Organizing Committee
  • Miranda Cheng
    University of Amsterdam
  • Sergei Gukov
    Caltech
Abstract

A long-standing problem in quantum topology is to find a function, more precisely a q-series with integer coefficients, such that its limiting values at primitive roots of unity yield invariants of Witten and Reshetikhin-Turaev. In other words, such a function would be to 3-manifolds what the Jones polynomial is to knots. Somewhat surprisingly, recent physics developments suggest that, in order to solve this problem, one must associate to a 3-manifold not a single function (q-series), but rather a collection of functions. Very recently, based on both physical intuition and explicit computations, it was suggested that these 3-manifold invariants display (modified) modularity properties of various types and are related to number theoretic objects including mock and false theta functions and quantum modular forms. This workshop will bring experts from the fields of topology, physics and number theory together, with the goal of combining knowledge and computational skills and furthering the understanding of the modular properties of the 3-manifold invariants.

This workshop is fully funded by a Simons Foundation Targeted Grant to Institutes.

Image for "Modularity and 3-manifolds"

Confirmed Speakers & Participants

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee

Workshop Schedule

Friday, March 8, 2019
TimeEventLocationMaterials
8:30 - 9:25am ESTRegistration121 S Main St, Providence, RI 02903, USA 
9:25 - 9:30am ESTWelcome - ICERM Director  
9:30 - 10:15am ESTWelcome and Preliminary Discussions - Miranda Cheng and Sergei Gukov11th Floor Lecture Hall 
10:30 - 11:30am ESTPractical computations of q-series \hat Z_a (q) - Du Pei, CalTech and QGM, Aarhus University11th Floor Lecture Hall 
11:30 - 12:00pm ESTCoffee/Tea Break11th Floor Collaborative Space 
12:00 - 1:00pm EST3d N=2 theory and knot complements - Ciprian Manolescu, University of California, Los Angeles11th Floor Lecture Hall
1:00 - 1:10pm ESTGroup Photo11th Floor Lecture Hall 
1:10 - 2:30pm ESTBreak for Lunch  
2:30 - 3:30pm ESTIntroduction to mock modular forms - Amanda Folsom, Amherst College11th Floor Lecture Hall
3:30 - 4:00pm ESTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 5:00pm EST3-manifolds, false theta functions and resurgence - Sarah Harrison, McGill11th Floor Lecture Hall 
5:00 - 6:30pm ESTWelcome Receptions11th Floor Collaborative Space 
Saturday, March 9, 2019
TimeEventLocationMaterials
9:15 - 10:15am ESTIntroduction to quantum modular forms - Don Zagier, Max Planck Institute for Mathematics11th Floor Lecture Hall 
10:30 - 11:30am ESTPractical computations with hyperbolic 3-manifolds - Nathan Dunfield, University of Illinois, Urbana-Champaign11th Floor Lecture Hall
11:30 - 12:00pm ESTCoffee/Tea Break11th Floor Collaborative Space 
12:00 - 1:00pm ESTDiscussion Session- Resurgence Questions - Moderated by: Gerald Dunne, Sarah Harrison, Sergei Gukov11th Floor Lecture Hall 
1:00 - 2:30pm ESTBreak for Lunch  
2:30 - 3:30pm ESTDiscussion Session- False Theta Functions and Homological Blocks - Moderated by: Miranda Cheng, Antun Milas, Kazuhiro Hikami11th Floor Lecture Hall 
3:30 - 4:00pm ESTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 5:00pm ESTMock Modular Forms and 3-Manifolds - Francesca Ferrari, SISSA (Trieste)11th Floor Lecture Hall 
Sunday, March 10, 2019
TimeEventLocationMaterials
9:15 - 10:15am EDTVertex Operator Algebras and False/Mock Modular Forms - Antun Milas, SUNY Albany11th Floor Lecture Hall 
10:30 - 11:30am EDTDiscussion Session- VOA characters, quantum modular forms, and homological blocks - Moderated by: Boris Feigin and Pavel Etingof11th Floor Lecture Hall 
11:30 - 12:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
12:00 - 1:00pm EDTDiscussion Session- Mock modular forms and Homological Blocks - Moderated by: Miranda Cheng, Sarah Harrison, Francesca Ferrari11th Floor Lecture Hall 
1:00 - 2:30pm EDTBreak for Lunch  
2:30 - 3:30pm EDTDiscussion Session- calculations for higher rank gauge groups - Moderated by: Hee-Joong Chung, Sunghyuk Park, Francesca Ferrari11th Floor Lecture Hall 

Lecture Videos

Mock modular forms and 3-manifolds

Francesca Ferrari
SISSA (Trieste)
March 9, 2019

Practical computations with hyperbolic 3-manifolds

Nathan Dunfield
University of Illinois, Urbana-Champaign
March 9, 2019

Introduction to quantum modular forms

Don Zagier
Max Planck Institute for Mathematics
March 9, 2019

3d N=2 theory and knot complements

Ciprian Manolescu
University of California, Los Angeles
March 8, 2019

Practical computations of q-series \hat Z_a (q)

Du Pei
Caltech and QGM, Aarhus University
March 8, 2019