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PRODID:Mathematics Seminar Calendar
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UID:20210506T224516-26968@math.msu.edu
DTSTAMP:20210506T224516Z
SUMMARY:Surgery Exact Triangles in Involutive Floer homology
DESCRIPTION:Speaker\: Matt Stoffregen, MSU\r\nWe'll sketch the definition of the involutive Heegaard Floer homology constructed by Hendricks-Manolescu, and then explain how this homology theory behaves under surgery. As a consequence, we can use the surgery formula to construct three-manifolds which are not homology cobordant to any combination of Seifert fiber spaces. This is joint work Kristen Hendricks, Jen Hom and Ian Zemke.
LOCATION:Online (virtual meeting)
DTSTART:20210126T195000Z
DTEND:20210126T204000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=26968
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BEGIN:VEVENT
UID:20210506T224516-26986@math.msu.edu
DTSTAMP:20210506T224516Z
SUMMARY:Wrapped Fukaya category via gluing sheaves, and the case of pinwheels
DESCRIPTION:Speaker\: Dogancan Karabas, Northwestern University\r\nIn this talk, I will discuss some gluing techniques for microlocal sheaves, and calculate wrapped Fukaya category of some rational homology balls, which are quotients of $A_n$ Milnor fibres, via gluing sheaves on their skeleta, i.e. pinwheels.
LOCATION:Online (virtual meeting)
DTSTART:20210202T195000Z
DTEND:20210202T204000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=26986
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BEGIN:VEVENT
UID:20210506T224516-26942@math.msu.edu
DTSTAMP:20210506T224516Z
SUMMARY:Lattice homology and instantons
DESCRIPTION:Speaker\: Irving Dai, MIT\r\nWe show that if Y is the boundary of an almost-rational plumbing, then the framed instanton Floer homology of Y is isomorphic to its Heegaard Floer homology. This class of 3-manifolds includes all Seifert fibered rational homology spheres. Our proof utilizes lattice homology, and relies on a decomposition theorem for instanton Floer cobordism maps established by John Baldwin and Steven Sivek. This is joint work with Antonio Alfieri, John Baldwin, and Steven Sivek.\r\n
LOCATION:Online (virtual meeting)
DTSTART:20210209T195000Z
DTEND:20210209T204000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=26942
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BEGIN:VEVENT
UID:20210506T224516-26953@math.msu.edu
DTSTAMP:20210506T224516Z
SUMMARY:Upsilon invariant and right-veering open book decompositions
DESCRIPTION:Speaker\: Linh Truong, University of Michigan\r\nIn 2010, Hedden showed that the Ozsvath-Szabo concordance invariant tau can detect whether a fibered knot induces the tight contact structure on the three-sphere. In 2017, Ozsvath-Stipsicz-Szabo constructed a one-parameter family of concordance invariants Upsilon, which recovers tau as a special case. I will discuss a sufficient condition using Upsilon for the monodromy of the open book decomposition of a fibered knot to be right-veering. As an application, I will discuss a generalization of Baker's conjecture on the concordance of tight, fibered knots. This is joint work with Dongtai He and Diana Hubbard.
LOCATION:Online (virtual meeting)
DTSTART:20210216T195000Z
DTEND:20210216T204000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=26953
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BEGIN:VEVENT
UID:20210506T224516-26951@math.msu.edu
DTSTAMP:20210506T224516Z
SUMMARY:Quantum trace map for $SL_n$ skein algebras of surfaces
DESCRIPTION:Speaker\: Thang Le, Georgia Tech\r\nFor a punctured surface there are two quantizations of the $SL_n$ character variety. The first quantization is the $SL_n$ skein algebra, and the second one is the quantization of the higher Teichmuller space.\r\nWhen $n=2$ Bonahon and Wong showed that there is an algebra homomorphism, called the quantum trace, from the first quantized algebra to the second one. We show for general n a similar quantum trace map exists.\r\nThe construction of the $SL_n$ quantum trace is based on the theory of stated $SL_n$ skein algebra, developed in a joint work with A. Sikora, and a work of Chekhov and Shapiro.
