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Mathematical Sciences Research Institute

Home » Hot Topics: Kadison-Singer, Interlacing Polynomials, and Beyond

Workshop

Hot Topics: Kadison-Singer, Interlacing Polynomials, and Beyond March 09, 2015 - March 13, 2015
To apply for Funding you must register by: January 05, 2015 about 1 month ago
Series: Hot Topic, Hot Topic
Location: MSRI: Simons Auditorium, Atrium
Organizers Sorin Popa (University of California), LEAD Daniel Spielman (Yale University), Nikhil Srivastava (University of California, Berkeley), Cynthia Vinzant (North Carolina State University)
Speaker(s)

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Description

In a recent paper, Marcus, Spielman and Srivastava solve the Kadison-Singer Problem by proving Weaver's KS2 conjecture and the Paving Conjecture. Their proof involved a technique they called the “method of interlacing families of polynomials” and a “barrier function” approach to proving bounds on the locations of the zeros of real stable polynomials. Using these techniques, they have also proved that there are infinite families of Ramanujan graphs of every degree, and they have developed a very simple proof of Bourgain and Tzafriri's Restricted Invertibility Theorem. The goal of this workshop is to help build upon this recent development by bringing together researchers from the disparate areas related to these techniques, including Functional Analysis, Spectral Graph Theory, Free Probability, Convex Optimization, Discrepancy Theory, and Real Algebraic Geometry.

Bibliography (PDF)


Funding & Logistics Show All Collapse

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To apply for funding, you must register by the funding application deadline displayed above.

Students, recent Ph.D.'s, women, and members of underrepresented minorities are particularly encouraged to apply. Funding awards are typically made 6 weeks before the workshop begins. Requests received after the funding deadline are considered only if additional funds become available.

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MSRI has preferred rates at the Rose Garden Inn, depending on room availability. Reservations may be made by calling 1-800-992-9005 OR directly on their website. Click on "Promo/Corporate Code" at the top of the page. When prompted, select the "Promo/Corporate Code" option and enter the code MATH (this code is not case sensitive). By using this code, a new calendar will appear an will show the MSRI rate on all room types available. Click the gold "View Full Calendar" button to see the lowest rate for each day.

MSRI has preferred rates at the Hotel Durant. Reservations may be made by calling 1-800-238-7268. When making reservations, guests must request the MSRI preferred rate. If you are making your reservations on line, please go to this link. Click on "Promo/Corporate Code" at the top of the page. When prompted, select the "Promo/Corporate Code" option and enter the code 123MSRI (this code is not case sensitive). Our lowest preferred rate is $139 per night for a Deluxe Queen, based on availability.

MSRI has a preferred rate of $174 plus tax at the Hotel Shattuck Plaza, depending on room availability. Guests can call the hotel's main line at 510-845-7300 and ask for the MSRI- Mathematical Science Research Inst. discount. To book online visit this page. You must select "My dates are: Firm" in order to use the promotional code. Click on "Promo/Corporate Code" at the top of the page. When prompted, select the "Promo/Corporate Code" option and enter the code MSRI (this code is not case sensitive).

MSRI has preferred rates of $130 - $160 at the Berkeley Lab Guest House, depending on room availability. Reservations may be made by calling 510-495-8000 or directly on their website. Select “I am an individual traveler affiliated with the Space Sciences Lab, Lawrence Hall of Science or MSRI.” When prompted for your UC Contact/Host, please list Chris Marshall (coord@msri.org).

Additional lodging options may be found on our short term housing page.

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Schedule
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Mar 09, 2015
Monday
09:15 AM - 09:30 AM
  Welcome
09:30 AM - 10:30 AM
  Introduction to Interlacing Polynomials, Barrier Functions, and Kadison-Singer
Daniel Spielman (Yale University)
10:30 AM - 11:00 AM
  Tea
11:00 AM - 12:00 PM
  Hyperbolic polynomials, Strong Rayleigh matroids and the Marcus-Spielman-Srivastava theorem
Petter Branden (Royal Institute of Technology (KTH))
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Determinants, Hyperbolicity, and Interlacing
Cynthia Vinzant (North Carolina State University)
03:00 PM - 03:30 PM
  Tea
03:30 PM - 04:30 PM
  An overview of the Matching Polynomial
Chris Godsil (University of Waterloo)
Mar 10, 2015
Tuesday
09:30 AM - 10:30 AM
  Laws of non-commutative polynomials in $n$-tuples of free variables
Dimitri Shlyakhtenko (University of California, Los Angeles)
10:30 AM - 11:00 AM
  Tea
11:00 AM - 12:00 PM
  Free probability, random matrices and transport maps
Alice Guionnet (Massachusetts Institute of Technology)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Polynomial convolutions and connections to free probability
Adam Marcus (Yale University)
03:00 PM - 03:30 PM
  Tea
03:30 PM - 04:30 PM
  Ramanujan graphs from finite free convolutions.
Nikhil Srivastava (University of California, Berkeley)
04:30 PM - 06:20 PM
  Reception
Mar 11, 2015
Wednesday
09:30 AM - 10:30 AM
  Towards Constructing Expanders via Lifts: Hopes and Limitations
Alexandra Kolla (University of Illinois at Urbana-Champaign)
10:30 AM - 11:00 AM
  Tea
11:00 AM - 12:00 PM
  Expanders and box spaces
Alain Valette (Université de Neuchâtel)
Mar 12, 2015
Thursday
09:30 AM - 10:30 AM
  Commutators in L(X) for some Banach spaces X
William Johnson (Texas A & M University)
10:30 AM - 11:00 AM
  Tea
11:00 AM - 12:00 PM
  A quantitative version of the commutator theorem for zero trace matrices
Gideon Schechtman (Weizmann Institute of Science)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Paving over arbitrary MASAs in von Neumann algebras
Sorin Popa (University of California)
03:00 PM - 03:30 PM
  Tea
03:30 PM - 04:30 PM
  A survey of discrepancy theory
Nicholas Harvey (University of British Columbia)
Mar 13, 2015
Friday
09:30 AM - 10:30 AM
  Hyperbolic Polynomials in Optimization
Osman Guler (University of Maryland, Catonsville)
10:30 AM - 11:00 AM
  Tea
11:00 AM - 12:00 PM
  Effective-Resistance-Reducing Flows, Spectrally Thin Trees, and Asymmetric TSP
Shayan Oveis Gharan (University of Washington)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Approximating the covariance matrix by the empirical covariance matrices; non-limiting random matrix approach
Nicole Tomczak Jaegermann (University of Alberta)
03:00 PM - 03:30 PM
  Tea
03:30 PM - 04:30 PM
  Hyperbolicity and determinantal representations for higher-codimensional subvarieties
Victor Vinnikov (Ben Gurion University of the Negev)