Israel Science Foundation

University of Haifa

Hebrew University

Researh Workshop of the Israel Science Foundation on Factorization Homology

June 18 - 20 , 2018. Caesarea Maritime Center.

Main speakers

       John Francis

Northwestern University

David Ayala       

Montana State University

Find out more


Monday, June 18, 2018

Time Name Title
10:00 - 11:00 Arrival & Registration
11:00 - 12:00 John Francis Outline of a proof of the cobordism hypothesis
12:30 - 13:30 Lunch
13:30 - 14:00 Asaf Horev Stratified spaces
14:45 - 15:45 Shay Ben Moshe Exit-path oo-categories
15:45 - 16:15 Coffee break
16:15 - 17:15 Shachar Carmeli Correspondences and exponentiable fibrations
17:30 - 18:30 John Francis Bun, the oo-category classifying constructible bundles
18:30 - 20:00 Supper

Tuesday, June 19, 2018

Time Name Title
8:00 - 9:00 Breakfast
9:00 - 10:00 Samik Basu Theta_n, Segal sheaves, and (oo,n)-categories
10:15 - 11:15 Ariel Davis Tangential structures on stratified spaces
11:45 - 12:45 Ayala/Francis Factorization homology (I)
12:45 - 14:00 Lunch
14:00 - 15:00 Lior Yanovsky Factorization homology from E_n-algebras
15:15 - 16:15 Ayala/Francis Factorization homology (II)
16:30 - 19:00 Afternoon Excursion
19:00 - 20:00 Supper/Supper outing

Wednesday, June 20, 2018

Time Name Title
8:00 - 9:00 Breakfast
9:00 - 10:00 Shaul Barkan The Pontryagin–Thom theorem
10:15 - 11:15 Ayala/Francis The cobordism hypothesis (I)
11:30 - 12:30 Ayala/Francis The cobordism hypothesis (II)
12:30 - 13:30 Lunch
13:30 - 14:30 Ayala/Francis The cobordism hypothesis (III)
14:30 Departure



  1. David Ayala (Montana State University) v
  2. Ilan Barnea (Hebrew University)
  3. Samik Basu (Indian Statistical Institute Kolkata)
  4. Oren Ben-Bassat (University of Haifa)
  5. David Blanc (University of Haifa)
  6. Boris Chorny (University of Haifa - Oranim)
  7. Emmanuel Farjoun (Hebrew University) v
  8. John Francis (Northestern University) v
  9. Moshe Kamensky (BGU)
  10. Anton Khoroshkin (Higher School of Economics)
  11. Peter Nelson (University of Haifa)
  12. Marina Prokhorova (Technion)
  13. Karol Szumilo (University of Haifa)
  14. Drew Heard (University of Haifa)
  15. Tomer Schlank (Hebrew University)

Graduate Students

  1. Shaul Barkan (Tel Aviv University) v
  2. Shay Ben Moshe (Hebrew University) v
  3. Shachar Carmeli (Weizmann Institute of Science) v
  4. Ariel Davis (Hebrew University)
  5. Asaf Horev (Hebrew University)
  6. Shay Keidar (Weizmann Institute of Science) v
  7. Jonatan Kogan (Tel Aviv University)
  8. Evgeny Musicantov (Tel Aviv University)
  9. Nikitas Nikandros (Utrecht University)
  10. Alon Nissan-Cohen (Hebrew University) v
  11. Stephan Snigerov (Tel Aviv University) v
  12. Lior Yanovski (Hebrew University)
  13. Yitzhak Zangi (Hebrew University)


Asaf Horev:

The inductive definition of C0 stratified spaces, involving cones. An indication of conically smooth stratified spaces -- notably so that strata, as well as links, are equipped with smooth structure. Unzips (aka blow-ups). The simplicially enriched category Strat of conically smooth stratified spaces.

Ref: Local structures on stratified spaces.

Shay Ben Moshe:

The internal definition of the oo-category of oo-categories as an oo-subcategory of Fun(\Delta^{\op}, Spaces). Construction of functor \Delta ---> Strat sending [p] to \Delta^p=Cone^p(point) with the standard stratification. Exit-path oo-categories as the restricted Yoneda functor \Delta ---> Strat. Spaces of objects in Exit(X) as strata, and morphisms in Exit(X) as links between strata. (Optional: discuss the identification Fun(Exit(X),Spaces) = Shv^{constructible}(X) , which contextualizes Exit(X) .)

Ref: A stratified homotopy hypothesis.

Shachar Carmeli:

This talk is an opportunity to discuss oo-categories in more depth beyond the definition. Here are some specific points to address. Correspondences (as opposed to spans). The (flagged) oo-category Corr whose objects are oo-categories and whose morphisms are correspondences. Pushforward along an exponentiable fibration.

Ref: Fibrations of oo-categories.

Samik Basu:

Definition of Theta_n and of the oo-category of (oo,n)-categories as an oo-subcategory of Fun(\Theta_n^{\op}, Spaces).

Ref: Rezk, A cartesian presentation of weak n-categories. Factorization homology I.

Ariel Davis:

The oo-category Vect^{inj} of (finite-dimensional) vector spaces (over R) and injections among them. Tangential structures as oo-categories over Vect^{inj}. Vari-framings. Framed suspension. Solid n-framings. Examples of vari-framed, and solid n-framed, stratified spaces, including the hemispherically-stratified n-disk D^n. Aut^{vfr}(D^n) is discrete.

Ref: Factorization homology I.

Lior Yanovsky:

Definition of the symmetric monoidal oo-category Mfld_n; likewise, the definition of Mfld_n^{fr}. The definition of Disk_n, as well as Disk_n^{fr}. The definition of Disk_n-algebras, and E_n-algebras, in these terms. The definition of ``\otimes-excisive'' functors from Mfld_n, and Mfld_n^{fr}. The classification of such as Disk_n-algebras, and E_n-algebras, respectively, via factorization homology. Non-abelian Poincare' duality.

Ref: Factorization homology of topological manifolds.

Shaul Barkan:

Proof of the Pontryagin–Thom theorem: inverse images of regular values; Pontryagin–Thom collapse maps of open embeddings.

Ref: Milnor, Topology from the differentiable viewpoint.

How to get there

By car:

Take the coastal road (No. 2) to the Caesarea Interchange West (towards the sea). Drive for a kilometer or two past the gas station (with the power station smokestacks on your left) till you reach a stop sign at a T junction (with an anchor marked "Palyam" directly in front of you).

Turn left and immediately right - there is a blue sign for "The Caesarea Maritime Center and Sports Center". The Center itself is by the sea, just south of Kibbutz Sdot Yam. You can park outside, or use the intercom at the barrier to enter the Center parking lot. We will meet outside the office, which is in the building on your right as you enter.

For further details on the location, see Maritime Center - MERKAZ YAMI. You can call Sima at the Center office at 050-2340169 in case of need.

Easiest way by public transportation:

Take a train the the Pardes Khana - Caesarea train station, and a cab from there.

Bus 76 operated by Nateev Express leaves the Hadera Central Bus Station for Sdot Yam on Monday at 06:40, 08:20, 11:25, 13:10, and later. It takes about 40 minutes, and you should get off at the Caesarea Rothschild Hotel (about one kilometer from the Caesarea Maritime Center).

For more information see: (Hebrew or Arabic) or call either *3553, or 1-599-559-559 (Hebrew, Arabic or Russian)