LOCATION:Online (virtual meeting)
DTSTART:20210223T195000Z
DTEND:20210223T204000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=26951
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BEGIN:VEVENT
UID:20210506T224516-26967@math.msu.edu
DTSTAMP:20210506T224516Z
SUMMARY:No talk
DESCRIPTION:Speaker\: Break Day, no talk\r\n
LOCATION:Online (virtual meeting)
DTSTART:20210302T195000Z
DTEND:20210303T204000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=26967
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BEGIN:VEVENT
UID:20210506T224516-26966@math.msu.edu
DTSTAMP:20210506T224516Z
SUMMARY:Lagrangian Fillings of Legendrian links: Two Constructions in Floer Theory
DESCRIPTION:Speaker\: Roger Casals, UC Davis\r\nIn this talk I will review our current understanding in the classification of Lagrangian fillings for Legendrian links in the standard contact 3-sphere. The talk will present two illustrative constructions: one explaining how to build and detect infinitely many Lagrangian fillings using the Legendrian Contact DGA, and the other explaining how to classify fillings for the Hopf link using pseudo-holomorphic foliations. First, I will present the basic objects of interest and survey the recent developments in the field (work with H. Gao, and work with E. Zaslow). Then I will delve into new and in-progress results on the Legendrian Contact DGA (work with L. Ng). Finally, I will report on how pseudo-holomorphic curves might help us classify Lagrangian fillings in certain cases. During the course of the talk, I will try to highlight some of the interesting open questions and new methods that arise from our current work as well as future directions.
LOCATION:Online (virtual meeting)
DTSTART:20210309T195000Z
DTEND:20210309T204000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=26966
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BEGIN:VEVENT
UID:20210506T224516-26978@math.msu.edu
DTSTAMP:20210506T224516Z
SUMMARY:Equivariant genera of strongly invertible knots
DESCRIPTION:Speaker\: Keegan Boyle, UBC\r\nGiven a knot $K$, the minimum genus of an orientable surface embedded in $S^3$ or $B^4$ with boundary $K$ is a natural measure of knot complexity. In this talk I will generalize this idea to involutions on knots, focusing on the case where the involution preserves the orientation of $S^3$, but reverses the orientation of $K$. This talk is elementary in nature and will be very accessible. This is joint work with Ahmad Issa.\r\n
LOCATION:Online (virtual meeting)
DTSTART:20210316T185000Z
DTEND:20210316T194000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=26978
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BEGIN:VEVENT
UID:20210506T224516-26992@math.msu.edu
DTSTAMP:20210506T224516Z
SUMMARY:Using surgery to study unknotting with a single twist
DESCRIPTION:Speaker\: Samantha Allen, Dartmouth\r\nOhyama showed that any knot can be unknotted by performing two full twists, each on a set of parallel strands. We consider the question of whether or not a given knot can be unknotted with a single full twist, and if so, what are the possible linking numbers associated to such a twist. It is observed that if a knot can be unknotted with a single twist, then some surgery on the knot bounds a rational homology ball. Using tools such as classical invariants and invariants arising from Heegaard Floer theory, we give obstructions for a knot to be unknotted with a single twist of a given linking number. In this talk, I will discuss some of these obstructions, their implications (especially for alternating knots), many examples, and some unanswered questions. This talk is based on joint work with Charles Livingston.
LOCATION:Online (virtual meeting)
DTSTART:20210323T185000Z
DTEND:20210323T194000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=26992
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BEGIN:VEVENT
UID:20210506T224516-26980@math.msu.edu
DTSTAMP:20210506T224516Z
SUMMARY:A quantum obstruction to purely cosmetic surgeries
DESCRIPTION:Speaker\: Renaud Detcherry, Bourgogne\r\nThe cosmetic surgery conjecture asks whether it is possible that two Dehn-surgeries on the same non-trivial knot in S³ give the same oriented 3-manifolds. We will present new obstructions for a knot to admit purely cosmetic surgeries, using Reshetikhin-Turaev invariants. In particular, we will show that if a knot admits purely cosmetic surgeries, then the slopes of the surgery are +-1/5k unless the Jones polynomial of K is 1 at the fifth root of unity.
