Modern Applications of Representation Theory

July 20 - August 06, 2014

Content

Overview

Advisory:

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:

Risi Kondor	University of Chicago
Lek-Heng Lim	University of Chicago
Jason Morton	The Pennsylvania State University

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

Participants

Name	Department	Affiliation
Tejal Bhamre	Department of Physics and Applied Mathematics	Princeton University
Mario Borha	Department of Mathematical Sciences	Northern Illinois University
Sixia Chen	Department of Computer Science & Engineering	University of Connecticut
Yutong Chen	PACM	Princeton University
Gregory Chirikjian	Department of Mechanical Engineering	Johns Hopkins University
Justin Curry	Department of Mathematics	Duke University
Walter Dempsey		University of Chicago
Samuel Denton		York University
Cameron Farnsworth	Department of Mathematics	Texas A & M University
Jonathan Fernandes	Department of Mathematics	University of Maryland
Brett Geiger	Department of Mathematics	University of Houston
Renato Ghini Bettiol	Department of Mathematics	University of Notre Dame
Jonathan Godbout	Department of Mathematics	Worcester Polytechnic Institute
William Grodzicki	Department of Mathematics	University of Minnesota, Twin Cities
Shamgar Gurevich	Department of Mathematics	University of Wisconsin, Madison
Jing Hao	Department of Mathematics	University of Wisconsin, Madison
Pamela Harris	Department of Mathematical Sciences	United States Military Academy
Peng He	Department of Mathematics	University of Pittsburgh
Mee Seong Im		University of Illinois at Urbana-Champaign
Shahrzad Jamshidi	Department of Mathematics	The Pennsylvania State University
Matthew Joseph		University of Chicago
Joseph Kileel	Department of Mathematics	University of California, Berkeley
Hwamog Kim	Department of Mathematics and Statistics	Mississippi State University
Risi Kondor	Departments of Computer Science and Statistics	University of Chicago
Robert Krone	Department of Mathematics	Georgia Institute of Technology
Joseph Landsberg	Department of Mathematics	Texas A & M University
Kang-Ju Lee	Department of Mathematical Sciences	Seoul National University
Lek-Heng Lim	Department of Statistics	University of Chicago
Ye Luo	Department of Mathematics	Georgia Institute of Technology
Peter McCullagh	Department of Statistics	University of Chicago
Cristopher Moore		Santa Fe Institute
Jason Morton	Department of Mathematics	The Pennsylvania State University
Ketan Mulmuley	Department of Computer Science	University of Chicago
Tatiana Orlova	Department of Computer Science	University of Chicago
Michael Orrison	Department of Mathematics	Harvey Mudd College
Deepti Pachauri	Department of Computer Sciences	University of Wisconsin, Madison
Daniel Rockmore	Department of Mathematics	Dartmouth College
Zvi Rosen	Department of Mathematics	University of California, Berkeley
Hans-Christian Ruiz	Department of Biophysics	Radboud Universiteit Nijmegen
John Santerre	Department of Computer Science	University of Chicago
Tony Se	Department of Mathematics	University of Kansas
Amit Singer	Department of Mathematics	Princeton University
Roberto Soto	Department of Mathematics	The University of Iowa
Ben Strasser	Department of Mathematics	University of Minnesota, Twin Cities
Yi Sun	Department of Mathematics	Massachusetts Institute of Technology
Nedelina Teneva	Department of Computer Science	University of Chicago
Bolor Turmunkh	Department of Mathematics	University of Illinois at Urbana-Champaign
Jacob Turner	Mathematics Department	The Pennsylvania State University
Chris Umans	Department of Computer Science	California Institute of Technology
Chen Wan	School of Mathematics	University of Minnesota, Twin Cities
Jiuya Wang	Department of Mathematics	University of Wisconsin, Madison
Tyson Williams	Computer Science	University of Wisconsin, Madison
Ken Sze-Wai Wong	Department of Statistics	University of Chicago
Angela Wu	Department of Mathematics	University of Chicago
Yifei Xu	Department of Basic Science	Mississippi State University