An introduction to some basic geometry principles - the sum of angles on a straight line, angles around a point and vertically opposite angles.
Yong-Geun Oh Disjunction energy of compact Lagrangian submanifold from open subset Study of displacement energy of a subset of symplectic manifold is one important tool for study of symplectic topology, but is a highly nontrivial matter to perform actual measurement.
So far such a measurement has been carried out between open subsets and between Lagrangian subamanifolds. In this talk, I will present recent progress of such a measurement for the case of mixture of the two, i.
Eaman Eftekhary Foliations, formal power series and gauge theory We apply gauge theory to study the space of co-oriented smooth codimension foliations on a smooth manifold M.
The quotient of Maurer-Cartan elements by the action of an infinite dimensional non-abelian gauge groupoid forms a moduli space, which contains the space of foliations as a subspace.
The quotient of the moduli space under concordance is identified as the space of homotopy classes of maps to the classifying space associated with the groupoid of formal power series under formal composition.
This gives a treatment Geometry conjectures to study of foliations through Haefliger structures, which may be repeated by replacing real numbers with any commutative algebra of finite rank over reals.
In particular, starting from complex numbers we arrive at a residue formula for the Godbillon-Vey invariant. This is joint work with Mehrzad Ajoodanian. Cheol Hyun Cho Homological mirror functors via Maurer-Cartan formalism Using formal deformation theory of Lagrangian submanifolds in a symplectic manifold, we can define canonical A-infinity functors from Fukaya category tomatrix factorization category of Landau-Ginzburg models.
Different choice of Lagrangians correspond to different charts of the mirror LG model. Building from the basic example of pair of pants, we explain the case of punctured Riemann surfaces via pair of pants decomposition.
Bohan Fang Crepant resolution conjecture and holomorphic anomaly equation from the remodeling conjecture I will survey some applications of the remodeling conjecture, such as holomorphic anomaly equations and the crepant resolution conjectures. This is a joint work with L.
Solorzano Shuai Guo Higher genus mirror symmetry for quintic 3-fold In this talk. I will try to explain the physics and mathematics that related to a quintic Calabi-Yau hypersurface in the 4-dimensional complex projective space.
On the physics side, I will talk about Yamaguchi-Yau's finite generation conjecture, holomorphic anomaly equation and their application in higher genus computation by Huang-Klemm-Quackenbush.
On the mathematics side, I will talk about our recent progress on the structures of higher genus Gromov-Witten invariants. This talk is based on the joint works with F. Ruan and with H-L Chang and J. Bumsig Kim Localized Chern characters for 2-periodic complexes For a two-periodic complex of vector bundles, Polishchuk and Vaintrob have constructed its localized Chern character.
I will explore some basic properties of this localized Chern character. In particular, I will show that the cosection localization defined by Kiem and Li is equivalent to a localized Chern character operation for the associated two-periodic Koszul complex, strengthening a work of Chang, Li, and Li.
This strong equivalence will be applied to the comparison of virtual classes of the moduli of epsilon-stable quasimaps and the moduli of the corresponding LG epsilon-stable quasimaps, in full generality.
The talk is based on joint work with Jeongseok Oh. We study the properties of the critical surfaces of the functionals. We study the compactness of the critical surfaces. Xiaobo Liu Connecting Hodge integrals to Gromov-Witten invariants by Virasoro operators Kontsevich-Witten tau function and Hodge tau functions are important tau functions for KP hierarchy which arise in geometry of moduli space of curves.
Alexandrov conjectured that these two functions can be connected by Virasoro operators. In a joint work with Gehao Wang, we have proved Alexandrov's conjecture. In a joint work with Haijiang Yu, we show that this conjecture can also be generalized to Gromov-Witten invariants and Hodge integrals over moduli spaces of stable maps to smooth projective varieties.
Yi Liu Virtual homological spectral radii for automorphisms of surfaces A surface automorphism is an orientation-preserving self-homeomorphism of a compact orientable surface. A virtual property for a surface automorphism refers to a property which holds up to lifting to some finite covering space.
It has been conjectured by C. McMullen that any surface automorphism of positive mapping-class entropy possesses a virtual homological eigenvalue which lies outside the unit circle of the complex plane.
In this talk, I will review some background and outline a proof of the conjecture. Meysam Nassiri Boundary dynamics for surface homeomorphisms We discuss some aspects of the topological dynamics of surface homeomorphisms concerning the dynamics on the boundary of invariant domains.
In particular, we study the problem of existence of a periodic point on the boundary of an invariant domain for a surface homeomorphism.
The most important consequences are for the generic area-preserving diffeomorphisms, building on previous work of J.Lists of unsolved problems in mathematics. Over the course of time, several lists of unsolved mathematical problems have appeared.
The Canadian publication The Walrus today has a wonderful article about Robert Langlands, focusing on his attitude towards the geometric Langlands program and its talented proponent Edward Frenkel.I watched Frenkel’s talk at the ongoing Minnesota conference via streaming video (hopefully the video will be posted soon), and it was an amazing performance on multiple levels.
Silk Road Geometry Conference (Jun 04 - Jun 08, ) Türk Matematik Derneği bu etkinliğe destek vermektedir. This book offers a survey of recent developments in the analysis of shock reflection-diffraction, a detailed presentation of original mathematical proofs of von Neumann's conjectures for potential flow, and a collection of related results and new techniques in the analysis of partial differential equations (PDEs), as well as a set of fundamental open problems for further development.
Eversion of the Laves graph. The Laves graph is triply-periodic (on a bcc lattice) and pfmlures.com is of interest for a variety of reasons, not least because a left- and right-handed pair of these graphs (an.
As we encounter conjectures in the text, we will be adding them to our set of terms to know. Learn with flashcards, games, and more — for free.