LOCATION:Online (virtual meeting)
DTSTART:20210330T150000Z
DTEND:20210330T155000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=26980
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BEGIN:VEVENT
UID:20210506T224516-26979@math.msu.edu
DTSTAMP:20210506T224516Z
SUMMARY:A Geometric Kauffman Bracket
DESCRIPTION:Speaker\: Charlie Frohman, U Iowa\r\nThis is joint work with Joanna Kania-Bartoszynska and Thang Le $\\$\r\n\r\nI will discuss the representation theory of the Kauffman bracket skein algebra of a finite type surface at a root of unity whose order is not divisible by 4. $\\$\r\n\r\nSpecifically, the Kauffman bracket skein algebra is an algebra with trace in the sense of De Concini, Procesi, Reshetikhin and Rosso, so it has a well defined character variety of trace preserving representations, which can be identified with a branched cover of the SL(2,C)-character variety of the fundamental group of the underlying surface. $\\$\r\n\r\nIn the case of a closed surface the branched cover is trivial so its just the character variety of the fundamental group of the surface. $\\$\r\n\r\nThe skein algebra is also a Poisson order, so the character variety representations of the Kauffman bracket skein algebra of a closed surface decomposes into representations corresponding to irreducible, abelian and central representations of the fundamental group of the underlying surface. The irreducible representations of the fundamental group of the surface correspond to irreducible representations of the skein algebra. $\\$\r\n\r\nWe then use this as basic data to define an invariant of framed links in a three-manifold equipped with an irreducible representation of its fundamental group. The invariant satisfies the Kauffman bracket skein relations. $\\$\r\n\r\nSuch a representation could be the lift of the holonomy of a hyperbolic structure on the three-manifold, hence the title : A Geometric Kauffman Bracket. $\\$
LOCATION:Online (virtual meeting)
DTSTART:20210406T185000Z
DTEND:20210406T194000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=26979
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BEGIN:VEVENT
UID:20210506T224516-26972@math.msu.edu
DTSTAMP:20210506T224516Z
SUMMARY:Algebraically-Informed Deep Networks (AIDN): A Deep Learning Approach to Represent Algebraic Structures
DESCRIPTION:Speaker\: Mustafa Hajij, Santa Clara University \r\nOne of the central problems in the interface of deep learning and mathematics is that of building learning systems that can automatically uncover underlying mathematical laws from observed data. In this work, we make one step towards building a bridge between algebraic structures and deep learning, and introduce\textbf {AIDN},\textit {Algebraically-Informed Deep Networks}.\textbf {AIDN} is a deep learning algorithm to represent any finitely-presented algebraic object with a set of deep neural networks. The deep networks obtained via\textbf {AIDN} are\textit {algebraically-informed} in the sense that they satisfy the algebraic relations of the presentation of the algebraic structure that serves as the input to the algorithm. Our proposed network can robustly compute linear and non-linear representations of most finitely-presented algebraic structures such as groups, associative algebras, and Lie algebras. We evaluate our proposed approach and demonstrate its applicability to algebraic and geometric objects that are significant in low-dimensional topology. In particular, we study solutions for the Yang-Baxter equations and their applications on braid groups. Further, we study the representations of the Temperley-Lieb algebra. Finally, we show, using the Reshetikhin-Turaev construction, how our proposed deep learning approach can be utilized to construct new link invariants. We believe the proposed approach would tread a path toward a promising future research in deep learning applied to algebraic and geometric structures.
LOCATION:Online (virtual meeting)
DTSTART:20210413T185000Z
DTEND:20210413T194000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=26972
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BEGIN:VEVENT
UID:20210506T224516-26982@math.msu.edu
DTSTAMP:20210506T224516Z
SUMMARY:The failure of the 4D light bulb theorem with dual spheres of non-zero square
DESCRIPTION:Speaker\: Hannah Schwartz, Princeton\r\nExamples of surfaces embedded in a 4-manifold that are homotopic but not isotopic are neither rare nor surprising. It is then quite amazing that, in settings such as the recent 4D light bulb theorems of both Gabai and Schneiderman-Teichner, the existence of an embedded sphere of square zero intersecting a surface transversally in a single point has the power to "upgrade" a homotopy of that surface into a smooth isotopy. We will discuss the limitations of this phenonemon, using contractible 4-manifolds called corks to produce homotopic spheres in a 4-manifold with a common dual of non-zero square that are not smoothly isotopic.
LOCATION:Online (virtual meeting)
DTSTART:20210420T185000Z
DTEND:20210420T194000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=26982
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BEGIN:VEVENT
UID:20210506T224516-27026@math.msu.edu
DTSTAMP:20210506T224516Z
SUMMARY:Diffeomorphisms of the 4-sphere, Cerf theory and Montesinos twins
DESCRIPTION:Speaker\: David Gay, University of Georgia \r\n I'm interested in the smooth mapping class group of $S^4$, i.e. $\pi_0(\mathrm{Diff}^+(S^4))$. We know that every orientation preserving diffeomorphism of $S^4$ is pseudoisotopic to the identity (Proving this is a fun exercise, starting with the fact that there are no exotic 5-spheres). Cerf theory studies the problem of turning pseudoisotopies into isotopies using parametrized Morse theory. Most of what works in Cerf theory works in dimension 5 and higher, but with a little digging one discovers statements that work in dimension 4 as well. Putting all this stuff together we can show that there is a surjective homomorphism from (a certain limit of) fundamental groups of spaces of embeddings of 2-spheres in connected sums of $S^2\times S^2$ onto this smooth mapping class group of $S^4$. Furthermore, we can identify two natural, and in some sense complementary, subgroups of this fundamental group, one in the kernel of this homomorphism and one whose image we can understand explicitly in terms of Dehn twist-like diffeomorphisms supported near pairs of embedded $S^2$'s in $S^4$ (Montesinos twins).
LOCATION:Online (virtual meeting)
DTSTART:20210427T185000Z
DTEND:20210427T194000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=27026
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