(Mock) Modularity, Moonshine and String Theory

Conference Date: 
Monday, April 13, 2015 (All day) to Friday, April 17, 2015 (All day)
Scientific Areas: 
String Theory

 

Modular and mock modular forms have appeared in new and intriguing roles in relation to Mathieu and Umbral moonshine.  They also appear in studies of the quantum geometry of Calabi-Yau manifolds, three dimensional gravity, and other aspects of string theory.  This workshop will be focused on the recent developments in these intertwined directions.

This workshop is also part of the UNIFY network.  Participants from the UNIFY nodes are welcome to register and participate.

Registration for this workshop is now closed.

Sponsorship for this workshop has been provided by:

  • Miranda Cheng, University of Amsterdam
  • John Duncan, Case Western Reserve University
  • Matthias Gaberdiel, ETH Zurich
  • Terry Gannon, University of Alberta
  • Sarah Harrison, Harvard University
  • Jeffrey Harvey, University of Chicago
  • Shamit Kachru, Stanford University
  • Christoph Keller, Rutgers University
  • Heeyeon Kim, Perimeter Institute
  • Albrecht Klemm, University of Bonn
  • Ching Hung Lam, Institute of Mathematics, Academia Sinica
  • Geoffrey Mason, Universityof California, Santa Cruz
  • Greg Moore, Rutgers University
  • Sameer Murthy, Kings College, London
  • Hirosi Ooguri, California Institute of Technology
  • Daniel Persson, Chalmers University of Technology
  • Anne Taormina, Durham University
  • Roberto Volpato, SLAC & Stanford University
  • Katrin Wendland, University of Freiburg
  • Nathan Benjamin, Stanford University
  • Lakshya Bhardwaj, Perimeter Institute
  • Christopher Brust, Perimeter Institute
  • Miranda Cheng, University of Amsterdam
  • Nima Doroud, University of Cambridge
  • John Duncan, Case Western Reserve University
  • Matthias Gaberdiel, ETH Zurich
  • Terry Gannon, University of Alberta
  • Jaume Gomis, Perimeter Institute
  • Sarah Harrison, Harvard University
  • Jeffrey Harvey, University of Chicago
  • Shamit Kachru, Stanford University
  • Christoph Keller, Rutgers University
  • Heeyeon Kim, Perimeter Institute
  • Albrecht Klemm, University of Bonn
  • Peter Korotev, Perimeter Institute
  • Ching Hung Lam, Institute of Mathematics, Academia Sinica
  • Geoffrey Mason, Universityof California, Santa Cruz
  • Greg Moore, Rutgers University
  • Seyed Faroogh Moosavian, Perimeter Institute
  • Sameer Murthy, Kings College, London
  • Hirosi Ooguri, California Institute of Technology
  • Natalie Paquette, Stanford University
  • Daniel Persson, Chalmers University of Technology
  • Callum Quigley, University of Alberta
  • Miroslav Rapcak, Perimeter Institute
  • Anne Taormina, Durham University
  • Roberto Volpato, SLAC & Stanford University
  • Katrin Wendland, University of Freiburg
  • Jie Zhou, Perimeter Institute

Monday, April 13, 2015

Time

Event

Location

9:30 – 10:00am

Registration

Reception

10:00 – 10:05am

Welcome and Opening Remarks

Bob Room

10:05 – 11:00am

Jeffrey Harvey, University of Chicago
TBA

Bob Room

11:00 – 12:00pm

Albrecht Klemm, University of Bonn
TBA

Bob Room

12:00 – 2:00pm

Lunch

Bistro – 2nd Floor

2:00 – 3:00pm

Geoffrey Mason, University of California, Santa Cruz
Symplectic automorphisms of some hyperk\"ahler manifolds

Bob Room

3:00 – 4:00pm

Shamit Kachru, Stanford University
TBA

Bob Room

 

Tuesday, April 14, 2015

Time

Event

Location

10:00 – 11:00am

John Duncan, Case Western Reserve University
Umbral Moonshine Modules

Bob Room

11:00 – 12:00pm

Daniel Persson, Chalmers University of Technology
Second quantized Mathieu moonshine and vector valued Siegel modular forms

Bob Room

12:00 – 2:00pm

Lunch Break

Bistro – 2nd Floor

2:00 – 3:00pm

Roberto Volpato, SLAC & Stanford University
Fricke S-duality in CHL models

Bob Room

3:00 – 4:00pm

Miranda Cheng, University of Amsterdam
TBA

Bob Room

6:00pm Onwards

Reception

Bistro – 2nd Floor

 

Wednesday, April 15, 2015

Time

Event

Location

10:00 – 11:00am

Katrin Wendland, University of Freiburg
How does extended supersymmetry affect the elliptic genus?

