Lecture Series. The presentations will consist of three lecture series.
David Nadler — From manifolds to symplectic manifolds via examples
From manifolds, submanifolds, and maps to symplectic manifolds, Lagrangians, and correspondences. The focus will be on examples -- typically in low dimensions -- where we also know how to go from symplectic topology back to manifold topology.
The goal will be to develop intuitions and formulate questions where further research is still needed.
Peter Haine — From stratifications to singular Lagrangians
From stratifications and sheaves on a manifold to singular Lagrangians and microsheaves on a cotangent bundle. The focus will be on how basic results in homological algebraic topology appear from the perspective of a cotangent bundle.
The goal will be to become comfortable with a symplectic viewpoint on "basic" homological algebraic topology (such as loop spaces) and to begin to approach more "advanced" questions (such as exit paths).
References.
Kashiwara-Schapira, Sheaves on Manifolds
https://arxiv.org/abs/1905.07341
Xin Jin — On the geometry of polarizations
To study a symplectic manifold with techniques from algebraic topology, one often needs to choose a polarization. Focus will be on the geometry of such choices (Lagrangian Grassmannians, Lagrangian plane fields) and their impact (local: singularities of front projections; global: homotopical monodromy).
The goal will be to have a clear picture of obstructions, local vs global, homotopic vs geometric, to directly applying manifold theory.
References.
https://arxiv.org/abs/2004.14270
https://arxiv.org/pdf/1605.07259
Location and amenities. All activities (presentations & discussions, meals, lodging) will take place at the North Yellowstone Lodge. Here is a map that includes this Lodge, as well as other landmarks (eg, Gardner, which is the nearest town; Bozeman, which is where MSU's campus is, and which is near the main airport of the region.)
Though along a highway, this is a remote setting: visiting restaurants or shops is not realistic without a personal vehicle.
If weather permits, some activities may take place outside under gigantic `wedding' tent.
Hikes from The Lodge. Here is a link, with downloadable GPS files, to some nearby walks/hikes.
https://caltopo.com/m/K0TGE
Food. All meals will be provided on site. There will be 24-hour access to a kitchen space, as well as an assortment of snacks. Prior to the event, participants will be asked via a survey about dietary restrictions and preferences.
We will do our best to accommodate dietary restrictions and preferences. (Certainly, every meal will have vegan options.)
Accommodations. The North Yellowstone Lodge is a hostel, which will be entirely reserved for this event. The default lodging will be dormitory-style twin beds in shared rooms, with group bathrooms. (Soap, linens, and towels will be provided; other toiletries such as shampoo will not be provided.)
As best we can, we will work with (potential) participants seeking other lodging options.
Schedule. A typical daily schedule will look like this:
7:30-9:00am coffee and breakfast
9:00-10:30am lecture and break,
10:30-11:30am lecture,
11:30am-3:45pm lunch, discussions and/or walking & hiking,
3:45-5:00pm lecture and break,
5:00-6:00pm supplementary talk or exercises,
6:30pm+ dinner.
Friday's schedule will be different, to accommodate an excursion, of which there will be two options:
a guided trip to some geysers in Yellowstone National Park (and a stop in the small town of Gardner for any personal resupply);
a guided hike up Emigrant Peak.
Vehicles/shuttles will be arranged for both of these excursions.
Timing. We will assume participants will arrive in Bozeman on Tuesday just before the event, and depart from Bozeman on Monday (possibly Sunday night) just after the event. Accordingly, we will arrange a few shuttles to move participants from Bozeman to the Lodge on Tuesday night, and from the Lodge to Bozeman on Monday morning (or possibly Sunday night).
As best we can, we will work with (potential) participants intending to arrive earlier or depart later.
Travel. The best option for flying to this event is through Bozeman airport (code: BZN). In August, the Bozeman airport is relatively well-connected to other hubs. It is easy to hire a ride/taxi from the Bozeman airport to the town of Bozeman, though at the cost of about $50. We will do our best to fetch participants from the Bozeman airport.
For those who travel by personal vehicle to the event, there will be plenty of (free) parking at the Lodge.
Participants will be asked to fill out a survey prior to the event -- based on that, we will issue recommendations for how to connect with the arranged shuttle(s) (be it at the airport, or at a spot downtown).
Participant costs. Thanks to the NSF Award 1945639, and support from Montana State University, the conference will cover all food and lodging at the Lodge, as well as the arranged shuttles between Bozeman and the Lodge. Travel funds are also available, though not enough to cover all participants' travel costs. Decisions to (partially) fund travel will be based on responses to the form on the Registration Page. Participants who are awarded travel funds must fly to BZN within the expected dates -- exceptions can be made though a discussion with the Event Organizers about price-comparisons would be necessary.
Extended visit. In August, Southwest Montana is a lovely place for hiking and generally touring. We're happy to work with participants interested in extending their stay for personal reasons.