This workshop will take place February 24 - 27, 2025 at the TUM Akademiezentrum Raitenhaslach , a former Cistercian monastery.
We will have two experts who will be mentoring us during the workshop: Fernando Abellán and Hadrian Heine. Additionally, we will have David Gepner as a special guest for the last two days.
Fernando Abellán
Victor Carmona
David Gepner
Johannes Glossner
Jonte Gödicke
Ben Haïoun
Hadrian Heine
Patrick Kinnear
Naruki Masuda
Angus Rush
Claudia Scheimbauer
Pelle Steffens
Walker Stern
Will Stewart
Anja Svraka
Jackson van Dyke
Tashi Walde
Yang Yang
Markus Zetto
The conference location is a bit remote and not trivial to reach with public transport. For this reason we have booked busses from Garching (suburb of Munich, easily reachable by train and not far from the airport) to Raitenhaslach, and vice versa.
Departure on Monday (February, 24th) will be at 10:00. We arrive in Raitenhaslach for lunch and the mathematical program will start afterwards. On Thursday (February, 27th), we leave after lunch and the busses will reach Garching around 15:00. Unfortunately this means that if you are travelling from outside of Bavaria, you might need to find accommodation for one night (23-24) in Munich to take the bus in the morning. Hopefully the return trip is such that most of you will be able to return home on the same day.
FEBRUARY 24 | ||
10:00-11:30 | BUS: Garching → Monastery (DEPARTS 10:00) | |
12:30-13:30 | Lunch | |
13:45-14:45 | Speaker 1 | Gray's original tensor productThe Gray tensor product was first introduced in the setting of strict 2- categories, where it is far more amenable to direct computation. This talk will survey the original definition and construction from [Gra74] and its first properties - in particular, the connection to lax transformations. Time permitting, the talk may also cover homotopical aspects of Gray's construction (e.g., the Quillen bifunctoriality of [Lac04]) or variants (such as the variant representing pseudonaturality of [GPS95]). |
15:00-16:00 | Ben Haïoun | The scaled simplicial set approachThis talk should briefly introduce scaled simplicial sets, and the construction of their Gray product, following section 2 of [GHL21]. It should then survey the relation to functor categories with lax (or oplax) transformations, and, time permitting, describe the universal property in terms of oplax normal functors. |
16:00-16:30 | Coffee | |
17:45-18:00 | BUS: Monastery → Hotel | |
18:30-19:30 | Dinner | |
FEBRUARY 25 | ||
9:10-9:30 | BUS: Hotel → Monastery | |
9:45-10:45 | Markus Zetto | The model-independent approachThe second talk of this series should survey the results of [CM23] providing a model-independent characterization of the Gray product of (∞, 2)-categories in terms of cubes. In particular, the talk should cover the universal properties of Corollary 3.5 in op. cit., which characterize the Gray product in terms of its operation on cubes. |
11:15-12:15 | Speaker 4 | The Gray tensor product of (∞, n)-categoriesThis talk should introduce cubical sets and marked cubical sets, and discuss the way in which they are expected to model (∞, ∞)-categories. The speaker should then cover the construction of the Gray tensor products of marked cubical sets in section 2.2 of [CKM20]. Time permitting, the talk can also discuss some of the model-categorical aspects of the Gray product of marked cubical sets. |
12:30-13:30 | Lunch | |
13:45-14-45 | Jonte Gödicke | The Gray tensor product of (Steiner) ω-categories IThis talk will survey the theory of Steiner ω-categories and their relation to augmented directed chain complexes, following the background in section 1 of [AGOR23], supplemented by the original reference [Ste04]. |
15:00-16:00 | Naruki Masuda | The Gray tensor product of (Steiner) ω-categories IIUsing the definitions and machinery established in the previous talk, this talk should introduce the tensor products of augmented directed complexes and strong Steiner ω-categories (section 7 of [Ste04]). It should discuss the monoidal closedness of this product, and, time permitting, its relation to the Gray product constructed in [AS93]. |
16:00-16:30 | Coffee | |
17:45-18:00 | BUS: Monastery → Hotel | |
18:30-19:30 | Dinner | |
FEBRUARY 26 | ||
9:10-9:30 | BUS: Hotel → Monastery | |
9:45-10:45 | Hadrian Heine | Talk I
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11:15-12:15 | Hadrian Heine | Talk II
|
12:30-13:30 | Lunch | |
13:45-14:45 | Hadrian Heine | Talk III
|
15:00-16:00 | Fernando Abellán | Talk I
|
16:00-16:30 | Coffee | |
17:45-18:00 | BUS: Monastery → Hotel | |
18:30-19:30 | Dinner | |
FEBRUARY 27 | ||
9:10-9:30 | BUS: Hotel → Monastery | |
9:45-10:45 | Fernando Abellán | Talk II
|
11:00-12:00 | Fernando Abellán | Talk III
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12:00-13:00 | Lunch | |
13:00-15:00 | BUS: Monastery → Garching (ARRIVING AROUND 15:00) |