Eckhart Hall

Institute for Mathematics and Its Applications
2014 PI Summer Graduate Program

Modern Applications of Representation Theory

The University of Chicago, Chicago, IL
July 20-August 6, 2014

IMA Program Application Form

Description

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.

Organizers

Guest Lecturers

Check the poster and the IMA program homepage. For questions, write to conference organizers.


Schedule

July 21 | July 22 | July 23 | July 24 | July 25 | July 28 | July 29 | July 30 | July 31
August 1 | August 4 | August 5

PDF Version of Schedule

MONDAY, July 21, 2014, in Room 112, at 5727 S. University Avenue

MANDATORY SAFETY PRESENTATION, 8:30–9:00 AM

LECTURE 1, 9:00–10:00 AM, J. M. Landsberg (Texas A&M University)
Video, Vimeo
Topic Grouping: Introductory Representation Theory

LECTURE 2, 10:30–11:30 AM, Michael Orrison (Harvey Mudd College)
"Algebraic Voting Theory"
Slides, Video,Vimeo
Topic Grouping: Learning, Statistics, and Optimization

WELCOME LUNCH, 11:45 AM–1:30 PM, ECKHART 110

LECTURE 3, 1:30–2:30 PM, Jason Morton (The Pennsylvania State University)
Notes, Video, Vimeo
Topic Grouping: Tensor Networks, Categories, Quantum

LECTURE 4, 3:00–4:00 PM, Risi Kondor (The University of Chicago)
"Introduction to Harmonic Analysis On Groups"
Slides, Video, Vimeo
Topic Grouping: Learning, Statistics, and Optimization

LECTURE 5, 4:30–5:30 PM, "Review and Problems, Introductory Representation Theory"
Topic Grouping: Introductory Representation Theory

TUESDAY, July 22, 2014, in Room 112, at 5727 S. University Avenue

LECTURE 1, 9:00–10:00 AM, J. M. Landsberg (Texas A&M University)
Video, Vimeo
Topic Grouping: Introductory Representation Theory

LECTURE 2, 10:30–11:30 AM, Michael Orrison (Harvey Mudd College)
"Adapted Bases and Fast Transforms"
Slides, Video, Vimeo
Topic Grouping: FFT, Signal Processing, Imaging

LUNCH BREAK, 11:30 AM–1:30 PM

LECTURE 3, 1:30–2:30 PM, Jason Morton (The Pennsylvania State University)
Notes, Video, Vimeo
Topic Grouping: Tensor Networks, Categories, Quantum

LECTURE 4, 3:00–4:00 PM, Risi Kondor (The University of Chicago)
"Fourier Analysis on the Symmetric Group"
Slides, Video, Vimeo
Topic Grouping: Learning, Statistics, and Optimization

LECTURE 5, 4:30–5:30 PM, "Review and Problems, Introductory Representation Theory"
Topic Grouping: Introductory Representation Theory

WEDNESDAY, July 23, 2014, in Room 112, at 5727 S. University Avenue

LECTURE 1, 9:00–10:00 AM, J. M. Landsberg (Texas A&M University)
Video, Vimeo
Topic Grouping: Introductory Representation Theory

LECTURE 2, 10:30–11:30 AM, Amit Singer (Princeton University)
"Introduction to Three Dimensional Structure Determination of Macromolecules by Cryo-Electron Microscopy"
Slides, Video, Vimeo
Topic Grouping: FFT, Signal Processing, Imaging

LUNCH BREAK, 11:30 AM–1:30 PM

LECTURE 3, 1:30–2:30 PM, Jason Morton (The Pennsylvania State University)
Notes, Video, Vimeo
Topic Grouping: Tensor Networks, Categories, Quantum

LECTURE 4, 3:00–4:00 PM, Samuel Denton, Cameron Farnsworth, Mee Seong Im,
Deepti Pachauri, Zvi Rosen

Topic Grouping: Short Talks

LECTURE 5, 4:30–5:30 PM, "Review and Problems, FFT, Signal Processing, Imaging"
Topic Grouping: FFT, Signal Processing, Imaging

THURSDAY, July 24, 2014, in Room 112, at 5727 S. University Avenue

LECTURE 1, 9:00–10:00 AM, J. M. Landsberg (Texas A&M University)
Video, Vimeo
Topic Grouping: Introductory Representation Theory

LECTURE 2, 10:30–11:30 AM, Amit Singer (Princeton University)
"Orientation Assignment in Cryo-EM"
Slides, Video, Vimeo
Topic Grouping: FFT, Signal Processing, Imaging

LUNCH BREAK, 11:30–1:30 PM

LECTURE 3, 1:30–2:30 PM, Jason Morton (The Pennsylvania State University)
Notes, Video, Vimeo
Topic Grouping: Tensor Networks, Categories, Quantum

