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IMA Newsletter #423

January 2012

2011-2012 Program

See http://www.ima.umn.edu/2011-2012/ for a full description of the 2011-2012 program on Mathematics of Information.

IMA Events

IMA Workshop

Second Abel Conference: A Celebration of John Milnor

January 30 - February 1, 2012

Organizers: Alejandro Adem (University of British Columbia), Geir Ellingsrud (University of Oslo), Michael J. Hopkins (Harvard University), Robion Kirby (University of California), James Stasheff (University of Pennsylvania)
Schedule

Monday, January 2

All Day University Holiday. The IMA is closed.

Monday, January 9

2:30pm-3:00pm Coffee breakLind Hall 400

Tuesday, January 10

2:30pm-3:00pm Coffee breakLind Hall 400

Wednesday, January 11

2:30pm-3:00pm Coffee breakLind Hall 400

Thursday, January 12

2:30pm-3:00pm Coffee breakLind Hall 400

Friday, January 13

2:30pm-3:00pm Coffee breakLind Hall 400

Monday, January 16

All Day Martin Luther King, Jr. Day. The IMA is closed.

Tuesday, January 17

2:30pm-3:00pm Coffee breakLind Hall 400

Wednesday, January 18

2:30pm-3:00pm Coffee breakLind Hall 400

Thursday, January 19

2:30pm-3:00pm Coffee breakLind Hall 400

Friday, January 20

2:30pm-3:00pm Coffee breakLind Hall 400

Monday, January 23

2:30pm-3:00pm Coffee breakLind Hall 400

Tuesday, January 24

2:30pm-3:00pm Coffee breakLind Hall 400
3:00pm-4:00pm TBDMary Therese Padberg (University of Iowa)Lind Hall 305 PS

Wednesday, January 25

2:30pm-3:00pm Coffee breakLind Hall 400

Thursday, January 26

12:00pm-1:00pm MSI PresentationLind Hall 305 S
2:30pm-3:00pm Coffee breakLind Hall 400

Friday, January 27

2:30pm-3:00pm Coffee breakLind Hall 400

Monday, January 30

10:00am-11:00am Registration and coffeeKeller Hall 3-176 SW1.30-2.1.12
11:00am-11:15am Welcome to the IMAKeller Hall 3-180 SW1.30-2.1.12
11:15am-12:15pm Exotic spheres via topological modular formsMark Behrens (Massachusetts Institute of Technology)Keller Hall 3-180 SW1.30-2.1.12
12:15pm-2:00pm Lunch SW1.30-2.1.12
2:00pm-3:00pm Dynamical MilnorJohn Fornaess (University of Michigan)Keller Hall 3-180 SW1.30-2.1.12
2:30pm-3:00pm Coffee breakLind Hall 400
3:00pm-3:10pm Group photoKeller Hall 3-180 SW1.30-2.1.12
3:10pm-3:30pm Coffee breakKeller Hall 3-176 SW1.30-2.1.12
3:30pm-3:40pm Film Showing - Niles Johnson will screen his short film on the 7-dimensional exotic sphereNiles Johnson (University of Georgia)Keller Hall 3-180 SW1.30-2.1.12
3:40pm-4:40pm Around the genus-minimizing property of algebraic curves.Peter Kronheimer (Harvard University)Keller Hall 3-180 SW1.30-2.1.12
5:00pm-7:00pm Reception at the Campus Club Bar LoungeCampus Club SW1.30-2.1.12

Tuesday, January 31

8:30am-9:00am CoffeeKeller Hall 3-176 SW1.30-2.1.12
9:00am-10:00am Diffeomorphism groups of some high dimensional manifolds.Ib Madsen (University of Copenhagen)Keller Hall 3-180 SW1.30-2.1.12
10:00am-10:30am Coffee breakKeller Hall 3-176 SW1.30-2.1.12
10:30am-11:30am Geometric structures in dimension four Gang Tian (Princeton University)Keller Hall 3-180 SW1.30-2.1.12
11:30am-2:00pm Lunch SW1.30-2.1.12
2:00pm-3:00pm An overview of Heegaard Floer homologyPeter Ozsvath (Massachusetts Institute of Technology)Keller Hall 3-180 SW1.30-2.1.12
3:00pm-3:30pm Coffee breakKeller Hall 3-176 SW1.30-2.1.12
3:30pm-4:30pm Cobordisms: old and newUlrike Tillmann (University of Oxford)Keller Hall 3-180 SW1.30-2.1.12
6:00pm-8:00pm Banquet at McNamara Alumni Center, Heritage GalleryMcNamara Alumni Center SW1.30-2.1.12

