The 20162017 CMSA Colloquium will take place every Wednesday from 4:305:30pm in CMSA Building, 20 Garden Street, G10.
The schedule will be updated as details are confirmed.
Date  Name  Title/Abstract 
012517  Sam Gershman, Harvard Center for Brian Science, Department of Psychology 
Title: Spectral graph theory of cognitive maps Abstract: The concept of a “cognitive map” has played an important role in neuroscience and psychology. A cognitive map is a representation of the environment that supports navigation and decision making. A longstanding question concerns the precise computational nature of this map. I offer a new mathematical foundation for the cognitive map, based on ideas at the intersection of spectral graph theory and reinforcement learning. Empirical data from neural recordings and behavioral experiments supports this theory. 
020117  Sean Eddy, Harvard Department of Molecular and Cellular Biology  Title: Biological sequence homology searches: the future of deciphering the past
Abstract: Computational recognition of distant common ancestry of biological sequences is a key to studying ancient events in molecular evolution.The better our sequence analysis methods are, the deeper in evolutionary time we can see. A major aim in the field is to improve the resolution of homology recognition methods by building increasingly realistic, complex, parameterrich models. I will describe current and future research in homology search algorithms based on probabilistic inference methods, using hidden Markov models(HMMs) and stochastic contextfree grammars (SCFGs). We make these methods available in the HMMER and Infernal software from my laboratory, in collaboration with database teams at the EuropeanBioinformatics Institute in the UK. 
020817  Matthew Headrick, Brandeis University  Title: Quantum entanglement, classical gravity, and convex programming: New connections
Abstract: In recent years, developments from the study of black holes and quantum gravity have revealed a surprising connection between quantum entanglement and classical general relativity. The theory of convex programming, applied in the differentialgeometry setting, turns out to be useful for understanding what’s behind this correspondence. We will describe these developments, giving the necessary background in quantum information theory and convex programming along the way.

021517  Masahito Yamazaki, IMPU  Title: Geometry of 3manifolds and Complex ChernSimons Theory
Abstract: The geometry of 3manifolds has been a fascinating subject in mathematics. In this talk I discuss a “quantization” of 3manifold geometry, in the language of complex ChernSimons theory. This ChernSimons theory in turn is related to the physics of 30dimensional supersymmetric field theories through the socalled 3d/3d correspondence, whose origin can be traced back to a mysterious theory on the M5branes. Along the way I will also comment on the connection with a number of related topics, such as knot theory, hyperbolic geometry, quantum dilogarithm and cluster algebras. 
022217  Steven Rayan, University of Saskatchewan 
Title: Higgs bundles and the Hitchin system Abstract: I will give an informal introduction to the Hitchin system, an object lying at the crossroads of geometry and physics. As a moduli space, the Hitchin system parametrizes semistable Higgs bundles on a Riemann surface up to equivalence. From this point of view, the Hitchin map and spectral curves emerge. We’ll use these to form an impression of what the moduli space “looks like”. I will also outline the appearances of the Hitchin system in dynamics, hyperkaehler geometry, and mirror symmetry. 
030117  Jun Liu, Harvard University  Title: Expansion of biological pathways by integrative Genomics
Abstract: The number of publicly available gene expression datasets has been growing dramatically. Various methods had been proposed to predict gene coexpression by integrating the publicly available datasets. These methods assume that the genes in the query gene set are homogeneously correlated and consider no genespecific correlation tendencies, no background intraexperimental correlations, and no quality variations of different experiments. We propose a twostep algorithm called CLIC (CLustering by Inferred Coexpression) based on a coherent Bayesian model to overcome these limitations. CLIC first employs a Bayesian partition model with feature selection to partition the gene set into disjoint coexpression modules (CEMs), simultaneously assigning posterior probability of selection to each dataset. In the second step, CLIC expands each CEM by scanning the whole reference genome for candidate genes that were not in the input gene set but coexpressed with the genes in this CEM. CLIC is capable of integrating over thousands of gene expression datasets to achieve much higher coexpression prediction accuracy compared to traditional coexpression methods. Application of CLIC to ~1000 annotated human pathways and ~6000 poorly characterized human genes reveals new components of some wellstudied pathways and provides strong functional predictions for some poorly characterized genes. We validated the predicted association between protein C7orf55 and ATP synthase assembly using CRISPR knockout assays. Based on the joint work with Yang Li and the Vamsi Mootha lab. 
030817  Gabor Lippner, Northeastern University  Title: Evolution of cooperation in structured populations
Abstract: Understanding how the underlying structure affects the evolution of a population is a basic, but difficult, problem in the evolutionary dynamics. Evolutionary game theory, in particular, models the interactions between individuals as games, where different traits correspond to different strategies. It is one of the basic approaches to explain the emergence of cooperative behavior in Darwinian evolution. In this talk I will present new results about the model where the population is represented by an interaction network. We study the likelihood of a random mutation spreading through the entire population. The main question is to understand how the network influences this likelihood. After introducing the model, I will explain how the problem is connected to the study of meeting times of random walks on graphs, and based on this connection, outline a general method to analyze the model on general networks.