LECTURE 4, 3:00–4:00 PM, Risi Kondor (The University of Chicago)
"Invariants and Optimization"
Slides, Video, Vimeo
Topic Grouping: Learning, Statistics, and Optimization

LECTURE 5, 4:30–5:30 PM, "Review and Problems, Tensor Networks, Categories, Quantum"
Topic Grouping: Tensor Networks, Categories, Quantum

FRIDAY, July 25, 2014, in Room 112, at 5727 S. University Avenue

LECTURE 1, 9:00–10:00 AM, J. M. Landsberg (Texas A&M University)
Video, Vimeo
Topic Grouping: Introductory Representation Theory

LECTURE 2, 10:30–11:30 AM, Amit Singer (Princeton University)
"Class Averaging and Symmetry Detection in Cryo-EM"
Slides, Video, Vimeo
Topic Grouping: FFT, Signal Processing, Imaging

LUNCH BREAK, 11:30 AM–1:30 PM

LECTURE 3, 1:30–2:30 PM, Jason Morton (The Pennsylvania State University
Notes, Video, Vimeo
Topic Grouping: Tensor Networks, Categories, Quantum

LECTURE 4, 3:00–4:00 PM, Amit Singer (Princeton University)
"Covariance Matrix Estimation for the Cryo-EM Heterogeneity Problem"
Slides, Video, Vimeo
Topic Grouping: FFT, Signal Processing, Imaging

LECTURE 5, 4:30–5:30 PM, "Computational Complexity Introduction"
Topic Grouping: Computational Complexity

MONDAY, July 28, 2014, in Room 112, at 5727 S. University Avenue

LECTURE 1, 9:00–10:00 AM, J. M. Landsberg (Texas A&M University)
Video, Vimeo
Topic Grouping: Computational Complexity

LECTURE 2, 10:30–11:30 AM, Cristopher Moore (Santa Fe Institute)
"Shor’s Quantum Factoring Algorithm"
Video, Vimeo
Topic Grouping: Tensor Networks, Categories, Quantum

LUNCH BREAK, 11:30 AM–1:30 PM

LECTURE 3, 1:30–2:30 PM, Gregory Chirikjian (Johns Hopkins University)
"Representation Theory and Computational Harmonic Analysis on Euclidean Motion Groups"
Slides, Video, Vimeo
Topic Grouping: FFT, Signal Processing, Imaging

LECTURE 4, 3:00–4:00 PM, Gregory Chirikjian (Johns Hopkins University)
"Applications in Robotics and Biology"
Slides, Video, Vimeo
Topic Grouping: FFT, Signal Processing, Imaging

LECTURE 5, 4:30–5:30 PM, "Review and Problems, FFT, Signal Processing, Imaging"
Topic Grouping: FFT, Signal Processing, Imaging

TUESDAY, July 29, 2014, in Room 112, at 5727 S. University Avenue

LECTURE 1, 9:00–10:00 AM, Gregory Chirikjian (Johns Hopkins University)
"Discrete Subgroups, Almost-Uniform Sampling on Lie Groups and Implications for FFTs"
Slides, Video, Vimeo
Topic Grouping: FFT, Signal Processing, Imaging

LECTURE 2, 10:30–11:30 AM, Cristopher Moore (Santa Fe Institute)
"Representations of the Symmetric Grouping and the Hunt for a Quantum Algorithm for Graph Isomorphism"
Video, Vimeo
Topic Grouping: Tensor Networks, Categories, Quantum

LUNCH BREAK, 11:30 AM–1:30 PM

LECTURE 3, 1:30–2:30 PM, J. M. Landsberg (Texas A&M University)
Video, Vimeo

LECTURE 4, 3:00–4:00 PM, Daniel Rockmore (Dartmouth College)
Video, Vimeo
Topic Grouping: FFT, Signal Processing, Imaging

LECTURE 5, 4:30–5:30 PM, "Review and Problems, Computational Complexity"
Topic Grouping: Computational Complexity

WEDNESDAY, July 30, 2014, in Room 112, at 5727 S. University Avenue

LECTURE 1, 9:00–10:00 AM, J. M. Landsberg (Texas A&M University)
Video, Vimeo
Topic Grouping: Computational Complexity

LECTURE 2, 10:30–11:30 AM, Cristopher Moore (Santa Fe Institute)
"Estimating the Permanent with Nonabelian Determinants"
Video, Vimeo
Topic Grouping: Tensor Networks, Categories, Quantum

LUNCH BREAK, 11:30 AM–1:30 PM

LECTURE 3, 1:30–2:30 PM, Daniel Rockmore (Dartmouth College)
Video, Vimeo
Topic Grouping: FFT, Signal Processing, Imaging

