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PRODID:Mathematics Seminar Calendar
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UID:20191210T162620-18596@math.msu.edu
DTSTAMP:20191210T162620Z
SUMMARY:Applications of Constructible Sheaves to Symplectic Topology
DESCRIPTION:Speaker\: Eric Zaslow, Northwestern University\r\nMy goal is to explain a few applications of constructible sheaves to symplectic topology through examples that we can calculate together on the board.\r\n\r\nIn particular, I would like to explain how sheaves relate to: 1) Legendrian knot invariants, 2) cluster varieties, 3) nonfillability results for Legendrian surfaces.
LOCATION:C304 Wells Hall
DTSTART:20190905T201000Z
DTEND:20190905T210000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=18596
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UID:20191210T162620-18587@math.msu.edu
DTSTAMP:20191210T162620Z
SUMMARY:Introduction to the Energy Identity for Yang-Mills
DESCRIPTION:Speaker\: Aaron Naber, Northwestern University\r\nIn this talk we give an introduction to the analysis of the Yang-Mills equation in higher dimensions. In particular, when studying sequences of solutions we will study the manner in which blow up can occur, and how this blow up may be understood through the classical notions of the defect measure and bubbles. The energy identity is an explicit conjectural relationship relating the energy density of the defect measure at a point to the bubbles which occur at that point. This talk is introductory and we will spend most of our time understanding the words of this abstract. If time permits we will briefly discuss the ideas needed to prove this conjecture and the related $W^{2,1}$-conjecture. The work is joint with Daniele Valtorta.
LOCATION:C304 Wells Hall
DTSTART:20190919T201000Z
DTEND:20190919T210000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=18587
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BEGIN:VEVENT
UID:20191210T162620-18597@math.msu.edu
DTSTAMP:20191210T162620Z
SUMMARY:Modular symbols and the arithmetic of cyclotomic fields
DESCRIPTION:Speaker\: Romyar Sharifi, UCLA\r\nThe arithmetic of cyclotomic fields, and the structure of their class groups, has been studied since the time of Kummer in connection with Fermat’s Last Theorem. The work of Ribet in 1976 uncovered a subtle influence of the geometry of modular curves on this structure. I’ll discuss how this connection goes even deeper and define a surprisingly explicit map from the homology group of a modular curve to a K-group related to the class group of a cyclotomic field. I’ll then indicate how this is turning out to be just one instance of a more general phenomenon, touching briefly on joint work with Takako Fukaya and Kazuya Kato and separate joint work with Akshay Venkatesh.
LOCATION:C304 Wells Hall
DTSTART:20191010T201000Z
DTEND:20191010T210000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=18597
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BEGIN:VEVENT
UID:20191210T162620-18588@math.msu.edu
DTSTAMP:20191210T162620Z
SUMMARY:Higher convexity for complements of tropical objects
DESCRIPTION:Speaker\: Frank Sottile, Texas A&M University\r\nGromov generalized the notion of convexity for open subsets \r\nof $\mathbf{R}^n$ with hypersurface boundary, defining $k$-convexity, or\r\nhigher convexity and Henriques applied the same notion to \r\ncomplements of amoebas. He conjectured that the complement \r\nof an amoeba of a variety of codimension $k+1$ is $k$-convex. \r\nI will discuss work with Mounir Nisse in which we study the \r\nhigher convexity of complements of coamoebas and of tropical \r\nvarieties, proving Henriques' conjecture for coamoebas and \r\nestablishing a form of Henriques' conjecture for tropical varieties in some cases.
LOCATION:C304 Wells Hall
DTSTART:20191017T201000Z
DTEND:20191017T210000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=18588
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BEGIN:VEVENT
UID:20191210T162620-18600@math.msu.edu
DTSTAMP:20191210T162620Z
SUMMARY:Geodesic X-ray Transforms and Boundary Rigidity
DESCRIPTION:Speaker\: Robin Graham, University of Washington\r\nThis talk will introduce the problem of injectivity and\r\ninversion of geodesic X-ray transforms in various geometric settings. The\r\nassociated nonlinear boundary rigidity problem, which consists of\r\ndetermining a Riemannian metric on a compact manifold-with-boundary from\r\nthe lengths of its geodesics joining boundary points, will also be\r\ndiscussed. Classical results and recent progess will be described,\r\nincluding current research on the analogous questions in the setting of \r\nasymptotically hyperbolic manifolds.
LOCATION:C304 Wells Hall
DTSTART:20191024T201000Z
DTEND:20191024T210000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=18600
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BEGIN:VEVENT
UID:20191210T162620-18589@math.msu.edu
DTSTAMP:20191210T162620Z
SUMMARY:Dynamics in models of coagulation and fragmentation
DESCRIPTION:Speaker\: Robert Pego, Carnegie Mellon University\r\nCoaglation-fragmentation equations are simple, nonlocal models for evolution of the size distribution of clusters, appearing widely in science and technology. But few general analytical results characterize their dynamics. Solutions can exhibit self-similar growth, singular mass transport, and weak or slow approach to equilibrium. I will review some recent results in this vein, discussing: the cutoff phenomenon (as in card shuffling) for Becker-Doering equilibration; stationary and spreading profiles in a data-driven model of fish school size; and temporal oscillations recently found in models lacking detailed balance. A special role is played by Bernstein transforms and complex function theory for Pick or Herglotz functions.
LOCATION:C304 Wells Hall
DTSTART:20191031T201000Z
DTEND:20191031T210000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=18589
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BEGIN:VEVENT
UID:20191210T162620-21723@math.msu.edu
DTSTAMP:20191210T162620Z
SUMMARY:Smooth 4-manifolds and the geometry of 3-manifolds
DESCRIPTION:Speaker\: Matthew Stoffregen, Massachusetts Institute of Technology\r\nOne of the interests of low-dimensional topologists is understanding which smooth 4-manifolds can bound a given 3-manifold, or, as a special case, understanding the set of 3-manifolds up to so-called homology cobordism (to be defined in the talk). This question turns out to have applications to the study of triangulations of high-dimensional manifolds, and is a natural proving ground for Floer-theoretic techniques of studying 3-manifolds. In this talk, we will give some structure theorems about the homology cobordism group, and show that there are three-manifolds that are very far from having any of the seven non-hyperbolic Thurston geometries. This talk includes joint work with I. Dai, K. Hendricks, J. Hom, L. Truong, and I. Zemke.
LOCATION:C304 Wells Hall
DTSTART:20191210T211000Z
DTEND:20191210T220000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=21723
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BEGIN:VEVENT
UID:20191210T162620-21721@math.msu.edu
DTSTAMP:20191210T162620Z
SUMMARY:In and around stable homotopy groups of spheres
DESCRIPTION:Speaker\: Zhouli Xu, Massachusetts Institute of Technology\r\nThe computation of stable homotopy groups of spheres is one of the most fundamental problems in topology. Despite its simple definition, it is notoriously hard to compute. It has connections to many areas of mathematics. In this talk, I will discuss a recent breakthrough on this problem, which depends on motivic homotopy theory in a critical way. I will also talk about applications to smooth structures on spheres, and towards the open problem of Kervaire invariant one in dimension 126. This talk is based on several joint work with Bogdan Gheorghe, Daniel Isaksen, and Guozhen Wang.
LOCATION:C304 Wells Hall
DTSTART:20191212T211000Z
DTEND:20191212T220000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=21721
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