Fridays from 2:30-3:30pm in LGRT 1681 at UMass Amherst
Organizers: İnanç Baykur, Patricia Cahn, Miriam Kuzbary and Riccardo Pedrotti
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Speaker: ORGANISATION MEETING
Speaker: Patricia Cahn
Title: Rep-Tiles
Abstract: An n-dimensional rep-tile is a compact submanifold of R^n that can be decomposed into isometric re-scaled copies of itself, with non-overlapping interiors. We give a complete isotopy classification of rep-tiles in all dimensions. This is joint work with Blair, Kjuchukova, and Schwartz.
Institution: Smith College
Website: http://www.science.smith.edu/~pcahn/
Speaker: Riccardo Pedrotti
Title: On sections of Lefschetz fibrations over the disk
Abstract: I'll report on an ongoing project, joint work with J. Hillman, aimed at finding criteria for the existence of sections on a given Lefschetz fibration over a surface. We will start by presenting a nice algebraic criterion for the existence of sections in a surface bundle and explain what goes wrong if we try to apply it to the more general Lefschetz fibration case. The question of when a nullhomotopic loop in the boundary of a Lefschetz fibration over the disk can be extended to a section over the whole disk is one such subtle issue. Our computations suggest that working with continuous or smooth sections leads to different answers.
Institution: University of Massachusetts Amherst
Website: https://riccardopedrotti.github.io
Speaker: Abhishek Mallick
Title: Instanton Floer homology, involutions, and exotica
Abstract: Instanton Floer homology together with the Donaldson-invariant has played a central role in understanding many exotic phenomena in 4-manifold topology. In this talk, I will discuss some recent applications of instanton Floer homology to studying exotica via the TQFT-like structures within the theory together with actions of symmetry. In particular, we will discuss exotic smooth structures and exotic disks surviving stabilization by projective planes. This is based on a joint work with Alfieri, Dai, and Taniguchi and an ongoing work with Dai and Taniguchi.
Institution: Dartmouth College
Website: https://abhishekmallickmath.github.io
Speaker: Thomas Kindred
Title: Murasugi sum and arborescence in 3D and 4D
Abstract: Many invariants of knots and links in $S^3$ can be understood in terms of spanning surfaces---compact surfaces embedded in $S^3$ with boundary equal to a given knot or link. Murasugi sum, also called generalized plumbing, is a particular way of gluing together two spanning surfaces along a disk. I will begin by describing how these gluings work and how they improve our understanding of at least some of the following: the Alexander polynomial, the genus of a knot, fiberedness, incompressibility and the fundamental group, Tait's flyping conjecture, Kauffman states, state surfaces, Khovanov homology, and Heegaard Floer homology. Next, I will explain how plumbing unknotted annuli and Mobius bands in the pattern of a tree yields several important classes of links: 2-bridge, pretzel, Montesinos, and arborescent. The 2-bridge case is particularly rich, as described in a beautiful paper by Hatcher and Thurston, and I may go into some detail about current work on this topic. Finally, I will describe other current work that adapts Murasugi sum to an operation on spanning solids in $S^4$. Expect lots of pictures!
Institution: Smith College
Website: https://thomaskindred.com
Speaker: Laura Wakelin
Title: Dehn surgery functions are never injective.
Abstract: For any fixed rational number p/q, Dehn surgery gives a map from the set of knots in the 3-sphere to the set of closed orientable 3-manifolds. In 1978, Gordon conjectured that these maps are never injective. I will briefly discuss some results which demonstrate non-injectivity for some special cases of p/q, before going on to present joint work with Kyle Hayden and Lisa Piccirillo in which we prove the conjecture using rational RBG links and the zeroth HOMFLYPT polynomial.
Institution: UT Austin
Website: https://sites.google.com/view/laurawakelin
Spring Break
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Speaker: Pedro Brunialti Lima de Andrade
Title: Bi-incomplete Tambara functors are almost never free
Abstract: In equivariant homotopy theory, Mackey functors play the role of abelian (homotopy) groups and Tambara functors play the role of rings (algebras). In the category of abelian groups, free algebras are always free as abelian groups, however, in their work, Hill, Mehrle and Quigley show that free incomplete Tambara functors often fail to be free as Mackey functors. In this talk I will outline how this result extends to the case of bi-incmplete tambara functors, where now the underlying Mackey functor of the Tambara functor may also be incomplete. This is a joint work with Anna Marie Bohmann, Bertrand Guillou, David Mehrle and Chris Portwood.
Institution: University of Virginia
Website: https://pbrunialti.github.io/index.html
Speaker: Mike Sullivan
Title: Some quantitative results for Legendrian knots and submanifolds.
Abstract: Legendrians submanifolds of contact manifolds lie on both sides of the flexible/rigid divide in contact topology/geometry. I'll discuss results on the rigid side, which mostly rely on the barcodes (persistence) of various Floer-type pseudo-holomorphic curve theories associated to Legendrians. This includes: non-degeneracy of the Shelukhin-Hofer metric, C^0-closure, displacement energy bounds, existence of Reeb chords, flats in the group of contactomoprhisms, etc. I'll start with the definitions. This is old and new work, all joint with Georgios Dimitroglou Rizell.
Institution: UMass Amherst
Website: https://www.umass.edu/mathematics-statistics/about/directory/mike-sullivan
Speaker: Kyle Hayden
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Institution: Rutgers University-Newark
Website: https://sites.google.com/view/kylehayden/home
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