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upcoming events

  • February 7, 2020
    3:30 pm
    Science Center 507

    GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR

    Speaker: Zack Sylvan - Columbia   Title: TBA
  • February 21, 2020
    3:30 pm
    Science Center 507

    GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR

    Speaker: Mariano Echeverria - Rutgers   Title: TBA
  • March 6, 2020
    3:30 pm
    Science Center 507

    GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR

    Speaker: David Gabai - Princeton   Title: TBA
  • March 27, 2020
    3:30 pm
    Science Center 507

    GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR

    Speaker: Chris Wendl - Humboldt-Berlin   Title: TBA
  • May 1, 2020 - May 3, 2020
    Science Center Hall B

    CONFERENCE

    Title: JDG Conference
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  • 3:30 PMGAUGE-TOPOLOGY-SYMPLECTIC SEMINAR

    GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR

    3:30 PM-4:30 PM
    February 1, 2019

    1 Oxford Street, Cambridge, MA 02138 USA

    1 Oxford Street, Cambridge, MA 02138 USA

    Abstract:

    The aim of this talk is to present an algebraic description of knot Floer homology, discovered in a joint work with Peter Ozsváth.

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  • 3:30 PMGAUGE-TOPOLOGY-SYMPLECTIC SEMINAR
    3:30 PM-4:30 PM
    February 15, 2019

    1 Oxford Street, Cambridge, MA 02138 USA

    1 Oxford Street, Cambridge, MA 02138 USA

    Abstract:

    In joint work with Matic, Van Horn-Morris, and Wand, we seek an answer to this question. We define a refinement of the contact invariant in Heegaard Floer homology that takes values in Z_{\ge 0} \cup {\infty}, called (spectral) order. Among other things, we prove that overtwisted contact structures have zero order, whereas Stein fillable contact structures have infinite order. Furthermore, we show that a strictly increasing sequence of positive integers is realized as the order of a family of contact structures with vanishing Heegaard Floor contact invariant. After defining our contact invariant and discussing some of its key properties, I will talk about its computability and some problems that are content of work in progress.

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  • 3:30 PMGAUGE-TOPOLOGY-SYMPLECTIC SEMINAR

    GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR

    3:30 PM-4:30 PM
    February 22, 2019

    1 Oxford Street, Cambridge, MA 02138 USA

    1 Oxford Street, Cambridge, MA 02138 USA

    Abstract:

    A 3-manifold is said to be SU(2)-abelian if all homomorphisms from its fundamental group to SU(2) factor through the first homology of the manifold. Understanding which manifolds are SU(2)-abelian is a difficult and wide open problem, even in the case of 3-manifolds arising from surgery on a knot in the 3-sphere. Kronheimer and Mrowka showed, for instance, that n-surgery on a nontrivial knot is not SU(2)-abelian for n = 1 or 2, but it isn’t even known whether the same is true for n = 3 or 4 (the same isn’t true for n = 5 as 5-surgery on the right-handed trefoil is a lens space, which has abelian fundamental group). We approach this question by trying to understand which knots have instanton L-space surgeries. A rational homology sphere is said to be an instanton L-space if its framed instanton homology has the smallest rank possible, in analogy with Heegaard Floer homology; familiar examples include lens spaces and branched double covers of alternating knots. Moreover, it is generally the case that SU(2)-abelian manifolds are instanton L-spaces. We conjecture that if surgery on a knot K in the 3-sphere results in an instanton L-space then K is fibered and its Seifert genus equals its smooth slice genus, and we discuss a strategy for proving this.

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announcements

JDG Conference

May 1-3, 2020 Harvard University Science Center, Hall B Confirmed speakers: Toby Colding, MIT Tristan Collins, MIT Hélène Esnault, Freie Universität Berlin Kenji Fukaya, Stony...
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news

Alexander Smith Awarded David Goss Prize

Harvard Mathematics Department graduate student Alexander Smith, who is expected to receive his Ph.D. in 2020, was awarded the 2019 inaugural David Goss Prize in Number Theory at the JNT Biennial conference in Cetraro, Italy. The newly established David Goss Prize (10K USD) will be awarded every two years to...
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