031517  Spring Break: No session  
032217  Gunther Uhlmann, University of Washington 
Abstract: We will consider the inverse problem of determining the sound speed or index of refraction of a medium by measuring the travel times of
waves going through the medium. This problem arises in global seismology in an attempt to determine the inner structure of the Earth by measuring travel times of earthquakes. It has also applications in optics and medical imaging among others.
The problem can be recast as a geometric problem: Can one determine a Riemannian metric of a Riemannian manifold with boundary by measuring the distance function between boundary points? This is the boundary rigidity problem. We will also consider the problem of determining the metric from the scattering relation, the socalled lens rigidity problem. The linearization of these problems involve the integration of a tensor along geodesics, similar to the Xray transform.
We will also describe some recent results, joint with Plamen Stefanov and Andras Vasy, on the partial data case, where you are making measurements on a subset of the boundary. No previous knowledge of Riemannian geometry will be assumed.

032917  Leslie Greengard, Courant Institute  Title: Inverse problems in acoustic scattering and cryoelectron microscopy
Abstract: A variety of problems in image reconstruction give rise to largescale, nonlinear and nonconvex optimization problems. We will show how recursive linearization combined with suitable fast solvers are bringing such problems within practical reach, with an emphasis on acoustic scattering and protein structure determination via cryoelectron microscopy. NOTE: This talk will begin at 4:00pm 
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020117 
Date  Name  Title 
090916 
Bong Lian, Brandeis 
Title: RiemannHilbert Problem and Period Integrals Abstract: Period integrals of an algebraic manifolds are certain special functions that describe, among other things, deformations of the variety. They were originally studied by Euler, Gauss and Riemann, who were interested in analytic continuation of these objects. In this lecture, we will discuss a number of longstanding problems on period integrals in connection with mirror symmetry and CalabiYau geometry. We will see how the theory of Dmodules have led us to solutions and insights into some of these problems. 
091416  SzeMan Ngai, Georgia Southern University  Title: The multifractal formalism and spectral asymptotics of selfsimilar measures with overlaps
Abstract: Selfsimilar measures form a fundamental class of fractal measures, and is much less understood if they have overlaps. The multifractal formalism, if valid, allows us to compute the Hausdorff dimension of the multifractal components of the measure through its Lqspectrum. The asymptotic behavior of the eigenvalue counting function for the associated Laplacians is closely related to the multifractal structure of the measure. Throughout this talk, the infinite Bernoulli convolution associated with the golden ratio will be used as a basic example to describe some of the results. 
092116  Prof. L. Mahadevan, Harvard SEAS  Title: “Morphogenesis: Biology, Physics and Mathematics”
Abstract: A century since the publication of Darcy Thompson’s classic “On growth and form,” his vision has finally begun to permeate into the fabric of modern biology. Within this backdrop, I will discuss some simple questions inspired by the onset of form in biology wherein mathematical models and computations, in close connection with experiments allow us to begin unraveling the physical basis for morphogenesis in the context of examples such as tendrils, leaves, guts, and brains. I will also try and indicate how these problems enrich their roots, creating new questions in mathematics, physics, and biology. 
092816  Hong Liu, MIT  Title: A new theory of fluctuating hydrodynamics
Despite its long and glorious history, hydrodynamics has so far been formulated mostly at the level of equations of motion, which is inadequate for capturing fluctuations. In a fluid, however, fluctuations occur spontaneously and continuously, at both the quantum and statistical levels, the understanding of which is important for a wide variety of physical problems. Another unsatisfactory aspect of the current formulation of hydrodynamics is that the equations of motion are constrained by various phenomenological conditions on the solutions, which need to be imposed by hand. One of such constraints is the local second law of thermodynamics, which plays a crucial role, yet whose physical origin has been obscure. We present a new theory of fluctuating hydrodynamics which incorporates fluctuations systematically and reproduces all the phenomenological constraints from an underlying Z_2 symmetry. In particular, the local second law of thermodynamics is derived. The theory also predicts new constraints which can be considered as nonlinear generalizations of Onsager relations. When truncated to Gaussian noises, the theory recovers various nonlinear stochastic equations. Curiously, to describe thermal fluctuations of a classical fluid consistently one needs to introduce anticommuting variables and the theory exhibits an emergent supersymmetry. 
100516 
Alexander Logunov, TelAviv University 
Title: Zeroes of harmonic functions and Laplace eigenfunctions
Abs: Nadirashvili conjectured that for any nonconstant harmonic function in R^3 its zero set has infinite area. This question was motivated by the Yau conjecture on zero sets of Laplace eigenfunctions. Both conjectures can be treated as an attempt to control the zero set of a solution of elliptic PDE in terms of growth of the solution. For holomorhpic functions such kind of control is possible only from one side: there is a plenty of holomorphic functions that have no zeros. While for a realvalued harmonic function on a plane the length of the zero set can be estimated (locally) from above and below by the frequency, which is a characteristic of growth of the harmonic function. We will discuss the notion of frequency, its properties and applications to zero sets in the higher dimensional case, where the understanding is far from being complete. 
