Place: N820
Title: Universal simplicial complexes and the mod p Buchstaber invariant
Abstract: Universal simplicial complexes are important objects in toric topology, closely related to the classification of quasitoric manifolds and to small covers and Buchstaber’s invariant computation. In this talk, we present some recent results about the Tor algebra of the Stanley-Reisner ring of the universal simplicial complexes over the field of characteristic p, where p is a prime number and some new applications in toric topology.
Place: N820
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Place: MCM 110
Title: A infinity multi-modules from quilts and applications
Abstract: Invariants defined by counting pseudo-holomorphic maps from Riemann surfaces with boundary are uniquitous in symplectic geometry, low dimensional topology and mathematical physics. Some examples include various types of Floer homologies, Fukaya categories and Gromov-Witten theory. In this talk I will give a short survey about a generalization of this developed by Wehrheim-Woodward called pseudo-holomorphic quilts. Then I will present some applications of quilted invariants including a proof of a conjecture of Seidel regarding the Floer homology of composed Dehn twists.
Place: N820
Title: Compactification of homology cells and the complex projective space
Abstract: 很多例子表明正曲率（各种意义下）流形和具圆周作用的流形在一些情形具有相同或类似的拓扑推论。在这个报告中我们将回顾若干这方面的经典结果，并给出一个新的例子：在很多维数同调胞腔的凯莱紧化都是标准形式，或者具有圆周作用的辛紧化在同调意义下都是标准形式。
Place: N820
Title: A Bilinear Form for Spinc Manifolds
Abstract: Let M be a closed oriented spinc manifold of dimension (8n+2) with fundamental class [M], and let ρ2 : H4n(M; Z) → H4n(M; Z/2) denote the mod 2 reduction homomorphism. For any torsion class t ∈ H4n(M; Z), we establish the identity ⟨ρ2(t) · Sq2 ρ2(t), [M]⟩ = ⟨ρ2(t) · Sq2 v4n(M), [M]⟩, where Sq2 is the Steenrod square, v4n(M) is the 4n-th Wu class of M, x · y denotes the cup product of x and y, and ⟨· , ·⟩ denotes the Kronecker product. This result generalizes the work of Landweber and Stong from spin to spinc manifolds. As an application, let β Z/2: H4n+2(M; Z/2) → H4n+3(M; Z) be the Bockstein homomorphism associated to the short exact sequence of coefficients Z×2−−→ Z → Z/2. We deduce that βZ/2(Sq2v4n(M)) = 0, and consequently, Sq3v4n(M) = 0, for any closed oriented spinc manifold M with dim M ≤ 8n+1.
Place: Zoom: 6817169181 Password: 211748
Title: Classifying modules of equivariant Eilenberg–MacLane spectra
Abstract: Classically, since Z/p is a field, any module over the Eilenberg—MacLane spectrum HZ/p splits as a wedge of suspensions of HZ/p itself. Equivariantly, cohomology and the module theory of G-equivariant Eilenberg–MacLane spectra are much more complicated.For any p-group and the constant Mackey functor Z/p, there are infinitely many indecomposable HZ/p-modules. Previous work together with Dugger and Hazel classified all indecomposable HZ/2-modules for the group G=C2. The isomorphism classes of indecomposables fit into just three families. By contrast, joint work with Jacob Grevstad shows for G=Cp with p an odd prime, the classification of indecomposable HZ/p-modules is wild.
Place: N820
Title: Quantized nonabelianization
Abstract: Gaiotto-Moore-Neitzke introduced the notion of spectral network in the study of supersymmetric gauge theory. It provides a way to define a nonabelianization map (UV-IR map) from gl(1) local systems on a spectral curve to gl(N) local systems on the base surface. Neitzke-Yan considered a quantization of this map between skein algebras. In this work, we consider a different quantization in the sense of braid skein algebras using both Floer and Morse approach. This is joint work with Ko Honda and Yin Tian.
Place: N820
Title: Turaev-Viro invariant from the modular double of UqSL(2;R)
Abstract: In this talk we introduce recent collaboration work with Shuang Ming, Xin Sun, Baojun Wu, and Tian Yang. We define a family of Turaev-Viro type invariants of hyperbolic 3-manifolds with totally geodesic boundary from the 6j-symbols of the modular double of Uqsl(2;R), and prove that these invariants decay exponentially with the rate the hyperbolic volume of the manifolds.
Place: N933
Title: Homotopy theoretic properties of gyrations
Abstract: If M is a manifold, a gyration is a surgery on M\times S^k for some positive integer k. These appear prominently in work of Gitler-Lopez de Medrano on intersections of quadrics and recent work of Duan on the classification of certain types of manifolds. We will discuss homotopy theoretic properties of gyrations, such as loop space decompositions and classifications of homotopy types depending on how the surgery may be twisted by a nontrivial diffeomorphism. This is based on joint projects with Ruizhi Huang and Sebastian Chenery.