| Talk_id | Date | Speaker | Title |
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18593
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Thursday 8/29
2:00 PM
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Chris Gerig, Harvard University
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Probing 4-manifolds with near-symplectic forms
- Chris Gerig, Harvard University
- Probing 4-manifolds with near-symplectic forms
- 08/29/2019
- 2:00 PM - 3:00 PM
- C304 Wells Hall
Most closed 4-manifolds do not admit symplectic forms, but most admit "near-symplectic forms", certain closed 2-forms which are symplectic outside of a collection of circles. This provides a gateway from the symplectic world to the non-symplectic world. I will first briefly sketch a geometric interpretation of the Seiberg-Witten invariants in terms of J-holomorphic curves that are compatible with the near-symplectic form. Although the Seiberg-Witten invariants don't apply to (potentially exotic) 4-spheres, nor do these spheres admit near-symplectic forms, there is still a way to bring in near-symplectic techniques.
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19602
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Thursday 9/5
2:00 PM
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Alex Waldron, Michigan State University
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$G_2$-instantons on the 7-sphere
- Alex Waldron, Michigan State University
- $G_2$-instantons on the 7-sphere
- 09/05/2019
- 2:00 PM - 3:00 PM
- C304 Wells Hall
I'll discuss a forthcoming paper studying families of $G_2$-instantons on $S^7$, focusing on those which are obtained by pulling back asd instantons on $S^4 $ via the quaternionic Hopf fibration. In the charge-1 case this yields a smooth and complete 15-dimensional family. The situation for higher charge is more complicated, but we are able to compute all the infinitesimal deformations.
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19635
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Thursday 9/12
2:00 PM
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Honghao Gao, MSU
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Augmentations and sheaves for links
- Honghao Gao, MSU
- Augmentations and sheaves for links
- 09/12/2019
- 2:00 PM - 3:00 PM
- C304 Wells Hall
We study two different invariants of framed oriented links. Augmentations are rank one representations of a non-commutative algebra, whose definition is motivated by Floer homology. Sheaves in microlocal theory can be thought of as generalizations of link group representations. We will demonstrate two constructions going back and forth between these invariants. We will also tell a motivating story behind the scene, using SFT and microlocalization correspondence in symplectic topology.
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18580
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Thursday 9/26
2:00 PM
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David Boozer, UCLA
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Holonomy perturbations of the Chern-Simons functional for lens spaces
- David Boozer, UCLA
- Holonomy perturbations of the Chern-Simons functional for lens spaces
- 09/26/2019
- 2:00 PM - 3:00 PM
- C304 Wells Hall
We describe a scheme for constructing generating sets for Kronheimer and Mrowka's singular instanton knot homology for the case of knots in lens spaces. The scheme involves Heegaard-splitting a lens space containing a knot into two solid tori. One solid torus contains a portion of the knot consisting of an unknotted arc, as well as holonomy perturbations of the Chern-Simons functional used to define the homology theory. The other solid torus contains the remainder of the knot. The Heegaard splitting yields a pair of Lagrangians in the traceless $SU(2)$-character variety of the twice-punctured torus, and the intersection points of these Lagrangians comprise the generating set that we seek. We illustrate the scheme by constructing generating sets for several example knots. Our scheme is a direct generalization of a scheme introduced by Hedden, Herald, and Kirk for describing generating sets for knots in $S^3$ in terms of Lagrangian intersections in the traceless $SU(2)$-character variety for the 2-sphere with four punctures.
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18586
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Thursday 10/3
2:00 PM
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Rita Gitik, Michigan
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On Geodesic Triangles in the Hyperbolic Plane
- Rita Gitik, Michigan
- On Geodesic Triangles in the Hyperbolic Plane
- 10/03/2019
- 2:00 PM - 2:50 PM
- C304 Wells Hall
Let M be an orientable hyperbolic surface without boundary and
let c be a closed geodesic in M. We prove that any side of any triangle formed by distinct lifts of c in the hyperbolic plane is shorter than c.
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19632
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Thursday 10/17
2:00 PM
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Jesse Madnick , McMaster University
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TBD
- Jesse Madnick , McMaster University
- TBD
- 10/17/2019
- 2:00 PM - 3:00 PM
- C304 Wells Hall
No abstract available.
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19641
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Thursday 10/24
2:00 PM
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Lev Tovstopyat-Nelip, MSU
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TBA
- Lev Tovstopyat-Nelip, MSU
- TBA
- 10/24/2019
- 2:00 PM - 3:00 PM
- C304 Wells Hall
No abstract available.
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19619
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Thursday 10/31
2:00 PM
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Boyu Zhang, Princeton University
|
TBD
- Boyu Zhang, Princeton University
- TBD
- 10/31/2019
- 2:00 PM - 3:00 PM
- C304 Wells Hall
No abstract available.
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19622
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Thursday 11/14
2:00 PM
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Peter Lambert-Cole, Max Planck Institute for Mathematics
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TBA
- Peter Lambert-Cole, Max Planck Institute for Mathematics
- TBA
- 11/14/2019
- 2:00 PM - 3:00 PM
- C304 Wells Hall
TBA
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19628
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Thursday 11/21
2:00 PM
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Akram Alishahi, University of Georgia
|
TBA
- Akram Alishahi, University of Georgia
- TBA
- 11/21/2019
- 2:00 PM - 3:00 PM
- C304 Wells Hall
TBA
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19621
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Thursday 12/5
2:00 PM
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Shelly Harvey, Rice
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Pure braids and link concordance
- Shelly Harvey, Rice
- Pure braids and link concordance
- 12/05/2019
- 2:00 PM - 3:00 PM
- C304 Wells Hall
If one considers the set of m-component based links in R^3
with a 4-dimensional equivalence relationship on it, called
concordance, one can form a group called the link concordance group,
C^m. Questions in concordance are important in for classification
questions in topological and smooth 4-manifolds It is well known that
the link concordance group contains the isotopy class of pure braid
with m strands, P_m. That is, two braids are concordant if and only
if they are isotopic! In the late 90's Tim Cochran, Kent Orr, and
Peter Teichner defined a filtration of the knot/link concordance group
called the n-solvable filtration. This filtration gives a way to
approximate whether a link is trivial in the group. We discuss the
relationship between pure braids and the n-solvable filtration as well
as various other more geometrically defined filtrations coming from
gropes and Whitney towers. This is joint work with Aru Ray and Jung
Hwan Park.
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