[Alta-Logic] peripatetic seminar and cs theory talk tomorrow

[Jonathan Gallagher]

Greetings,

There are three talks tomorrow that you may be interested in!

*Peripatetic Seminar.  Location ICT 616 at 12:00 pm, Friday January 27*

Speaker 1: Geoff Vooys
*Title: A Categorical Introduction to the Theory of Witt Vectors, Part I*

Abstract: The theory of Witt vectors is traditionally used to lift
commutative rings with identity in positive characteristic to commutative
rings with identity in characteristic zero in a way that extends to a
functor from the opposite category of affine schemes to the category of
commutative rings with identity. However, the constructions that define the
ring operations on the ring of Witt vectors are frequently too complicated
to work with in practice, and many of the properties of Witt vectors useful
in arithmetic geometry are frustratingly difficult to derive. In this talk
we will provide an alternative, more categorical, development of Witt
vectors that will make the theory cleaner and clearer, as well as show that
many of the properties of Witt vectors are simple consequences of the
categorical perspective that we will provide. In particular, we will show
that the Witt vector functor arises as a left Kan extension and that the
ring of Ghost components associated a ring of Witt vectors comes from a
natural transformation induced by the universal property of left Kan
extensions.

Speaker 2: Jonathan Gallagher
*Title: Tangent categories are strong, but still need to be a little
coherent*

Abstract: We will show that the structural natural transformations that
define
a tangent category are strong transformations with respect to appropriate
strengths.
We will see that this strength gives almost enough coherence to ensure that
the
category of differential objects is a differential $\lambda$-category; and
we will
introduce the notion of coherent differential structure which ensures that
differential objects are a differential $\lambda$-category.



*CS Theory Seminar.  Location ICT 616 at 2:00 pm, Friday January 27*
Speaker: Jérôme Fortier (University of Ottawa)
*Title: Restriction lambda-calculus *

One of the most general, and therefore nicest, families of models for the
notion of partiality (as in partial functions: functions that may be
undefined sometimes) in categorical terms is the notion of a restriction
category. That is: we put a focus on the idea of restricting morphisms to
the domain of other morphisms via a restriction operator. There is also a
notion of a cartesian closed restriction category (CCRC), analogous to the
regular notion of a CCC. This work is an attempt to prove the Curry-Howard
property for CCRC's, by developing the corresponding syntax. Our solution
is something like simply typed lambda-calculus, with a restriction
operator. The resulting logic turns out to be substructural, and therefore
very nice!


Hope to see you all there!!
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