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Summer Graduate School

Algebraic Topology June 17, 2013 - June 28, 2013
Parent Program: Algebraic Topology
Location: MSRI: Simons Auditorium
Organizers Andrew Blumberg (University of Texas), Teena Gerhardt (Michigan State University), LEAD Michael Hill (University of Virginia)
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Description

Modern algebraic topology is a broad and vibrant field which has seen recent progress on classical problems as well as exciting new interactions with applied mathematics.  This summer school will consist of a series of lecture by experts on major research directions, including several lectures on applied algebraic topology.  Participants will also have the opportunity to have guided interaction with the seminal texts in the field, reading and speaking about the foundational papers.

For eligibility and how to apply, see the Summer Graduate Workshop homepage


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Schedule
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Jun 17, 2013
Monday
09:15 AM - 09:30 AM
  Welcome
09:30 AM - 10:45 AM
  Intro to stable homotopy and spectra I
Brooke Shipley (University of Illinois at Chicago)
10:45 AM - 11:15 AM
  Coffee Break
11:15 AM - 12:30 PM
  Intro to equivariant stable homotopy I
Michael Hill (University of Virginia)
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 02:45 PM
  Student Talk: Thom's "Quelque proprietes globales des varietes differentiables"
Cary Malkiewich (Stanford University)
02:45 PM - 03:30 PM
  Problem Session
03:30 PM - 04:00 PM
  Tea
04:00 PM - 04:45 PM
  Student Talk: Milnor's "The Steenrod algebra and its dual"
Jonathan Thompson (University of Kentucky)
Jun 18, 2013
Tuesday
09:30 AM - 10:45 AM
  Intro to stable homotopy and spectra II
Brooke Shipley (University of Illinois at Chicago)
10:45 AM - 11:15 AM
  Coffee Break
11:15 AM - 12:30 PM
  Intro to equivariant stable homotopy II
Michael Hill (University of Virginia)
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 02:45 PM
  Student Talk: Quillen's "Elementy proofs of some results of cobordism theory using Steenrod operations"
Gabriel Valenzuela (Wesleyan University)
02:45 PM - 03:30 PM
  Problem Session
03:30 PM - 04:00 PM
  Tea
04:00 PM - 04:45 PM
  Student Talk: Atiyah's "K-theory"
Michael Francis (University of Victoria)
Jun 19, 2013
Wednesday
09:30 AM - 10:45 AM
  Intro to stable homotopy and spectra III
Brooke Shipley (University of Illinois at Chicago)
10:45 AM - 11:30 AM
  Student Talk: Adams & Atiyah "K-theory and the Hopf invariant"
Charmaine Sia (Harvard University)
11:30 AM - 02:00 PM
  BBQ Lunch at Nearby Park
02:00 PM - 03:15 PM
  Intro to equivariant stable homotopy III
Michael Hill (University of Virginia)
03:15 PM - 03:45 PM
  Tea
03:45 PM - 05:00 PM
  Faculty and Postdoc Panel
Jun 20, 2013
Thursday
09:30 AM - 10:45 AM
  Intro to stable homotopy and spectra IV
Brooke Shipley (University of Illinois at Chicago)
10:45 AM - 11:15 AM
  Coffee Break
11:15 AM - 12:30 PM
  Intro to equivariant stable homotopy IV
Michael Hill (University of Virginia)
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 02:45 PM
  Student Talk: Milnor's & Stasheff's "Characteristic Classes"
Lorenzo Losa (Scuola Normale Superiore)
02:45 PM - 03:30 PM
  Problem Session
03:30 PM - 04:00 PM
  Tea
04:00 PM - 04:45 PM
  Student Talk: Becker & Gottlieb's "The transfer map and fiber bundles"
Jean Verrette (University of Hawaii at Manoa)
Jun 21, 2013
Friday
09:30 AM - 10:30 AM
  Applied algebraic topology I
Gunnar Carlsson (Stanford University)
10:30 AM - 11:00 AM
  Coffee Break
11:00 AM - 12:00 PM
  Applied Algebraic topology II
Gunnar Carlsson (Stanford University)
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 02:15 PM