Bob Room

11:00 – 12:00pm

Christoph Keller, Rutgers University
Modular invariance and holographic CFTs

Bob Room

12:00 – 12:15

Conference Photo

TBA

12:15 – 2:00pm

Lunch Break

Bistro – 2nd Floor

2:00 – 3:00pm

Ching Hung Lam, Institute of Mathematics, Academia Sinica
On holomorphic vertex operator algebras of central charge 24

Bob Room

 

Thursday, April 16, 2015

Time

Event

Location

10:00 – 11:00am

Hirosi Ooguri, California Institute of Technology
TBA

Bob Room

11:00 – 12:00pm

Terry Gannon, University of Alberta
TBA

Bob Room

12:00 – 2:00pm

Lunch Break

Bistro – 2nd Floor

2:00 – 3:00pm

Anne Taormina, Durham University
TBA

Bob Room

3:00 – 4:00pm

Heeyeon Kim, Perimeter Institute
TBA

Bob Room

 

Friday, April 17, 2015

Time

Event

Location

10:00 – 11:00am

Greg Moore, Rutgers University
TBA

Bob Room

11:00 – 12:00pm

Sarah Harrison, Harvard University
TBA

Bob Room

12:00 – 2:00pm

Lunch Break

Bistro – 2nd Floor

2:00 – 3:00pm

Sameer Murthy, King's College London
TBA

Bob Room

3:00 – 4:00pm

Matthias Gaberdiel, ETH Zurich
TBA

Bob Room

 

John Duncan, Case Western Reserve University

Umbral Moonshine Modules

Umbral moonshine attaches mock modular forms and meromorphic Jacobi forms to automorphisms of the Niemeier lattices. It is now known that this association can be recovered from specific, graded modules for the Niemeier lattice automorphism groups. We will describe recent progress in a program to realize these modules explicitly. 

Christoph Keller, Rutgers University

Modular invariance and holographic CFTs

Modular invariance plays an important role in AdS3/CFT2 holography. I discuss the structure of non-holomorphic CFT partition functions, namely in what sense the light spectrum determines the heavy spectrum and how to construct example partition functions using Poincare series. This yields necessary conditions on the spectrum of holographic CFTs. Finally I will discuss permutation orbifolds as examples of such theories.

Ching Hung Lam, Institute of Mathematics, Academia Sinica

On holomorphic vertex operator algebras of central charge 24

I will talk about the recent progress on the classification of (strongly regular) holomorphic vertex operator algebras of central charge 24. In particular, I will discuss a  construction of certain holomorphic vertex operator algebras of central charge 24 using orbifold construction associated to inner automorphisms.  This talk is based on a joint work with Hiroki Shimakura.

Geoffrey Mason, University of California, Santa Cruz

Symplectic automorphisms of some hyperk\"ahler manifolds

Daniel Persson, Chalmers University of Technology

Second quantized Mathieu moonshine and vector valued Siegel modular forms

Roberto Volpato, SLAC & Stanford University

Fricke S-duality in CHL models

We consider dual pairs of four dimensional heterotic/type IIA CHL models with 16 space-time supersymmetries.  We provide strong evidence for the existence of an S-duality acting on the heterotic axion-dilaton by a Fricke involution S --> -1/NS, where N is the order of the orbifold symmetry. While most models are self-dual, in some cases S-duality relates the CHL model to a compactification of type IIA on an orbifold of T^6. We provide a simple criterion to determine whether a model is self-dual or not. Finally, we argue that in self-dual CHL models the lattices of electric and magnetic charges must be N-modular and verify this prediction.

Katrin Wendland, University of Freiburg

How does extended supersymmetry affect the elliptic genus?