101216  Conan Nai Chung Leung, CUHK 
Title: Coisotropic Abranes and their SYZ transform Abstract: “Kapustin introduced coisotropic Abranes as the natural boundary condition for strings in Amodel, generalizing Lagrangian branes and argued that they are indeed needed to for homological mirror symmetry. I will explain in the semiflat case that the Nahm transformation along SYZ fibration will transform fiberwise YangMills holomorphic bundles to coisotropic Abranes. This explains SYZ mirror symmetry away from the large complex structure limit.” 
101916  Vaughan Jones, UC Berkeley  Title: Are the Thompson groups any good as a model for Diff(S^1)?
Abstract. The Thompson groups are by definition groups of piecewise linear 
102616 
Henry Cohn, Microsoft 
Sums of squares, correlation functions, and exceptional geometric structures Some exceptional structures such as the icosahedron or E_8 root system have remarkable optimality properties in settings such as packing, energy minimization, or coding. How can we understand and prove their optimality? In this talk, I’ll interweave this story with two other developments in recent mathematics (without assuming familiarity with either): how semidefinite optimization and sums of squares have expanded the scope of optimization, and how representation theory has shed light on higher correlation functions for particle systems. 
110216 
Christian Borgs, Microsoft 
Title: Graphon processes and limits of sparse graph sequences Abstract: The theory of graph limits for dense graphs is by now well established, with graphons describing both the limit of a sequence of deterministic graphs, and a model for socalled exchangeable random graphs. Here a graphon is a function defined over a “feature space’’ equipped with some probability measure, the measure describing the distribution of features for the nodes, and the graphon describing the probability that two nodes with given features form a connection. While there are rich models of sparse random graphs based on graphons, they require an additional parameter, the edge density, whose dependence on the size of the graph has either to be postulated as an additional function, or considered as an empirical observed quantity not described by the model. In this talk I describe a new model, where the underlying probability space is replaced by a sigmafinite measure space, leading to both a new random model for exchangeable graphs, and a new notion of graph limits. The new model naturally produces a graph valued stochastic process indexed by a continuous time parameter, a “graphon process”, and describes graphs which typically have degree distributions with long tails, as observed in large networks in real life. 
110916
TIME CHANGE: 4PM 
Norden E. Huang, National Central University, (Taiwan) 
Title: On HoloHilbert Spectral Analysis
Traditionally, spectral analysis is defined as transform the time domain data to frequency domain. It is achieved through integral transforms based on additive expansions of a priori determined basis, under linear and stationary assumptions. For nonlinear processes, the data can have both amplitude and frequency modulations generated by intrawave and interwave interactions involving both additive and nonlinear multiplicative processes. Under such conditions, the additive expansion could not fully represent the physical processes resulting from multiplicative interactions. Unfortunately, all existing spectral analysis methods are based on additive expansions, based either on a priori or adaptive bases. While the adaptive Hilbert spectral analysis could accommodate the intrawave nonlinearity, the interwave nonlinear multiplicative mechanisms that include crossscale coupling and phase lock modulations are left untreated. To resolve the multiplicative processes, we propose a full informational spectral representation: The HoloHilbert Spectral Analysis (HHSA), which would accommodate all the processes: additive and multiplicative, intramode and intermode, stationary and nonstationary, linear and nonlinear interactions, through additional dimensions in the spectrum to account for both the variations in frequency and amplitude modulations (FM and AM) simultaneously. Applications to waveturbulence interactions and other data will be presented to demonstrate the usefulness of this new spectral representation. 
111616  Tristan Collins, Harvard University
TIME CHANGE: 3:30PM 
Title: Restricted volumes and finite time singularities of the KahlerRicci flow Abstract: I will discuss the relationship between restricted volumes, as defined algebraically or analytically, and the finite time singularities of the KahlerRicci flow. This is joint work with Valentino Tosatti. 
112216 TUESDAY
TIME CHANGE: 45PM 
Xiangfeng Gu, Stonybrook 
Title: Differential Geometric Methods for Engineering Applications Abstract: With the development of virtual reality and augmented reality, many challenging problems raised in engineering fields. Most of them are with geometric nature, and can be explored by modern geometric means. In this talk, we introduce our approaches to solve several such kind of problems: including geometric compression, shape classification, surface registration, cancer detection, facial expression tracking and so on, based on surface Ricci flow and optimal mass transportation. 
113016
TIME CHANGE: 4:20PM 
Sharad Ramanathan, Harvard MCB & SEAS 
Title: Finding coordinate systems to monitor the development of mammalian embryos 
120716 
Valentino Tosatti, Northwestern 
Title: Metric limits of hyperkahler manifolds Abstract: I will discuss a proof of a conjecture of KontsevichSoibelman and GrossWilson about the behavior of unitdiameter Ricciflat Kahler metrics on hyperkahler manifolds (fibered by holomorphic Lagrangian tori) near a large complex structure limit. The collapsed GromovHausdorff limit is a special Kahler metric on a halfdimensional complex projective space, away from a singular set of Hausdorff codimension at least 2. The resulting picture is also compatible with the StromingerYauZaslow mirror symmetry. This is joint work with Yuguang Zhang. 
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