LECTURE 4, 3:00–4:00 PM, Daniel Rockmore (Dartmouth College)
Video, Vimeo
Topic Grouping: FFT, Signal Processing, Imaging

LECTURE 5, 4:30–5:30 PM, "Review and Problems, Tensor Networks, Categories, Quantum"
Topic Grouping: Tensor Networks, Categories, Quantum

THURSDAY, July 31, 2014, in Room 112, at 5727 S. University Avenue

LECTURE 2, 10:30–11:30 AM, Chris Umans (California Institute of Technology)
"I. Approaches to Bounding the Exponent of Matrix Multiplication"
Slides, Video
Topic Grouping: Computational Complexity

LUNCH BREAK, 11:30 AM–1:30 PM

LECTURE 3, 1:30–2:30 PM, Jason Morton (The Pennsylvania State University)
Video, Vimeo
Topic Grouping: Tensor Networks, Categories, Quantum

LECTURE 4, 3:00–4:00 PM, Chris Umans (California Institute of Technology)
"II. Group-Theoretic Approach"
Slides, Video
Topic Grouping: Computational Complexity

LECTURE 5, 4:30–5:30 PM, "Review and Problems, Computational Complexity"
Topic Grouping: Computational Complexity

FRIDAY, August 1, 2014, in Room 112, at 5727 S. University Avenue

LECTURE 1, 9:00–10:00 AM, Chris Umans (California Institute of Technology)
"III. Matrix Multiplication Using Coherent Configuations"
Slides, Video
Topic Grouping: Computational Complexity

LECTURE 2, 10:30–11:30 AM, J. M. Landsberg (Texas A&M University)
Video, Vimeo
Topic Grouping: Computational Complexity

LUNCH BREAK, 11:30–1:30 PM

LECTURE 3, 1:30–2:30 PM, J. M. Landsberg (Texas A&M University)
Special Seminar: "Geometric Complexity Theory and Minimal Free Resolutions"
Video, Vimeo
Topic Grouping: Computational Complexity

LECTURE 4, 3:00–4:00 PM, Jacob Turner (The Pennsylvania State University)
"Relating Orbit Spaces and Quivers"
Video, Vimeo
Topic Grouping: Tensor Networks, Categories, Quantum

LECTURE 5, 4:30–5:30 PM, "Review and Problems, FFT, Signal Processing, Imaging"
Topic Grouping: FFT, Signal Processing, Imaging

MONDAY, August 4, 2014, in Room 112, at 5727 S. University Avenue

LECTURE 1, 9:00–10:00 AM, Peter McCullagh (The University of Chicago)
"Statistical Models and Representation Theory"
Video1, Video2, Vimeo
Topic Grouping: Learning, Statistics, and Optimization

LECTURE 2, 10:30–11:30 AM, Ketan Mulmuley (The University of Chicago)
"Kronecker Coefficients and Geometric Complexity Theory"
Video, Vimeo
Topic Grouping: Computational Complexity

LUNCH BREAK, 11:30 AM–1:30 PM

LECTURE 3, 1:30–2:30 PM, Shamgar Gurevich (University of Wisconsin, Madison)
"The Heisenberg Representation and The Fast Fourier Transform"
Slides, Video, Vimeo
Topic Grouping: FFT, Signal Processing, Imaging

LECTURE 4, 3:00–4:00 PM, Samuel Denton (York University)
"Compressed Combinatorics"
Video, Vimeo
Topic Grouping: FFT, Signal Processing, Imaging

LECTURE 5, 4:30–5:30 PM, Shamgar Gurevich (University of Wisconsin, Madison)
"Diagonalization of the Discrete Fourier Transform and the Weil Representation"
Slides, Video
Topic Grouping: FFT, Signal Processing, Imaging

TUESDAY, August 5, 2014, in Room 112, at 5727 S. University Avenue

LECTURE 1, 9:00–10:00 AM, Peter McCullagh (The University of Chicago)
"Statistical Models and Representation Theory"
Video, Vimeo
Topic Grouping: Learning, Statistics, and Optimization

LECTURE 2, 10:30–11:30 AM, Ketan Mulmuley (The University of Chicago)
"Kronecker Coefficients and Geometric Complexity Theory"
Video, Vimeo
Topic Grouping: Computational Complexity

LUNCH BREAK, 11:30 AM–1:30 PM

LECTURE 3, 1:30–2:30 PM, Shamgar Gurevich (University of Wisconsin, Madison)
"The Geometric Weil Representation and Pseudo-Random Vectors"
Slides
Topic Grouping: FFT, Signal Processing, Imaging

