Schedule for: 19w5232 - Spaces of Embeddings: Connections and Applications

A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

A brief introduction to BIRS with important logistical information, technology instruction, and opportunity for participants to ask questions.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Meet in foyer of TCPL to participate in the BIRS group photo. The photograph will be taken outdoors, so dress appropriately for the weather. Please don't be late, or you might not be in the official group photo!

A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

We prove that knot invariants $\pi_0\ev_n:\pi_0\Emb_\partial(\D^1,\D^3)\rightarrow\pi_0\pT_n$ obtained from the Goodwillie-Weiss calculus of embeddings are \textit{surjective}, which completes one missing case in Goodwillie-Klein connectivity estimates and confirms a part of the conjecture by Budney-Conant-Koytcheff-Sinha. Crucial ingredients are our geometric understanding of the layer of the tower and an explicit interpretation of the evaluation maps using capped gropes (a variant of Gusarov-Habiro claspers). Actually, we prove a stronger result: if a knot is obtained from the unknot by surgery on a degree $n-1$ capped grope, then its first potentially non-vanishing embedding calculus invariant $\pi_0\ev_n(K)$ is precisely the class of the underlying tree of the grope in $\pi_0\pT_n$.

I will explain some of the basic ideas behind a joint work in progress with Joao Faria Martins, investigating the relation between the Kontsevich integral and higher order invariants of the same nature.

A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

5-day workshop participants are welcome to use BIRS facilities (BIRS Coffee Lounge, TCPL and Reading Room) until 3 pm on Friday, although participants are still required to checkout of the guest rooms by 12 noon.