PCMI 2006 Proceedings, Lectures and Notes
Please note that all lecture notes will be published on the PCMI website as they become available during the Summer Session. Contact us at pcmi@ias.edu with any questions.
Graduate Summer School
Schedule
| Monday | Tuesday | Wednesday | Thursday | Friday | |
| Week 1 | 8:30 Khavanov 11:00 Morgan 2:00 Szabo |
8:30 Khavanov 11:00 Gordon 2:00 Szabo |
8:30 Khavanov 11:00 Szabo (2:00 no lecture) |
8:30 Khavanov 11:00 Gordon 2:00 Szabo |
8:30 Khavanov 11:00 Gordon 2:00 Szabo |
| Week 2 | 8:30 Khavanov 11:00 Gordon 2:00 Etnyre |
PCMI is not in Session to celebrate Independence Day - July 4th | 8:30 Gabai 11:00 Gordon 2:00 Etnyre |
8:30 Gabai 11:00 Gordon 2:00 Etnyre |
8:30 Gabai 11:00 Fintushel/Stern 2:00 Etnyre |
| Week 3 | 8:30 Gabai 11:00 Fintushel/Stern 2:00 Morgan |
8:30 Gabai 11:00 Fintushel/Stern 2:00 Morgan |
8:30 Etnyre 11:00 Fintushel/Stern (2:00 no lecture) |
8:30 Etnyre 11:00 Fintushel/ Stern 2:00 Morgan |
8:30 Morgan 11:00 Fintushel/Stern 2:00 Morgan |
GSS Lecture Notes as provided to PCMI by the lecturer and/or TA:
Yakov Eliashberg, Stanford University
John Etnyre, University of Pennsylvania
GSS Lecture Notes as recorded by Gabriel Drummond-Cole: http://www.math.sunysb.edu/~blafard/notes
Research Program Schedule
 |
Title and Reseacher (subject to change) | Time | Date | ||
| Week 1 | Reeb vector fields and open book decompositions, Ko Honda | n/a | Monday | 06/26/06 | |
| Hyperbolic rational homology 3-spheres with large injective radius, Nathan Dunfield |
9:40-11:00 a.m. | Tuesday | 06/27/06 | ||
| Knot Floer homology and various satellite constructions, Michael Heddon |
4:30-5:30 p.m. | ||||
| Rohlin's invariant and gauge theory, Nikolai Saveliev | 9:40-11:00 a.m. | Wednesday | 06/28/06 | ||
| Knot Floer homology detects genus one fibred knots, Paolo Ghiggini | 9:40-11:00 a.m. | Thursday | 06/29/06 | ||
| Legendrian knots and the spanning tree model of the Khovanov homology, Hao Wu | 4:30-5:30 p.m. | ||||
| From the SO(3) monopole cobordism formula to Witten's conjecture, Thomas Leness |
9:40-11:00 a.m. | Friday | 06/30/06 | ||
| On embedded contact homology, Michael Hutchings | 4:30-5:30 p.m. | ||||
| Week 2 | Disoriented and confused: fixing the functoriality of Khovanov homology, Scott Morrison |
9:40-10:40 a.m. | Monday | 07/03/06 | |
| Commensurability classes of 2-bridge knots, Genevieve. Walsh (Grand Theater) | 4:30-5:30 p.m. | ||||
| Convexity of Morse stratifications and spines of 3-manifolds, Gabriel Katz (Silver King 1) |
4:30-5:30 p.m. | ||||
| Differentials on Khovanov-Rozansky homology, Jacob Rasmussen | 9:40-11:00 a.m. | Wednesday | 07/05/06 | ||
| Gromov-Witten "equals" Reshetikhin-Turaev, David Auckly (Grand Theater) | 4:30-5:30 p.m. | ||||
| 4-manifolds, links and Alexander duality, Slava Krushkal (Silver King 1) | 4:30-5:30 p.m. | ||||
| Symplectic mapping classes and fillings, Emmanuel Giroux | 9:40-11:00 a.m. | Thursday | 07/06/06 | ||
| High distance knots, Saul Schleimer | 4:30-5:30 p.m. | ||||
| Knot surgeries and negative definite four-manifolds, Brendan Owens (Grand Theater) |