The elliptic genus of K3 and its decomposition into characters of the N=4 superconformal algebra of associated conformal field theories can be viewed as the outset of Mathieu Moonshine. Thus, extended supersymmetry induces additional properties of the elliptic genus, which so far lack a satisfactory geometric interpretation. We investigate the implications of this decomposition on geometric structures that underlie the elliptic genus.
 

If you are an invited speaker to this event, Perimeter Institute staff will contact you to coordinate ground transportation arrangements on your behalf.

If you need transportation while attending the conference, we offer suggestions below. If flying, we suggest that you book your flight to arrive at Toronto International Airport (YYZ) or the Region of Waterloo International Airport (YKF).


Boulevard Limousine (estimated travel time 1hr) The fare for Boulevard Limousine for one passenger is $118.00 to the Toronto Airport.  The fare for one passenger from the Toronto Airport to Waterloo is $133.00.  To make reservations, please visit their website or call 519-886-8090.


Airways Transit (estimated travel time 1hr) Airways Transit connects Toronto (Pearson), Hamilton (Munro), and Region of Waterloo International Airports with the Kitchener-Waterloo area by providing 24 hour shared ride door-to-door service. To make reservations online please visit their webiste of contact them by phone 24 hours: 519-886-2121.


0001 Toronto Cabs (estimated travel time 1hr)  Approximately $160.00 rate for one-way: Toronto International Airport to Waterloo. Call 416-809-5656. 
Note: One or more passengers can split this $160.00 rate.


Car Rentals Upon arrival in any of the terminals at Pearson International Airport there are a number of car rental agencies to choose from. Their booths are located on the arrivals level. The cost of a car rental is dependent upon the type of vehicle you would like and the length of the stay. 

Driving Directions 

  • From the airport, follow signs for Highway 427 South/Highway 401.  
  • Continue to follow signs for Highway 401 West - London.  
  • Proceed West on Highway 401.  
  • Exit Highway 401 at Highway 8 West.  
  • Take exit 278 (Highway 8 West) and follow 8 West for 5 km to Highway 85, towards Highway 7 East. 
  • Proceed on Highway 85 for 5 km to Bridgeport Road exit. Turn right at the off-ramp, traveling west.  
  • Follow Bridgeport Road for 2 km into downtown Waterloo.  
  • Bridgeport is a four-lane one-way road. It becomes Caroline Street at Albert Street. Continue straight ahead.  
  • Travel forward another 200 metres, but ease over into the right-hand lane. As you go down a hill and around a curve, look for the green Perimeter Institute sign on the right hand side. The parking lot entrance is just after the sign (past the historic grist mill that sits on the edge of Silver Lake).  
  • Turn right into the PI parking lot entrance.

If you are an invited speaker to this event, Perimeter Institute staff will contact you to coordinate hotel accommodations on your behalf.

If you need accommodations while attending the conference, we offer suggestions for lodging below.  When booking your reservation, please indicate that you will be attending a conference at Perimeter in order to receive the best possible rate.


Delta Waterloo 110 Erb Street West Waterloo, ON N2L 0C6
Phone: 1-888-890-3222

Distance from PI: 450 m


Waterloo Hotel 2 King Street North Waterloo, ON N2J 2W7
Phone: 519-885-2626
Distance from PI: 500 m


Comfort Inn 190 Weber Street North Waterloo, ON N2J 3H4
Phone: 519-747-9400
Distance from PI: 2.3 km


Walper Terrace Hotel 1 King Street West Kitchener, ON N2G 1A1
Phone: 519-745-4321
Distance from PI: 3.7 km


Waterloo Inn 475 King Street North Waterloo, ON N2J 2Z5
Reservation line: 1-800-361-4708
Reservation e-mail: reserve@waterlooinn.com
Distance from PI: 4.2 km


Four Points by Sheraton 547 King Street North Waterloo, ON N2L 5Z7
Phone: 519-884-0100
Distance from PI: 4.3 km


Courtyard by Marriott 50 Benjamin Road East St. Jacobs, ON N2V 2J9
Phone: 519-884-9295
Distance from PI: 5.6 km

Scientific Organizers:

  • Miranda Cheng, University of Amsterdam
  • Matthias Gaberdiel, ETH Zurich
  • Jaume Gomis, Perimeter Institute
  • Shamit Kachru, Stanford University