The CMSA Members’ Seminar will occur every Friday at 5pm in CMSA G10. The Schedule will be updated below.
Date  Speaker  Title/abstract 
9/7/2018  Yang Zhou  Title: Counting curves in algebraic geometry
Abstract: The classical mirror symmetry predicts that counting holomorphic curves on a CalabiYau 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 CalabiYau threefold. 
9/14/2018  YuWei Fan  Title: BPS data, RiemannHilbert problem, and curvecounting 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 RiemannHilbert problems associated to BPS data, and sketch the relation between solutions of these problems and curvecounting invariants on CalabiYau threefolds. 
9/21/2018  TsungJu  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. BodohCreed 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, singleunit 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 2unit, uniformprice 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 quasilocal energy for the perturbative theory. 
10/12/2018  Shuliang Bai  Title: RicciCurvature for graphs and Ricciflat 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 LinLuYau so that it is more suitable for graphs. A graph is called Ricciflat if Ricci curvatures varnish on all edges. In this talk, we classify connected Ricciflat 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: RobinsonTrautman Spacetimes
Abstract: Spacetime dynamics are governed by Einstein’s equations, typically thought of as a second order nonlinear hyperboelliptic system of equations. It is of great interest to produce explicit examples of spacetimes satisfying Einstein’s equations, both those which are timeindependent and those which feature dynamics. The RobinsonTrautman 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 longrange behavior of RobinsonTrautman solutions via an analysis of gravitational radiation. 
11/9/2018  Dingxin Zhang  Title: padic methods.
Abstract: For decades, methods from padic analysis have been applied to number theory and geometry. For example, Dwork used spectral theory of padic 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 “indpadicBanach 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 “indBanach algebras” approach into the classical “tubular neighborhood” approach. 
11/30/2018  Enno Kessler  Title: SuperRiemann 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 twodimensional harmonic maps can be understood best on superRiemann surfaces which are a generalization of Riemann surfaces in supergeometry. 
2/1/2019  Xiaojue Zhu  Title: Exploring the ultimate of turbulence
Abstract: In this talk, we will present our newest results on fully developed turbulence. We mainly focus on two systems, RayleighBénard and TaylorCouette flows, which share many similar features. In RayleighBénard turbulence, for the first time in twodimensional numerical simulations we find the transition to the ultimate regime, namely at critical Rayleigh number Ra*= 10^13. We reveal how the emission of thermal plumes enhances the global heat transport, leading to a steeper increase of the Nusselt number than the classical Malkus scaling. Beyond the transition, the temperature profiles are only locally logarithmic, namely within the regions where plumes are emitted, and where the local Nusselt number has an effective scaling Nu∝Ra^0.38, corresponding to the effective scaling in the ultimate regime. In TaylorCouette turbulence, we show how wall roughness greatly enhances the overall transport properties and the corresponding scaling exponents associated with wallbounded turbulence. We reveal that if only one of the walls is rough, the bulk velocity is slaved to the rough side, due to the much stronger coupling to that wall by the detaching flow structures. If both walls are rough, the viscosity dependence is eliminated, giving rise to asymptotic ultimate turbulence—the upper limit of transport—the existence of which was predicted more than 50 years ago. In this limit, the scaling laws can be extrapolated to arbitrarily large Reynolds numbers. 
2/8/2019  Xinqi Gong  Title: Mathematical Intelligence Applications for BioMacromolecular Problems
Abstract: The intersection among mathematics, information and biology has becoming more and more interesting and important. Many studies in this direction have led to developments of theories, methods and applications. But the too fast advancing of nowadays forefront information technology and biology knowledge, have triggered two obviously emerging phenomena, tremendous brandnew peaks accessible by new kinds of efforts, randomly meaningless results by incorrect intersections. Here I will show some of our recent results in developing and distinguishing efficiently intelligent approaches and applications for computational molecular biology and medical problems, such as protein structurefunctioninteraction prediction and pancreas cancer CT image analysis using algorithms like Fast Fourier transform, Monte Carlo, and deep learning, and some new designed physical and geometrical features. 
2/15/2019  Salem Al Mosleh  Title: Rigidity Theory and Projective Geometry.
Abstract: We will discuss the relationship between projective geometry and the rigidity of frameworks and surfaces embedded in R^d. Starting with a simple overview of rigidity theory and projective geometry separately, we then move on to explain the projective invariance of infinitesimal isometric deformations. Lastly, we will describe projective invariants built from infinitesimal isometric deformation fields of a given framework or surface and end by discussing ongoing efforts to extend this to finite deformations. This is joint work with S.T. Yau. 
2/22/2019  Dennis Borisov  Title: Operator product expansion and factorization algebras in differential geometry
Abstract: I will start with a motivation from Physics – operator product expansion in quantum field theory – and then I will describe a joint work with K.Kremnizer (Oxford UK), where we construct factorization algebras in differential geometry out of multiplicative Deligne cohomology classes. 
3/1/2019  Guangwei Si  Title: Structures in an olfactory code
The nervous system uses a population of neurons to encode the environment. The codes are not random but appear lowdimensional structures. They could be the consequence of the invariant properties of the neurons, neuronal circuit, and the environment. Characterizing and understanding the structures in neuronal population codes are the essential questions in systems neuroscience. Here, I will share our recent progress on understanding the neuronal code for the smell. The olfactory system uses a relatively small number of sensory neurons to encode the odor environment with a vast number of odor molecules and a broad range of odor concentration. The question is what kind of structure in the code could support the odor perception, which allows animals to distinguish odors, recognize the same odor across concentrations, and determine concentration changes? To address the question, the experiment needs to record all the olfactory sensory neurons with singlecell resolution and study a broad range of odors and concentration. We achieved that in the small animal called fruit fly larva, with the microfluidic technology. We found that odor identity and intensity are coded by orthogonal features of the population code. Each odor’s representation forms a vector in the neuronal activity space, with the distance of the vector related to the odor concentration, and the direction of the vector related to the odor’s molecular structure. To understand the mechanism underline the structures, we analyzed individual neuron’s activation property. We further found that the activity of each sensory neuron scales with the concentration of any odor via a fixed activation function with variable sensitivity. The sensitivities across odors and sensory neurons follow a power law distribution. Much of receptor sensitivity to the odor is accounted for by a single geometrical property of the odor molecular structure. These microscopic properties contribute to the structures we observed in the population olfactory code. Together, these individual and population level patterns lend structure in the neural population code to support odor perceptions. 
3/8/2019  YuWei Fan  Title: Surface, Categories, and Dynamics
Abstract: We will review basic results on diffeomorphisms of Riemann surfaces. Then we will discuss ways to measure the complexity of dynamical systems formed by diffeomorphisms. Finally, we will briefly mention some analogue categorical results, which are motivated from the parallel between Teichmuller theory and the theory of stability conditions on triangulated categories.

3/15/2019  Jingyu Zhao  TBA 
3/29/2018  Tianqi Wu  Title: Koebe circle domain conjecture and the Weyl problem in hyperbolic 3space
Abstract: In 1908, Paul Koebe conjectured that every open connected set in the plane is conformally diffeomorphic to an open connected set whose boundary components are either round circles or points. We prove that the Koebe circle domain conjecture is equivalent to a hyperbolic Weyl type problem. This is a joint work with Prof. Feng Luo. 
4/5/2019  Artan Sheshmani  TBA 
4/12/2019  Charles Doran  TBA 
4/19/2019  Min Zhang  TBA 
4/26/2019  Jörn Boehnke  TBA 