9:40-10:40 a.m. | Friday | 07/07/06 | ||
| Poisson Structures on Moduli of SL(3)-Bundles over a Punctured Surface, Sean Lawton (Coalition 3) |
9:40-10:40 a.m | ||||
| Engel Structures, Thomas Vogel (Grand Theater) | 4:30-5:30 p.m. | ||||
| Groping around link concordance, Tim Cochran (Silver King 1) | 4:30-5:30 p.m. | ||||
| Week 3 | Open books and hyperbolic Dehn Survery, David Futer (Grand Theater) | 9:40-11:00 a.m. | Monday | 07/10/06 | |
| A rational blowdown surgery revisited, Jongil Park (Coalition 3) | 9:40-11:00 a.m. | ||||
| Non-compact Heegaard splittings anda theorem of Casson and Gordon, Scott Taylor (Grand Theater) | .4:30-5:30 p.m. | ||||
| Extending knot Floer homology to higher genus boundary, Robert Lipschitz (Silver King 1) |
.4:30-5:30 p.m. | ||||
| Hyperbolic arborescent links, Francois Gueritaud (Grand Theater) | 9:40-11:00 a.m. | Tuesday | 07/11/06 | ||
| An exact triangle for knot Floer homology, Ciprian Manolescu (Coalition 3) | 9:40-11:00 a.m. | ||||
| A local cobordism formula for sl(3) link homology, Ari Nieh (Grand Theater) |
4:30-5:30 p.m. | ||||
| Form Seiberg-Witten to Gromov: Floer theory versions, Yi-Jen Lee (Silver King 1) |
4:30-5:30 p.m. | ||||
| Knot Contact homology, Lenny Ng (Grand Theater) | 9:40-11:00 a.m. | Wednesday | 07/12/06 | ||
Symplectic S^1 x N^3 and subgroup separability, Abstract: A folklore conjecture asserts that $S^1 \times N$ admits a symplectic structure only if $N$ fibers over the circle. In this talk we discuss the relation between this problem and the subgroup separability properties of $N$. In particular, this allows us to show that the conjecture holds true when $N$ has vanishing Thurston norm. |
9:40-11:00 a.m. | ||||
| EXTRA LECTURE | Topological 4-manifolds - a survey for grad students, Peter Teichner (Grand Theater) |
1:00 p.m. | |||
| On knot Floer homology, Peter Ozsvath (Grand Theater) | 9:40-11:00 a.m. | Thursday | 07/13/06 | ||
| Singular archiral Lefschetz fibrations, Robion Kirby (Grand Theater) | 4:30-5:30 p.m. | ||||
| Quantum hyperbolic geometry, Francis Bonahon (Silver King 1) | 4:30-5:30 p.m. | ||||
Tigh contact structures and contact Ozsvath-Szabo invariants, Andras Stipsicz (Grand Theater) |
9:40-11:00 a.m. | Friday | 07/14/06 |
Undergraduate Summer School
|
Francis Bonahon | Introduction |
| Chapter 1 | ||
| Chapter 2 | ||
| Chapter 3 | ||
| Chapter 4 | ||
| Chapter 5 |
|
Erica Flapan | Chapter 1 |
| Chapters 2 & 3 | ||
| Chapter 4 | ||
| Chapter 5 | ||
| Chapter 6 | ||
| Chapter 7 | ||
| Chapter 8 | ||
| Chapter 9 | ||
| Chapter 10 | ||
| Chapter 11 | ||
| Chapter 12 | ||
| Chapter 13 |
Cross Program Activities
Pizza and Problem Solving
Francis Su, Harvey Mudd College and Andrew J. Bernoff, Harvey Mudd College - Digits and Divisibility
For more information, please visit: http://www.math.hmc.edu/~ajb/PCMI/problem_solve.html
July 4th Parade Update
PCMI won most original entry in this year's 4th of July Parade in Park City, UT
For more information, click here http://mathforum.org/pcmi/hstp/sum2006/photos/