Other area seminars. Our e-mail list. Archive of previous semesters
Columbia Geometric Topology SeminarSpring 2025 |
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Organizers: Ross Akhmechet, Deeparaj Bhat, Siddhi Krishna, Francesco Lin
The GT seminar typically meets on Fridays at 2:00pm Eastern time in Room 407, Mathematics Department, Columbia University.
Other area seminars. Our e-mail list. Archive of previous semesters
| Date | Time (Eastern) | Speaker | Title |
|---|---|---|---|
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January 24 |
2pm |
no seminar |
first week of classes |
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January 31 |
4pm in Room 407 (note unusual time!!) | Jonathan Zung (MIT) |
Expansion and torsion homology of 3-manifolds |
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February 7 |
2pm |
Juan Munoz-Echaniz (SCGP) |
Monodromy of singularities and Seiberg—Witten theory |
|
February 14 |
2pm | Luya Wang (IAS) |
Algebraic torsion and symplectic linear plumbings |
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February 21 |
2pm | Seraphina Lee (UChicago) |
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February 28 |
2pm | no seminar |
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March 7 |
2pm | Dave Rose (UNC Chapel Hill) | |
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March 14 |
2pm | Boyu Zhang (Maryland) |
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March 21 |
2pm | no seminar | happy spring break! |
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March 28 |
2pm |
no seminar |
Simons annual meeting |
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April 4 |
2pm |
Mike Miller Eismeier (Vermont) |
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April 11 |
2pm |
Laura Wakelin (King's College London) (TBC) |
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April 18 |
2pm |
Bena Tshishiku (Brown) | |
| April 25 |
2pm |
Thomas Massoni (MIT) | |
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May 2 |
2pm |
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May 9 |
2pm |
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Name: Jonathan Zung
Title: Expansion and torsion homology of 3-manifolds
Abstract: nally null-homologous i-cycle bounds an i+1 chain of comparatively small volume. The interactions between expansion, spectral geometry, and topology have long been studied in the settings of graphs and surfaces. In this talk, I will explain how to construct rational homology 3-spheres which are good higher expanders. On the other hand, I will show that such higher expanders must be rather topologically complicated: they must have lots of torsion homology.
Name: Juan Munoz-Echaniz
Title: Monodromy of singularities and Seiberg—Witten theory
Abstract: The monodromy of a complex isolated hypersurface singularity captures geometric and topological information about how the nearby smooth fibers degenerate into the singularity. The homological monodromy—the action on the homology of the Milnor fiber—has been extensively studied ever since pioneering work of Brieskorn and Milnor. However, the monodromy diffeomorphism itself—acting on the Milnor fiber as a mapping class—is comparatively less understood. In this talk I will discuss the following result: the monodromy diffeomorphism of a weighted-homogeneous isolated hypersurface singularity of complex dimension 2 has infinite order in the smooth mapping class group of the Milnor fiber (fixing the boundary) provided the singularity is not ADE. (In turn, the monodromy of an ADE singularity has finite order in the smooth mapping class group, by a classical result of Brieskorn). The proof involves studying the Seiberg—Witten equation along the fibers of the Milnor fibration, by a combination of techniques from Floer homology, symplectic and contact geometry. This is based on joint work with Hokuto Konno, Jianfeng Lin and Anubhav Mukherjee.
Name: Luya Wang
Title: Algebraic torsion and symplectic linear plumbings
Abstract: Given a contact three-manifold, one can ask what types of symplectic four-manifolds it can bound, if any. This is related to the question whether certain complex algebraic curves can be realized with prescribed singularities. A key tool in this study is the embedded contact homology algebraic torsion, which encodes information about the Reeb dynamics of the contact manifold and the behavior of pseudoholomorphic curves in its symplectization. In this talk, I will describe this quantity and its geometric implications. We will do some calculations for the concave boundaries of symplectic linear plumbings of disk bundles and see how they agree with predictions coming from toric geometry. This is based on joint work with Aleksandra Marinkovic, Jo Nelson, Ana Rechtman, Laura Starkston, and Shira Tanny.