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2014 PI Summer Graduate Program

Modern Applications of Representation Theory

Modern Applications of Representation Theory

July 20 - August 6, 2014

Program Website

University of Chicago, Chicago, IL

The IMA will need to receive a personal statement describing your background and reasons for wanting to attend, and a letter of nomination from your department chair. Please send letters to Applications. Deadline for applications is April 30th, 2014.

Organizers | |
---|---|

University of Chicago | |

University of Chicago | |

The Pennsylvania State University | |

Guest Lecturers | |

University of Wisconsin, Madison | |

University of Texas, Austin | |

University of Chicago | |

Texas A & M University | |

University of Chicago | |

University of Chicago | |

Santa Fe Institute | |

The Pennsylvania State University | |

University of Chicago | |

Harvey Mudd College | |

Dartmouth College | |

Princeton University | |

California Institute of Technology |

This program is for graduate students from both IMA Participating Institutions as well as other U.S. universities. We expect to be able to fund up to 35 students from IMA Participating Institutions and 15 students from other U.S. universities. In order to participate, students must complete the online application form, provide a personal statement, and submit 1) a letter of nomination from the PI chair (for students from an IMA PI) or (2) a recommendation letter (for students from institutions that are not an IMA PI).

A main portion of this program consists of a three-week summer school for graduate students to be held in Summer 2014 on the campus of the University of Chicago. It will focus on modern applications of representation theory discovered largely within approximately the last 10 years.

Specifically, we intend to cover applications of representation theory in algebraic and geometric computational complexity, cryo-electron imaging, digital signal processing, holographic algorithms and quantum computing, machine learning and pattern recognition, and a few other specialized topics.

The instruction in the summer school comprises several week-long lecture series supplemented by a foundational tutorial and two days of short hour-long lectures on specialized topics. The objectives are to (i) quickly review the basic materials (tutorial); (ii) focus on the developments of the last 10 years (several long lecture series); and (iii) provide a glimpse of the state of current research and open problems (a number of short talks).

Most of the materials intended to be covered in (ii) and (iii) are at this point not easily accessible — not covered in any textbooks, courses, or even survey articles — they are only available in the form of original research papers or preprints. It is our hope that the summer school will bring these materials to graduate students, postdocs, and in general, any nonspecialist.

**Main Lectures**

- Introduction to representation theory
- Introduction to representation theory of tensors
- Representation theory in cryoelectron microscopy
- Representation theory in computational complexity
- Representation theory in digital signal processing
- Representation theory in fast matrix multiplication
- Representation theory in machine learning
- Representation theory and quantum computation

**Special Lectures**

- Alpha permanents and random processes
- Mutually unbiased bases
- Representation theory in compressive sensing
- Representation theory in identity management
- Representation theory in phylogetics
- Representation theory in statistics