Participants

  1. Tejal Bhamre, Department of Physics and Applied Mathematics, Princeton University
  2. Mario Borha, Department of Mathematics, Northern Illinois University
  3. Sixia Chen, Department of Computer Science & Engineering, University of Connecticut
  4. Yutong Chen, Program in Computational and Applied Mathematics, Princeton University
  5. Gregory Chirikjian, Department of Mechanical Engineering, Johns Hopkins University
  6. Justin Curry, Department of Mathematics, Duke University
  7. Walter Dempsey, Department of Statistics, The University of Chicago
  8. Samuel Denton, Department of Mathematics, York University
  9. Cameron Farnsworth, Department of Mathematics, Texas A & M University
  10. Jonathan Fernandes, Department of Mathematics, University of Maryland
  11. Brett Geiger, Department of Mathematics, University of Houston
  12. Renato Ghini Bettiol, Department of Mathematics, University of Notre Dame
  13. Jonathan Godbout, Department of Mathematics, Worcester Polytechnic Institute
  14. William Grodzicki, Department of Mathematics, University of Minnesota, Twin Cities
  15. Shamgar Gurevich, Department of Mathematics, University of Wisconsin, Madison
  16. Jing Hao, Department of Mathematics, University of Wisconsin, Madison
  17. Pamela Harris, Department of Mathematical Sciences, United States Military Academy
  18. Peng He, Department of Mathematics, University of Pittsburgh
  19. Mee Seong Im, Department of Mathematics, University of Illinois at Urbana-Champaign
  20. Shahrzad Jamshidi, Department of Mathematics, The Pennsylvania State University
  21. Matthew Joseph, Department of Mathematics, The University of Chicago
  22. Joseph Kileel, Department of Mathematics, University of California, Berkeley
  23. Hwamog Kim, Department of Mathematics and Statistics, Mississippi State University
  24. Risi Kondor, Departments of Computer Science and Statistics, The University of Chicago
  25. Robert Krone, Department of Mathematics, Georgia Institute of Technology
  26. J. M. Landsberg, Department of Mathematics, Texas A & M University
  27. Kang-Ju Lee, Department of Mathematics, Texas A & M University
  28. Lek-Heng Lim, Department of Statistics, The University of Chicago
  29. Ye Luo, Department of Mathematics, Georgia Institute of Technology
  30. Peter McCullagh, Department of Statistics, The University of Chicago
  31. Cristopher Moore, Santa Fe Institute
  32. Jason Morton, Department of Mathematics, The Pennsylvania State University
  33. Ketan Mulmuley, Department of Computer Science, The University of Chicago
  34. Tatiana Orlova, Department of Computer Science, The University of Chicago
  35. Michael Orrison, Department of Mathematics, Harvey Mudd College
  36. Deepti Pachauri, Department of Computer Sciences, University of Wisconsin, Madison
  37. Daniel Rockmore, Department of Mathematics, Dartmouth College
  38. Zvi Rosen, Department of Mathematics, University of California, Berkeley
  39. Hans-Christian Ruiz Department of Biophysics, Radboud Universiteit Nijmegen
  40. John Santerre, Department of Computer Science, The University of Chicago
  41. Tony Se, Department of Mathematics, University of Kansas
  42. Amit Singer, Department of Mathematics, Princeton University
  43. Roberto Soto, Department of Mathematics, The University of Iowa
  44. Benjamin Strasser, Department of Mathematics, University of Minnesota, Twin Cities
  45. Yi Sun, Department of Mathematics, Massachusetts Institute of Technology
  46. Nedelina Teneva, Department of Computer Science, The University of Chicago
  47. Bolor Turmunkh, Department of Mathematics, University of Illinois at Urbana-Champaign
  48. Jacob Turner, Department of Mathematics, The Pennsylvania State University
  49. Chris Umans, Department of Computer Science, California Institute of Technology
  50. Chen Wan, School of Mathematics, University of Minnesota, Twin Cities
  51. Jiuya Wang, Department of Mathematics, University of Wisconsin, Madison
  52. Tyson Williams, Department of Computer Sciences, University of Wisconsin, Madison
  53. Ken Sze-Wai Wong, Department of Statistics, The University of Chicago
  54. Angela Wu, Department of Mathematics, The University of Chicago
  55. Yifei Xu, Department of Basic Science, Mississippi State University

Practical information

All lectures will take place in Room 112, of the Financial Mathematics/Stevanovich Center, at 5727 S. University Avenue, Chicago, Illinois, unless otherwise noted. On-campus accommodation and meals will be provided as well as support towards travel expenses.

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 30, 2014.

Boat Tour Photos


We also thank the IMA for providing the application website and general sponsorhip.

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Any opinions, findings and conclusions or recomendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF).