FRG: Semidefinite Optimization and Convex Algebraic Geometry

Guests:

Pablo Parrilo (MIT)

Bernd Sturmfels (Berkeley)

Rekha Thomas (Washington)

Joao Gouveia (Washington)

Megan McCormick (Washington)

Philippe Rostalski (ETH)

Frank Vallentin (CWI)

Cynthia Vinzant (Berkeley)

  Hotel Information
  Name: La Jolla Shores Hotel (formerly Sea Lodeg)
  Phone: (858)459-8271

Local Participants:

Jeremy Greene (UCSD)

Bill Helton (UCSD)

Igor Klep (UCSD)

Jiawang Nie (UCSD)

Mauricio de Oliveira (UCSD)

Ruth Williams (UCSD)

Program

  Thursday Dec 4:

    Place: TBA
 
    Departmental Colloquium Talk
    2:30 - 3:30  Pablo Parrilo
                 Title: Computing equilibria of continuous games
                 Abstract: 
There has been much recent interest in effective methods to compute Nash or
correlated equilibria for finite games. In this talk we present an overview
of some of our recent results for the computation of equilibria in games
where the players have an infinite number of pure strategies. In particular,
we discuss games where the payoff functions are a polynomial expression of
the actions of the players. In the zero-sum case, we show that the value of
the game, and the corresponding optimal mixed strategies, can be computed by
solving a single semidefinite programming problem, thus providing a natural
generalization of the well-known LP characterization of finite games. We
also discuss some further extensions to the general nonzero sum case, for
both Nash and correlated equilibria. Much of the material is joint work with
Asu Ozdaglar and Noah Stein.
   
    Department Tea
    3:30 - 4:00
  
    FRG Group Discussion
        co-PIs each present  descriptions of various projects 
        each project gets 5 minutes max. Everyone gives ideas-opinions.
        Make requests for tomorrow's emphasis
    4:00 - 6:00pm
    Room: TBA

    Dinner at La Jolla Shores Hotel
    6:30 - 8:00:
   
    PI meeting  at the hotel
    8:00 - Business stuff


  Friday (Dec 5)
    
    Place: APM 6402

    Departmental Talks
 
     9:00 - 10:00  Rekha Thomas
                   Title: From Lovasz's theta body of a graph to convex algebraic geometry

    10:00 - 10:30  Philippe Rostalski
                   Title: TBA

    10:30 - 11:00  Frank Vallentin
                   Title: Approximating maxcut in infinite graphs

    11:00 - 12:00  Group discussion

    12:00 - 1:00   Lunch (Faculty club)

    Departmental Talks

     1:00 -  2:00  Bernd Sturmfels
                  Title: An invitation to algebraic statistics
                  Abstract:
Algebraic statistics is concerned with the development of techniques in
algebraic geometry, commutative algebra and combinatorics, to address
problems in statistics and its applications. This lecture gives an
elementary and self-contained introduction to this subject. Particular
emphasis will be placed on connections to optimization.  Along the way,
the speaker will shamelessly advertise his new book with Mathias Drton
and Seth Sullivant, as well as an upcoming MSRI workshop.


    Informal  Group  Discussions. Speakers spend about 15 mins to 
    describe their research status and challenges, and then the
    group spends about 10 mins for discussions. 
     
     2:00 - 2:30  Group Discussion
     2:30 - 3:00  Joao Gouveia
     3:00 - 3:30  Cynthia Vinzant
     3:30 - 4:00  de Oliveira  
     4:00 - 4:30  Igor Klep
     4:30 - 5:00  Jiawang Nie   

     6:30 - 8:00    DINNER AT TOM HAMS (Harbor Island by airport)

Contact Information

  Local orgainzers:
    Bill Helton (helton@math.ucsd.edu)
    Jiawang Nie (njw@math.ucsd.edu)
   
  Phone numbers:(858)534-2653
                (858)534-6015