Wednesday, February 1

8:30am-9:00am CoffeeKeller Hall 3-176 SW1.30-2.1.12
9:00am-10:00am The Milnor Conjectures and Quadratic FormsParimala Raman (Emory University)Keller Hall 3-180 SW1.30-2.1.12
10:00am-10:30am Coffee breakKeller Hall 3-176 SW1.30-2.1.12
10:30am-11:30am A solution to the Arf-Kervaire invariant problemDouglas Conner Ravenel (University of Rochester)Keller Hall 3-180 SW1.30-2.1.12
11:30am-1:00pm Lunch SW1.30-2.1.12
1:00pm-2:00pm On the homology of Lie groups made discreteFabien Morel (Ludwig-Maximilians-Universität München)Keller Hall 3-180 SW1.30-2.1.12
2:00pm-2:05pm Closing remarksKeller Hall 3-180 SW1.30-2.1.12
2:30pm-3:00pm Coffee breakLind Hall 400
Abstracts
MSI Presentation
Abstract: Ravi Chityala and Haoyu Yu from the Minnesota Supercomputer Institute will present on the resources available through MSI to postdocs and researchers. Ravi is MSI's Scientific Development and Visualization Lab Manager as well as an image processing and visualization developer. Haoyu is one of the scientific computing consultants and specializes in data mining.
Mark Behrens (Massachusetts Institute of Technology) Exotic spheres via topological modular forms
Abstract: In response to a question of Milnor, a collaboration of Mike Hill, Mike Hopkins, Mark Mahowald, and myself have been attempting to determine in which dimensions exotic spheres exist. We will review the work of Kervaire-Milnor, which reduces the problem to questions in the stable homotopy groups of spheres. Thanks to the solution of the Kervaire invariant one problem, the problem is reduced to producing certain infinite families in the stable stems. I will discuss what we know, and don't know about the stable stems these days, and discuss some joint work with Mark Mahowald, producing a plethora of 192-periodic families (the Hurewicz image of TMF) which give partial answers to the original question.
John Fornaess (University of Michigan) Dynamical Milnor
Abstract: The talk is an introduction to problems and results in Dynamics centering around contributions to the field by Milnor.
Peter Kronheimer (Harvard University) Around the genus-minimizing property of algebraic curves.
Abstract: In his 1968 book on singularities of complex hypersurfaces, Milnor asked a question about the "unknotting number" of knots that arise as the links of singular points of complex plane curves. The question was eventually answered in the affirmative, using gauge theory, by Kronheimer and Mrowka in 1992. A proof requiring only combinatorial techniques was found much later, by Rasmussen, using Khovanov homology. In this talk we will explore a surprising relationship between these two proofs: an interplay between gauge theory and Khovanov homology.
Ib Madsen (University of Copenhagen) Diffeomorphism groups of some high dimensional manifolds.
Abstract: I will discuss the homological structure of the classifying space of 2d-dimensional (d-1)-connected manifolds. This generalizes the case of surfaces where the stable homology was predicted by the Mumford conjecture and the actual homology by the Harer stability theorem. The methods involve rational homotopy theory and surgery theory.
Fabien Morel (Ludwig-Maximilians-Universität München) On the homology of Lie groups made discrete
Abstract: In this talk I will recall and discuss the conjecture of John Milnor on the homology of Lie groups made discrete, as well as its algebraic analogue, the Friedlander conjecture.

