We are delighted to announce the inaugural HoTTEST Distinguished Lecture Series to be given by Mike Shulman (University of San Diego). The series consists of three lectures which will take place on April 14, 21, and 28 at 11:30 AM Eastern time. The Eastern time zone is now observing daylight saving time, making it UTC-04:00. Each lecture will be one-hour long and will be followed by a 30-minute discussion. The title and abstract are below. The Zoom link is https://zoom.us/j/994874377 Further information, including our Google Calendar and Youtube channel, is available at http://uwo.ca/math/faculty/kapulkin/seminars/hottest.html We are looking forward to seeing many of you there! Best wishes, Carlo Angiuli Dan Christensen Chris Kapulkin * Mike Shulman University of San Diego Towards Third-Generation HOTT In Book HoTT, identity is defined uniformly by the principle of "indiscernibility of identicals". This automatically gives rise to higher structure; but many desired equalities are not definitional, and univalence must be asserted by a non-computational axiom. Cubical type theories also define identity uniformly, but using paths instead. This makes more equalities definitional, and enables a form of univalence that computes; but requires inserting all the higher structure by hand with Kan operations. I will present work in progress towards a third kind of homotopy type theory, which we call Higher Observational Type Theory (HOTT). In this system, identity is not defined uniformly across all types, but recursively for each type former: identifications of pairs are pairs of identifications, identifications of functions are pointwise identifications, and so on. Univalence is then just the instance of this principle for the universe. The resulting theory has many useful definitional equalities like cubical type theories, but also gives rise to higher structure automatically like Book HoTT. Also like Book HoTT, it can be interpreted in a class of model categories that suffice to present all Grothendieck-Lurie (∞,1)-toposes; and we have high hopes that, like cubical type theories, some version of it will satisfy canonicity and normalization. This is joint work with Thorsten Altenkirch and Ambrus Kaposi. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]