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.

Confirmed Speakers & Participants

  • Speaker
  • Poster Presenter
  • Attendee

Workshop Schedule

Friday, March 8, 2019
TimeEventLocationMaterials
8:30 - 9:25Registration121 S Main St, Providence, RI 02903, USA 
9:25 - 9:30Welcome - ICERM Director  
9:30 - 10:15Welcome and Preliminary Discussions - Miranda Cheng and Sergei Gukov11th Floor Lecture Hall 
10:30 - 11:30Practical computations of q-series \hat Z_a (q) - Du Pei, CalTech and QGM, Aarhus University11th Floor Lecture Hall 
11:30 - 12:00Coffee/Tea Break11th Floor Collaborative Space 
12:00 - 1:003d N=2 theory and knot complements - Ciprian Manolescu, University of California, Los Angeles11th Floor Lecture Hall
1:00 - 1:10Group Photo11th Floor Lecture Hall 
1:10 - 2:30Break for Lunch  
2:30 - 3:30Introduction to mock modular forms - Amanda Folsom, Amherst College11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 5:003-manifolds, false theta functions and resurgence - Sarah Harrison, McGill11th Floor Lecture Hall 
5:00 - 6:30Welcome Receptions11th Floor Collaborative Space 
Saturday, March 9, 2019
TimeEventLocationMaterials
9:15 - 10:15Introduction to quantum modular forms - Don Zagier, Max Planck Institute for Mathematics11th Floor Lecture Hall 
10:30 - 11:30Practical computations with hyperbolic 3-manifolds - Nathan Dunfield, University of Illinois, Urbana-Champaign11th Floor Lecture Hall
11:30 - 12:00Coffee/Tea Break11th Floor Collaborative Space 
12:00 - 1:00Discussion Session- Resurgence Questions - Moderated by: Gerald Dunne, Sarah Harrison, Sergei Gukov11th Floor Lecture Hall 
1:00 - 2:30Break for Lunch  
2:30 - 3:30Discussion Session- False Theta Functions and Homological Blocks - Moderated by: Miranda Cheng, Antun Milas, Kazuhiro Hikami11th Floor Lecture Hall 
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 5:00Mock Modular Forms and 3-Manifolds - Francesca Ferrari, SISSA (Trieste)11th Floor Lecture Hall 
Sunday, March 10, 2019
TimeEventLocationMaterials
9:15 - 10:15Vertex Operator Algebras and False/Mock Modular Forms - Antun Milas, SUNY Albany11th Floor Lecture Hall 
10:30 - 11:30Discussion Session- VOA characters, quantum modular forms, and homological blocks - Moderated by: Boris Feigin and Pavel Etingof11th Floor Lecture Hall 
11:30 - 12:00Coffee/Tea Break11th Floor Collaborative Space 
12:00 - 1:00Discussion Session- Mock modular forms and Homological Blocks - Moderated by: Miranda Cheng, Sarah Harrison, Francesca Ferrari11th Floor Lecture Hall 
1:00 - 2:30Break for Lunch  
2:30 - 3:30Discussion Session- calculations for higher rank gauge groups - Moderated by: Hee-Joong Chung, Sunghyuk Park, Francesca Ferrari11th Floor Lecture Hall 

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Acceptable Costs
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https://icerm.brown.edu/money/

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Reimbursement Tips
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Reimbursement Timing

6 - 8 weeks after all documentation is sent to ICERM. All reimbursement requests are reviewed by numerous central offices at Brown who may request additional documentation.

Reimbursement Deadline

Submissions must be received within 30 days of ICERM departure to avoid applicable taxes. Submissions after thirty days will incur applicable taxes. No submissions are accepted more than six months after the program end.

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