FRG Workshop: Manifolds, Strings and 2D Quantum Field Theory

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Housing and Conference Location

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Schedule

Click on hyperlinked titles to view abstracts.

• Monday, August 24th, 2009, 1:30PM - 5PM
  Science Center 507
  
  
  • 1:30PM - Welcome & Coffee
    Common Room on 4th Floor
    
    
  • 2-3PM - David Nadler, Northwestern
    Representation theory via topological field theory

    I'll describe how the representation theory of Lie groups is organized by the formalism of topological field theory. In particular, I'll discuss character sheaves and Langlands duality in 3d TFT, and relations with the 4d Geometric Langlands TFT. This is joint work with David Ben-Zvi (Texas).

    
    
  • 3-4PM - Tea
    Common Room on 4th Floor
    
    
  • 4-5PM - Curt McMullen, Harvard
    Perspectives on moduli space from topology, geometry and analysis
    
    
• Tuesday, August 25th, 2009, 9AM - 5PM
  Science Center 507
  
  
  • 9-9:30AM - Breakfast
    
    
  • 9:30-10:30AM - Dennis Sullivan, Stony Brook
    Stratification of String Space
    
    
  • 10:30-11AM - Coffee
    5th Floor
    
    
  • 11-12 - Kate Poirier, CUNY
    String diagrams and a compactification of moduli spaces of Riemann surfaces

    It is known that the original space of diagrams governing string topology operations and the moduli space of Riemann surfaces are not homotopy equivalent. We define a completion of the space of diagrams (over which string topology operations extend) and a compactification of the moduli space that is homotopy equivalent to the completed space of diagrams.

    
    
    
  • 12-1:30PM - Lunch
    
    
  • 1:30-2PM - Coffee
    5th Floor
    
    
  • 2-3PM - David Nadler, Northwestern
    Representation theory via topological field theory (II)
    
    
  • 3-4PM - Tea
    5th Floor
    
    
  • 4-5PM - Nathaniel Rounds, Stony Brook
    Local Poincare Duality

    Closed oriented manifolds satisfy Poincare Duality, but not every space satisfying Poincare Duality has the homotopy type of a closed manifold. We represent a Poincare Duality space as a chain complex with a fixed basis satisfying certain axioms. We use this basis to define an algebraic notion of locality, allowing us to characterize closed manifolds as based chain complexes with local Poincare Duality.

    
    
    
  • 5PM+ - Reception & Dinner
    In the Common Room on the 4th floor. BBQ from Redbones. Beer and Wine.
    
    
• Wednesday, August 26th, 2009, 9AM-5PM
  Science Center 507
  
  
  • 9-9:30AM - Breakfast
    
    
  • 9:30-10:30AM - David Nadler, Northwestern
    Representation theory via topological field theory (III)
    
    
  • 10:30-11AM - Coffee
    Common Room on 4th Floor
    
    
  • 11-12 - Joe Harris, Harvard
    Alternate Moduli Spaces of Curves (after David Smyth)
    
    
  • 12-1:30PM - Lunch
    
    
  • 1:30-2PM - Coffee
    Common Room on 4th Floor
    
    
  • 2-3PM - Group Discussion
    
    
  • 3-4PM - Tea
    Common Room on 4th Floor
    
    
  • 4-5PM - Group Discussion
    
    
• Thursday, August 27th, 2009, 9AM-5PM
  Science Center 530 (Different Room)
  
  
  • 9-9:30AM - Breakfast
    
    
  • 9:30-10:30AM - David Ayala, Harvard
    Geometric and singular cobordism categories

    We'll consider cobordism categories whose morphisms are, possibly singular, manifolds endowed with a geometric structure such as a metric, a complex structure, or a gauge theoretic connection. We will see in what sense the classifying space of such a geometric cobordism category approximates moduli spaces of such geometric structures; some relevant results will be discussed. A case study of particular interest to Gromov-Witten theory will be elaborated upon which will require a gentle account of manifolds with prescribed singularities.

    
    
  • 10:30-11AM - Coffee
    Common Room on 4th Floor
    
    
  • 11-12 - Chris Schommer-Pries
    A Generators and Relations Approach to Local Topological Field Theories

    There are multiple approaches to the classification of topological field theories. In this talk we will explain one approach based on explicit generators and relations presentations. Such presentations can be obtained by essentially elementary cerf-theoretic techniques. This approach has several advantages, both from its conceptual simplicity and its wide applicability. It can be adapted to include field theories with a large range of topological structures as well as to partially extended field theories. We hope to illustrate this with several examples.

    
    
  • 12-1:30PM - Lunch
    
    
  • 1:30-2PM - Coffee
    Common Room on 4th Floor
    
    
  • 2-3PM - Orlando Alvarez
    A Physicist's View (II)

    In these two talks I will describe the physicist's string theory view of elliptic genera. I will discuss the Dirac-Ramond operator (DR), i.e., the Dirac operator on loop space and why it plays a central role. I will explain why the theories studied are not TQFT yet they give topological information. I will explain the various ways that p_1 = 0 arises when trying to compute the index of the Dirac-Ramond operator using path integrals. I will also discuss how the path integral approach gives a candidate for a generalization of elliptic genera to higher genus at the price of losing analyticity (work with I.M. Singer). I will also discuss a cohomological formula for the analytic index for a family of Dirac-Ramond operators (work with P. Windey).

    
    
  • 3-4PM - Tea
    Common Room on 4th Floor
    
    
  • 4-5PM - Kevin Costello, Northwestern
    A mathematical approach to bosonic string theory

    I'll discuss how one can construct factorization algebras encoding the bosonic string theory, and certain related theories, using obstruction theory.

    
    
• Friday, August 28th, 2009, 9AM-Noon
  Science Center 507
  
  
  • 9-9:30AM - Breakfast
    
    
  • 9:30-10:30AM - Mark Behrens, MIT
    TBA
    
    
  • 10:30-11AM - Coffee
    Common Room on 4th Floor
    
    
  • 11-12 - Orlando Alvarez
    A Physicist's View (II)

    In these two talks I will describe the physicist's string theory view of elliptic genera. I will discuss the Dirac-Ramond operator (DR), i.e., the Dirac operator on loop space and why it plays a central role. I will explain why the theories studied are not TQFT yet they give topological information. I will explain the various ways that p_1 = 0 arises when trying to compute the index of the Dirac-Ramond operator using path integrals. I will also discuss how the path integral approach gives a candidate for a generalization of elliptic genera to higher genus at the price of losing analyticity (work with I.M. Singer). I will also discuss a cohomological formula for the analytic index for a family of Dirac-Ramond operators (work with P. Windey).

Reimbursement Information

Please see Robbie Miller in the Math Department Main Office (3rd Floor) to fill out reimbursement paperwork. For air travel, we will just need the receipt / confirmation email.