Geometry Seminar
The seminar meets Mondays at 3 o'clock and Fridays at 4 o'clock,
in BLOC 628.
Talks are 5060 minutes.
Visitor Information.
How to Give a Good Colloquium by John E. McCarthy.

Date Time 
Location  Speaker 
Title – click for abstract 

08/26 10:00am 
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Anna Seigal Oxford 
Ranks of Cubic Surfaces
There are various notions of rank, which measure the complexity of a tensor or polynomial. Cubic surfaces can be viewed as symmetric tensors. We consider the nonsymmetric tensor rank and the symmetric Waring rank of cubic surfaces, and show that the two notions coincide over the complex numbers. The results extend to order three tensors of all sizes, implying the equality of rank and symmetric rank when the symmetric rank is at most seven. We then explore the connection between the rank of a polynomial and the singularities of its vanishing locus, and we find the possible singular loci of a cubic surface of given rank. This talk is based on joint work with Eunice Sukarto. 

09/23 11:00am 
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Filip Rupniewski IMPAN 
Cactus rank and identification of secant inside cactus varieties
Every secant variety is contained in the corresponding cactus variety. However, according to our knowledge, there is no explicit equation of the secant variety which does not vanish on the cactus variety. I will present an algorithm for deciding if a given point in the cactus variety belongs to the secant variety in some special cases. I will also show the theorem for calculating the cactus rank of forms divisible by a large power of a linear form which allowed us to design the mentioned algorithm. Based on a joint work with M. Gałązka and T. Mańdziuk. 

09/28 3:00pm 
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Timothy Duff Georgia Tech 
TBA 

10/02 4:00pm 
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David, Sykes TAMU 
Local equivalence problems for 2nondegenerate, hypersurfacetype CR geometry studied via dynamical Legendrian contact structures.
The local differential geometry of Levinondegenerate CR structures is well understood due in large part to classical results of Cartan, Tanaka, Chern, and Moser, and yet comparatively little is known about other CR
structures. There is a natural association between 2nondegenerate, hypersurfacetype CR structures – which are the main focus of this talk – and dynamical Legendrian contact structures, and, moreover, there is a broad class of
these CR structures that can be uniquely recovered from their associated dynamical Legendrian contact structure. For these recoverable structures, we construct canonical absolute parallelisms on fiber bundles defined over a manifold
with the given CR structure. The construction can be applied to discern local equivalence between CR structures. Other applications that will be discussed include upper bounds for the dimension of a CR manifold’s symmetry group and a
characterization of local invariants of certain homogeneous CR manifolds. The latter application, coupled with results by Curtis Porter and Igor Zelenko, enables us to classify the local geometry of homogeneous, 2nondegenerate, hypersurfacetype CR manifolds in low dimensions.


10/07 Noon 
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J. Weyman U. Krakow 
TBA 

10/09 4:00pm 
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Leon Zhang UC Berkeley 
TBA 

10/19 3:00pm 
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Guangbo Xu Texas A&M University 
TBA 

11/13 4:00pm 
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Joe Kileel University of Texas Austin 
TBA
TBA 

11/23 3:00pm 
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Tom Gannon University of Texas 
TBA 