5:30 Christian Houzel (IUFM de Paris):
Riemann surfaces after Grothendieck
[presented by J.J. Szczeciniarz]

28th Saturday

9:00 – 10:00 Silvio Ghilardi (Univ. degli Studi, Milano):
Investigating definability in propositional logic
via Grothendieck topologies and sheaves

10:00 – 11:00 Matteo Viale (Univ. of Turin; by zoom):
The duality between Boolean valuated models and 
topological presheaves

11:00 – 11:15 Coffee Break

11:15 – 12:15 Benjamin Collas (RIMS, Kyoto Univ.):
Galois-Teichmüller: arithmetic geometric principles

12:15 – 1:15 Closing: general discussion
animated by Alex Kurz (Chapman)

Buffy: So, Giles! Got anything that can make this day any worse?
Giles: How about the end of the world?
Buffy: Knew I could count on you.

Giles: This is what we know. Some sixty years ago, a very old, very powerful vampire came to this shore, not just to feed.
Buffy: He came 'cause this town's a mystical who's it.
Giles: Yes. The Spanish who first settled here called it 'Boca del Infierno'. Roughly translated, 'Hellmouth'. It's a sort of, um, portal between this reality and the next. This vampire hopes to open it.
Buffy: Bring the demons back.
Xander: End of the world.
Willow: But he blew it! Or, I mean, there was an earthquake that swallowed half the town, and him, too.
Giles: You see, opening dimensional portals is a tricky business. Odds are he got himself stuck, rather like a, uh, cork in a bottle.
Xander: And this Harvest thing is to get him out.