  Student Talk: Kervaire's " A manifold which does not admit any differentiable structure"
Maxim Stykow (University of British Columbia)
02:15 PM - 02:30 PM
  Break
02:30 PM - 03:15 PM
  Student Talk: Milnor's "On manifolds homoemorphic to the 7-sphere" and Kervaire & Milnor's "Groups of homotopy spheres I"
Nathan Perlmutter (University of Oregon)
03:15 PM - 04:00 PM
  Tea and Problem Session
04:00 PM - 04:45 PM
  Student Talk: Bass' "Catefories of modules and their equivalences
Ernest Fontes (University of Texas)
Jun 24, 2013
Monday
09:30 AM - 10:30 AM
  Applied algebraic topology III
Gunnar Carlsson (Stanford University)
10:30 AM - 11:00 AM
  Coffee Break
11:00 AM - 12:00 PM
  Applied algebraic topology IV
Gunnar Carlsson (Stanford University)
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 02:15 PM
  Student Talk: Milnor's "The geometric realization of a semi-simplicial complex"
Scott Slinker (University of Virginia)
02:15 PM - 02:30 PM
  Break
02:30 PM - 03:15 PM
  Student Talk: Segal's "Classifying spaces and spectral sequences"
Aaron Mazel-Gee (University of California, Berkeley)
03:15 PM - 04:00 PM
  Tea and Problem Session
04:00 PM - 04:45 PM
  Student Talk: Quillen's "Homotopical algebra"
Deborah Vicinsky (University of Oregon)
Jun 25, 2013
Tuesday
09:30 AM - 10:45 AM
  Intro to computational techniques in stable homotopy I
Mark Behrens (Massachusetts Institute of Technology)
10:45 AM - 11:15 AM
  Coffee Break
11:15 AM - 12:30 PM
  Intro to algebraic K-theory I
Andrew Blumberg (University of Texas)
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 02:45 PM
  Student Talk: Bousfiled & Kan "Homotopy limits, completions, and localizations"
Robert Hank (University of Minnesota Twin Cities)
02:45 PM - 03:30 PM
  Problem Session
03:30 PM - 04:00 PM
  Tea
04:00 PM - 04:45 PM
  Student Talk: Dwyer & Kan's "Simplicial localization of categories" and "Calculating simplicial localizations"
Chris Kapulkin (University of Western Ontario)
Jun 26, 2013
Wednesday
09:30 AM - 10:45 AM
  Intro to computational techniques in stable homotopy II
Mark Behrens (Massachusetts Institute of Technology)
10:45 AM - 11:15 AM
  Coffee Break
11:15 AM - 12:30 PM
  Intro to algebraic K-theory II
Andrew Blumberg (University of Texas)
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 03:30 PM
  Job Skills Workshop
03:30 PM - 04:00 PM
  Tea
04:00 PM - 04:45 PM
  Student Talk: Brown's "Cohomology theories
Eric Bunch (Kansas State University)
Jun 27, 2013
Thursday
09:30 AM - 10:45 AM
  Intro to computational techniques in stable homotopy III
Mark Behrens (Massachusetts Institute of Technology)
10:45 AM - 11:15 AM
  Coffee Break
11:15 AM - 12:30 PM
  Intro to algebraic K-theory III
Andrew Blumberg (University of Texas)
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 02:45 PM
  Student Talk: May's "The geometry of iterated loop spaces"
Vitaly Lorman (Johns Hopkins University)
02:45 PM - 03:30 PM
  Problem Session
03:30 PM - 04:00 PM
  Tea
04:00 PM - 04:45 PM
  Student Talk: Segal's "Categories and cohomology theories"
Matthew Sartwell (University at Buffalo (SUNY))
Jun 28, 2013
Friday
09:30 AM - 10:45 AM
  Intro to computational techniques in stable homotopy IV
Mark Behrens (Massachusetts Institute of Technology)
10:45 AM - 11:15 AM
  Coffee Break
11:15 AM - 12:30 PM
  Intro to algebraic K-theory IV
Andrew Blumberg (University of Texas)
12:30 PM - 02:00 PM
  Lunch
02:00 PM - 02:45 PM
  Student Talk: Mandell, May, Schwede, & Shipley's " Model categories of diagram spectra"
Mona Merling (University of Chicago)
02:45 PM - 03:30 PM
  Problem Session
03:30 PM - 04:00 PM
  Tea
04:00 PM - 04:45 PM
  Student Talk: Mahowald's "Ring spectra which are Thom complexes
Eric Peterson (University of California, Berkeley)