Seminars and Colloquia by Series

Hypersurfaces with central convex cross sections

Series
Geometry Topology Seminar
Time
Monday, October 3, 2016 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Alper Gur – Indiana University –
The compact transverse cross-sections of a cylinder over a central ovaloid in Rn, n ≥ 3, with hyperplanes are central ovaloids. A similar result holds for quadrics (level sets of quadratic polynomials in Rn, n ≥ 3). Their compact transverse cross-sections with hyperplanes are ellipsoids, which are central ovaloids. In R3, Blaschke, Brunn, and Olovjanischnikoff found results for compact convex surfaces that motivated B. Solomon to prove that these two kinds of examples provide the only complete, connected, smooth surfaces in R3, whose ovaloid cross sections are central. We generalize that result to all higher dimensions, proving: If M^(n-1), n >= 4, is a complete, connected smooth hypersurface of R^n, which intersects at least one hyperplane transversally along an ovaloid, and every such ovaloid on M is central, then M is either a cylinder over a central ovaloid or a quadric.

Fillings of unit cotangent bundles of nonorientable surfaces

Series
Geometry Topology Seminar
Time
Monday, September 26, 2016 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Burak Ozbagci – UCLA and Koc University
We prove that any minimal weak symplectic filling of the canonical contact structure on the unit cotangent bundle of a nonorientable closed surface other than the real projective plane is s-cobordant rel boundary to the disk cotangent bundle of the surface. If the nonorientable surface is the Klein bottle, then we show that the minimal weak symplectic filling is unique up to homeomorphism. (This is a joint work with Youlin Li.)

Fox-Neuwirth cells, quantum shuffle algebras, and Malle’s conjecture for function fields

Series
Geometry Topology Seminar
Time
Monday, September 19, 2016 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Craig Westerland – University of Minnesota
I will describe new techniques for computing the homology of braid groups with coefficients in certain exponential coefficient systems. An unexpected side of this story (at least to me) is a connection with the cohomology of certain braided Hopf algebras — quantum shuffle algebras and Nichols algebras — which are central to the classification of pointed Hopf algebras and quantum groups. We can apply these tools to get a bound on the growth of the cohomology of Hurwitz moduli spaces of branched covers of the plane in certain cases. This yields a weak form of Malle’s conjecture on the distribution of fields with prescribed Galois group in the function field setting. This is joint work with Jordan Ellenberg and TriThang Tran.

When is a Knot Diagram Legendrian?

Series
Geometry Topology Seminar
Time
Monday, September 12, 2016 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Mark Lowell – University of Massachusetts
We consider two knot diagrams to be equivalent if they are isotopic without Reidemeister moves, and prove a method for determining if the equivalence class of a knot diagram contains a representative that is the Lagrangian projection of a Legendrian knot. This work gives us a new tool for determining if a Legendrian knot can be de-stabilized.

Dehn twists exact sequences through Lagrangian cobordism

Series
Geometry Topology Seminar
Time
Monday, August 29, 2016 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Weiwei Wu – University of Georgia

Please Note: In this talk we first introduce a new "singularity-free" approach to the proof of Seidel's long exact sequence, including the fixed-point version. This conveniently generalizes to Dehn twists along Lagrangian submanifolds which are rank one symmetric spaces and their covers, including RPn and CPn, matching a mirror prediction due to Huybrechts and Thomas. The idea of the proof can be interpreted as a "mirror" of the construction in algebraic geometry, realized by a new surgery and cobordism construction. This is a joint work with Cheuk-Yu Mak.

Lifting Homeomorphisms of Cyclic Branched Covers of Spheres

Series
Geometry Topology Seminar
Time
Monday, August 22, 2016 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Rebecca Winarski – University of Wisconsin at Milwaukee
Birman and Hilden ask: given finite branched cover X over the 2-sphere, does every homeomorphism of the sphere lift to a homeomorphism of X? For covers of degree 2, the answer is yes, but the answer is sometimes yes and sometimes no for higher degree covers. In joint work with Ghaswala, we completely answer the question for cyclic branched covers. When the answer is yes, there is an embedding of the mapping class group of the sphere into a finite quotient of the mapping class group of X. In a family where the answer is no, we find a presentation for the group of isotopy classes of homeomorphisms of the sphere that do lift, which is a finite index subgroup of the mapping class group of the sphere. Our family introduces new examples of orbifold Picard groups of subloci of Teichmuller space that are finitely generated but not cyclic.

Some hyperbolic non-fillable manifolds

Series
Geometry Topology Seminar
Time
Thursday, June 23, 2016 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Yajing Liu – UCLA
Existence of tight contact structures is a fundamental question of contact topology. Etnyre and Honda first gave the example which doesn't admit any tight structure. The existence of fillable tight structures is also a subtle question. Here we give some new examples of hyperbolic 3-manifolds which do not admit any fillable structures.

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