The SGGTC seminar meets on Fridays in Math 407 from 2:00 pm to 3:00 pm, unless noted otherwise (in red). If you would like to be on the mailing list, please subscribe here. 

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Schedule


Date
Speaker
Title
Jan 30, 2pm
Yikai Teng (Rutgers University-Newark)
 Khovanov homology and exotic planes
Feb 6, 2 pm Amanda Hirschi (Sorbonne University) On the Donaldson 4-6 problem
Feb 13, 2 pm Mihai Marian (University of British Columbia)  
Feb 20, 2 pm Daniel Pomerleano (UMass, Boston)  
Feb 27, 2 pm Yu-Shen Lin (Boston University)  
Mar 6, 2 pm    
Mar 13, details TBD Alberto Abbondandolo (Ruhr-Universitat Bochum) and Gabriele Benedetti (Vrije Universiteit Amsterdam)  
Mar 20 Spring Break  
Mar 27 Simons Conference  
Mar 30 Taketo Sano (RIKEN iTHEMS)  
Apr 3, 2 pm    
Apr 10, 2 pm Bulent Tosun (University of Alabama)  
Apr 17, 2 pm Danil Kozevnikov (University of Edinburgh)  
Apr 20, 2 pm Tye Lidman (North Carolina State University)  
May 1, 2 pm Fraser Binns (Princeton University)  

 

Abstracts

Jan 30: Yikai Teng (Rutgers University-Newark) "Khovanov homology and exotic planes"

Since the 1980s, mathematicians have discovered uncountably many "exotic" embeddings of R^2 in R^4, i.e., embeddings that are topologically but not smoothly isotopic to the standard xy-plane. However, until today, there have been no direct, computable invariants that could detect such exotic behavior (with prior results relying on indirect arguments). In this talk, we define the end Khovanov homology, which is the first known combinatorial invariant of properly embedded surfaces in R^4 up to ambient diffeomorphism. Moreover, we apply this invariant to detect new exotic planes, including the first known example of an exotic plane that is a Lagrangian submanifold of the standard symplectic R^4.

Feb 6: Amanda Hirschi (Sorbonne University) "On the Donaldson 4-6 problem"

The Donaldson 4-6 question asks how deformation classes of stabilised symplectic forms, i.e. after taking the product with S^2, are related to the underlying smooth structures on the underlying smooth manifold in dimension 4 I will describe one example of a smooth 4-manifold admitting two symplectic forms which remain deformation inequivalent after taking the product with S^2, giving counterexamples to one implication of the conjectured relation. On the other hand, I will explain why two symplectic manifolds, whose stabilisations are deformation equivalent, have the same Gromov-Witten invariants. This is joint work with Luya Wang.