In a work still partially in progress, we give a proof of that conjecture for algebraic groups G over algebraically closed fields. I will sketch some ideas behind this proof, in particular the role of A1-homotopy theory (already used by V. Voevodsky to prove other conjectures of John Milnor concerning mod 2 Galois cohomology and quadratic forms) and the role of a new object attached to G, its simplicial building. We will emphasize the case G = SL_2, SL_3,...
Peter Ozsvath (Massachusetts Institute of Technology) An overview of Heegaard Floer homology
Abstract: Heegaard Floer homology is an invariant for knots and three-manifolds defined using methods from Lagrangian Floer homology and symplectic geometry. I will describe a concrete model for computing this invariant for knots in S3. Time permitting, I will turn to some further developments in the theory. The material I will describe is joint with collaborators, including Robert Lipshitz, Ciprian Manolescu, Dylan Thurston, and Zoltán Szabó.
Parimala Raman (Emory University) The Milnor Conjectures and Quadratic Forms
Abstract: The Milnor conjectures relating the graded Witt ring and the mod-2 Galois cohomology ring of a field have been a driving force in the algebraic theory of quadratic forms.  The degree 2 norm residue isomorphism, due to Merkurjev, established the first case of the Milnor conjectures and ushered in a new era in the theory of quadratic forms. We shall explain some of the consequences of the Milnor conjectures, with particular reference to invariants of fields associated to quadratic forms.
Douglas Conner Ravenel (University of Rochester) A solution to the Arf-Kervaire invariant problem
Abstract: The 1963 work of Kervaire-Milnor on the classification of exotic spheres in terms of the stable homotopy groups of spheres left one unanswered question in dimensions congruent to two modulo four. Subsequent work by Brown-Peterson and Browder gave the answer in all dimensions that are not two less than a power of two.  We solve the problem in all remaining cases except 126. Our answer is the opposite of the one that many sought in the 1970s.
Gang Tian (Princeton University) Geometric structures in dimension four
Abstract: For the last 50 years or longer, it has been a basic question in topology to study differential structures of a given manifold. In the early 80's, Donaldson used anti-self solutions of the Yang-Mills equation to study differentiable 4-manifolds and construct a very useful class of differentiable invariants for 4-manifolds. In particular, he was able to show that a topological 4-manifold may have different differentiable structures. In this talk, I will discuss geometric methods in studying 4-manifolds and in particular, some recent progress.
Ulrike Tillmann (University of Oxford) Cobordisms: old and new
Abstract: Cobordisms have played an important role in the classification of manifolds ever since the 1950s. In a different way, they are fundamental to the mathematical formulation for topological quantum field theory. We will explain how recent results shed new light on both theories.
Visitors in Residence
Alejandro Adem University of British Columbia 1/29/2012 - 2/1/2012
Anar Akhmedov University of Minnesota 1/30/2012 - 2/1/2012
Brendan P.W. Ames University of Minnesota 8/31/2011 - 8/30/2012
Arindam Banerjee University of Minnesota 9/1/2011 - 6/30/2012
Hyman Bass University of Michigan 1/29/2012 - 2/1/2012
Maria Basterra University of New Hampshire 1/29/2012 - 2/1/2012
Mark Behrens Massachusetts Institute of Technology 1/29/2012 - 1/31/2012
Julie Bergner University of California, Riverside 1/29/2012 - 2/1/2012
Andrew John Beveridge Macalester College 9/1/2011 - 5/15/2012
Jodi Black Bucknell University 1/29/2012 - 2/1/2012
Sergey G Bobkov University of Minnesota 9/1/2011 - 6/30/2012
William Browder Princeton University 1/29/2012 - 2/1/2012
Luca Capogna University of Minnesota 8/15/2011 - 6/10/2012
Sylvain Edward Cappell New York University 1/29/2012 - 2/1/2012
Aycil Cesmelioglu University of Minnesota 9/30/2010 - 8/30/2012
Paolo Codenotti University of Minnesota 9/1/2011 - 8/30/2012
Frederick R. Cohen University of Rochester 1/29/2012 - 2/1/2012
Jintao Cui University of Minnesota 8/31/2010 - 8/30/2012
Xiaoyi Cui University of Minnesota 1/30/2012 - 2/1/2012
Isabel K. Darcy University of Iowa 9/1/2011 - 6/30/2012
James F Davis Indiana University 1/29/2012 - 2/1/2012
William G. Dwyer University of Notre Dame 1/29/2012 - 2/1/2012
Geir Ellingsrud University of Oslo 1/29/2012 - 2/1/2012
Leonardo Espin NONE 9/1/2011 - 6/30/2012
