The CMSA Members’ Seminar will occur every Friday at 5pm in CMSA G10. The Schedule will be updated below.
|9/7/2018||Yang Zhou||Title: Counting curves in algebraic geometry
Abstract: The classical mirror symmetry predicts that counting holomorphic curves on a Calabi-Yau manifold corresponds to the variation of Hodge structure of its mirror manifold. In this talk, we will briefly talk about various techniques of counting curves, from the perspective of algebraic geometry. We will go from “through two points there is a line” to counting curves on a quintic Calabi-Yau threefold.
|9/14/2018||Yu-Wei Fan||Title: BPS data, Riemann-Hilbert problem, and curve-counting invariants
Abstract: We start with the observation that linear maps between vector spaces give rise to the simplest example of family of BPS data. Then we introduce the Riemann-Hilbert problems associated to BPS data, and sketch the relation between solutions of these problems and curve-counting invariants on Calabi-Yau threefolds.
|9/21/2018||Tsung-Ju||Title: Hypergeometric systems and relative cohomology
Abstract: The hypergeometric equations, which were studied by Euler, Gauss, Appell, Laurecilia, etc, and generalized by Gel’fand, Kapranov and Zelevinsky, are ubiquitous in mathematics. In this talk, I will briefly talk about a cohomological interpretation of the hypergeometric system. This is a joint work with Dingxin Zhang.
|9/28/2018||Jörn Boehnke||Title: How Efficient are Decentralized Auction Platforms? (joint work with A. L. Bodoh-Creed and B. R. Hickman)
Abstract: We provide a model of a decentralized, dynamic auction market platform (e.g., eBay) in which a continuum of buyers and sellers participate in simultaneous, single-unit auctions each period. Our model accounts for the endogenous entry of agents and the impact of intertemporal optimization on bids. We estimate the structural primitives of our model using Kindle sales on eBay. We find that just over one third of Kindle auctions on eBay result in an inefficient allocation with deadweight loss amounting to 14\% of total possible market surplus. We also find that partial centralization–for example, running half as many 2-unit, uniform-price auctions each day – would eliminate a large fraction of the inefficiency, but yield slightly lower seller revenues. Our results also highlight the importance of understanding platform composition effects – selection of agents into the market – in assessing the implications of market redesign. We also prove that the equilibrium of our model with a continuum of buyers and sellers is an approximate equilibrium of the analogous model with a finite number of agents.
|10/05/2018||Nishanth Gudapati||Title: Remarks on the Notion of Energy for Perturbations of Black Hole Spacetimes
Abstract: The notion of energy for perturbations of black hole spacetimes is important from both geometric and physical perspectives. In this talk, after reviewing some background work on global energy for perturbations of black holes, we shall discuss possible extensions to quasi-local energy for the perturbative theory.
|10/12/2018||Shuliang Bai||Title: Ricci-Curvature for graphs and Ricci-flat graphs
Abstract: The Ricci curvature plays a very important role on geometric analysis on Riemannian manifolds. In 2009, Ollivier gave a notion of coarse Ricci curvature of Markov chains valid on arbitrary metric spaces. His definition of coarse Ricci curvature was adapted by Lin-Lu-Yau so that it is more suitable for graphs. A graph is called Ricci-flat if Ricci curvatures varnish on all edges. In this talk, we classify connected Ricci-flat graphs with maximal degree at most 4.
|10/19/2018||Kyle Luh||Title: Embedding Large Structures in Random Graphs
Abstract: In this talk, we will survey several general techniques of random graphs in the context of some recent results on embedding large graphs. Although the results are state of the art, the emphasis will be on robust probability tools and intuition. Several open problems will be mentioned at the end.
|10/26/2018||Aghil Alaee||Title: Recent developments in geometric inequalities for black holes
Abstract: General relativity is a geometric theory of gravitation and the most fascinating prediction of general relativity is black holes. In fact, the new gravitational wave (radiation) detection of black hole mergers provides compelling evidence for this prediction. In this talk, I will review recent developments in geometric inequalities for black holes.
|11/2/2018||Jordan Keller||Title: Robinson-Trautman Spacetimes
Abstract: Spacetime dynamics are governed by Einstein’s equations, typically thought of as a second order non-linear hyperbo-elliptic system of equations. It is of great interest to produce explicit examples of spacetimes satisfying Einstein’s equations, both those which are time-independent and those which feature dynamics. The Robinson-Trautman spacetimes form an interesting example of the latter. These spacetimes are constructed by means of an ansatz on the spacetime metric, under which the Einstein equations reduce to a Calabi equation for an unknown scalar quantity related to gravitational radiation. We discuss work of Chrusciel on the existence and long-range behavior of Robinson-Trautman solutions via an analysis of gravitational radiation.
|11/9/2018||Dingxin Zhang||Title: p-adic methods.
Abstract: For decades, methods from p-adic analysis have been applied to number theory and geometry. For example, Dwork used spectral theory of p-adic Banach spaces to study zeta functions of algebraic varieties. Inspired by Dwork’s methods, Monsky–Washnitzer defined a “formal cohomology” for affine varieties using a certain “ind-p-adic-Banach algebras”. I shall recall the work of Dwork–Monsky–Washnitzer. Time permits, I shall explain my method, which defines a cohomology for an arbitrary variety, by merging Monsky–Washnitzer’s “ind-Banach algebras” approach into the classical “tubular neighborhood” approach.
|11/30/2018||Enno Kessler||Title: Super-Riemann surfaces and the superconformal action
Abstract: With the help of a toy model, I will explain how supergeometry allows to give a geometric interpretation to supersymmetry. Analogously, a supersymmetric extension of two-dimensional harmonic maps can be understood best on super-Riemann surfaces which are a generalization of Riemann surfaces in supergeometry.