John Fornaess University of Michigan 1/28/2012 - 2/1/2012
Søren Galatius Stanford University 1/29/2012 - 2/1/2012
Tingran Gao Duke University 1/29/2012 - 2/1/2012
Carlos Andres Garavito-Garzon University of Minnesota 9/8/2011 - 6/30/2012
Stefan M. Giovan University of Texas at Dallas 1/9/2012 - 1/15/2012
Samuel Gitler CINVESTAV 1/29/2012 - 2/1/2012
Paul Goerss Northwestern University 1/29/2012 - 2/1/2012
Robert Gulliver University of Minnesota 1/30/2012 - 2/1/2012
Ian Hambleton McMaster University 1/29/2012 - 2/1/2012
Michael Hill University of Virginia 1/29/2012 - 2/1/2012
Michael J. Hopkins Harvard University 1/28/2012 - 2/1/2012
Yulia Hristova University of Minnesota 9/1/2010 - 8/31/2012
Dale Husemoller Max Planck Institute for Mathematics 1/29/2012 - 2/1/2012
Bjørn Jahren University of Oslo 1/29/2012 - 2/2/2012
Niles Johnson University of Georgia 1/29/2012 - 2/1/2012
Donald Kahn University of Minnesota 1/30/2012 - 2/1/2012
Hee Jung Kim Pohang University of Science and Technology (POSTECH) 1/29/2012 - 2/1/2012
Robion Kirby University of California, Berkeley 1/29/2012 - 2/1/2012
Peter Kronheimer Harvard University 1/29/2012 - 1/31/2012
Kee Yuen Lam University of British Columbia 1/29/2012 - 2/1/2012
Tsit Yuen Lam University of California, Berkeley 1/29/2012 - 2/1/2012
Tyler Lawson University of Minnesota 1/30/2012 - 2/1/2012
Gilad Lerman University of Minnesota 9/1/2011 - 6/30/2012
Stephen D. Levene University of Texas at Dallas 1/9/2012 - 1/15/2012
Tian-Jun Li University of Minnesota 1/30/2012 - 2/1/2012
Wenbo Li University of Delaware 9/1/2011 - 5/30/2012
Ayelet Lindenstrauss Indiana University 1/29/2012 - 2/1/2012
Xin Liu University of Minnesota 8/31/2011 - 8/30/2012
Tom Lyche University of Oslo 1/29/2012 - 2/1/2012
Shiqian Ma University of Minnesota 8/31/2011 - 8/30/2013
Ib Madsen University of Copenhagen 1/29/2012 - 2/1/2012
Yu (David) Mao University of Minnesota 8/31/2010 - 8/30/2012
Albert Marden University of Minnesota 1/30/2012 - 2/1/2012
Gabriela Martínez University of Minnesota 8/31/2011 - 8/30/2013
John McCleary Vassar College 1/29/2012 - 2/2/2012
Dusa McDuff Barnard College 1/27/2012 - 2/2/2012
William Messing University of Minnesota 1/30/2012 - 2/1/2012
John Milnor SUNY 1/27/2012 - 2/2/2012
Dimitrios Mitsotakis University of Minnesota 10/27/2010 - 8/31/2012
Jack Morava Johns Hopkins University 1/29/2012 - 2/2/2012
Fabien Morel Ludwig-Maximilians-Universität München 1/28/2012 - 2/2/2012
Walter Neumann Barnard College 1/29/2012 - 1/31/2012
Peter J. Olver University of Minnesota 1/30/2012 - 2/1/2012
Kent Orr Indiana University 1/29/2012 - 2/1/2012
Peter Ozsvath Massachusetts Institute of Technology 1/29/2012 - 2/1/2012
Mary Therese Padberg University of Iowa 8/16/2011 - 1/26/2012
Hyungju Park Pohang University of Science and Technology (POSTECH) 1/29/2012 - 2/1/2012
Erik Kjær Pedersen University of Copenhagen 1/29/2012 - 2/1/2012
Candice Renee Price University of Iowa 8/1/2011 - 7/31/2012
Weifeng (Frederick) Qiu University of Minnesota 8/31/2010 - 8/30/2012
Anca Ruxandra Radulescu University of Colorado 1/29/2012 - 2/1/2012
Parimala Raman Emory University 1/29/2012 - 2/1/2012
Andrew Ranicki University of Edinburgh 1/29/2012 - 2/1/2012
Douglas Conner Ravenel University of Rochester 1/29/2012 - 2/1/2012
Victor Reiner University of Minnesota 1/30/2012 - 2/1/2012
Dale Preston Odin Rolfsen University of British Columbia 1/29/2012 - 2/1/2012
Jeff A. Rosoff Gustavus Adolphus College 1/29/2012 - 2/1/2012
Lee Rudolph Clark University 1/29/2012 - 2/1/2012
Guillermo R. Sapiro University of Minnesota 9/1/2011 - 5/31/2012
Radmila Sazdanović University of Pennsylvania 1/29/2012 - 2/1/2012
Robert Glenn Scharein Hypnagogic Software 1/5/2012 - 2/4/2012
George R Sell University of Minnesota 1/30/2012 - 2/1/2012
Laurence Carl Siebenmann Université de Paris XI (Paris-Sud) 1/29/2012 - 2/3/2012
Steven Sperber University of Minnesota 1/30/2012 - 2/1/2012
Arthur Szlam University of Minnesota 8/31/2011 - 8/30/2012
Gang Tian Princeton University 1/29/2012 - 2/1/2012
Ulrike Tillmann University of Oxford 1/28/2012 - 2/1/2012
Victor Turchin Kansas State University 1/29/2012 - 2/1/2012
Divyanshu Vats University of Minnesota 8/31/2011 - 8/30/2012
Jonathan Wahl University of North Carolina 1/30/2012 - 2/1/2012
Lan Wang University of Minnesota 1/19/2012 - 5/12/2012
Helen Wong Carleton College 1/30/2012 - 2/1/2012
Lingzhou Xue University of Minnesota 9/1/2011 - 6/30/2012
Teng Zhang University of Minnesota 8/31/2011 - 8/30/2012
Legend: Postdoc or Industrial Postdoc Long-term Visitor

IMA Affiliates:
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