CMSA Colloquium 2016-2017

The 2016-2017 CMSA Colloquium will take place every Wednesday from 4:30-5:30pm in CMSA Building, 20 Garden Street, G10.

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The schedule will be updated as details are confirmed.

Date Name Title/Abstract
01-25-17 Sam Gershman, Harvard Center for Brian Science, Department of Psychology

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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.

02-01-17 Sean Eddy, Harvard Department of Molecular and Cellular Biology

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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, parameter-rich models. I will describe current and future research in homology search algorithms based on probabilistic inference methods, using hidden Markov models(HMMs) and stochastic context-free 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.

02-08-17 Matthew Headrick, Brandeis University

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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 differential-geometry 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.

 

02-15-17 Masahito Yamazaki, IMPU

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 Title: Geometry of 3-manifolds and Complex Chern-Simons Theory

Abstract: The geometry of 3-manifolds has been a fascinating subject in mathematics. In this talk I discuss a “quantization” of 3-manifold geometry, in the language of complex Chern-Simons theory. This Chern-Simons theory in turn is related to the physics of 30dimensional supersymmetric field theories through the so-called 3d/3d correspondence, whose origin can be traced back to a mysterious theory on the M5-branes. 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.

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02-22-17 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.

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03-01-17 Jun Liu, Harvard University

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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 co-expression by integrating the publicly available datasets. These methods assume that the genes in the query gene set are homogeneously correlated and consider no gene-specific correlation tendencies, no background intra-experimental correlations, and no quality variations of different experiments. We propose a two-step algorithm called CLIC (CLustering by Inferred Co-expression) 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 co-expression 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 co-expressed 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 co-expression methods. Application of CLIC to ~1000 annotated human pathways and ~6000 poorly characterized human genes reveals new components of some well-studied 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 knock-out assays. 

Based on the joint work with Yang Li and the Vamsi Mootha lab.

Video

03-08-17 Gabor Lippner, Northeastern University

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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.
03-15-17  Spring Break: No session
03-22-17 Gunther Uhlmann, University of Washington

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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 so-called lens rigidity problem. The linearization of these problems involve the integration of a tensor along geodesics, similar to the X-ray 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.
03-29-17 Leslie Greengard, Courant InstituteLeslie_Greengard Title: Inverse problems in acoustic scattering and cryo-electron microscopy

Abstract: A variety of problems in image reconstruction give rise to large-scale, nonlinear and non-convex 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 cryo-electron microscopy.

NOTE: This talk will begin at 4:00pm

04-05-17
04-12-17
04-19-17
04-26-17
05-03-17
05-10-17
05-17-17
05-24-17
05-31-17
02-01-17

 

Date Name Title
09-09-16

Bong Lian, Brandeis

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Title: Riemann-Hilbert 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 long-standing problems on period integrals in connection with mirror symmetry and Calabi-Yau geometry. We will see how the theory of D-modules have led us to solutions and insights into some of these problems.

09-14-16 Sze-Man Ngai, Georgia Southern Universityngai Title: The multifractal formalism and spectral asymptotics of self-similar measures with overlaps

Abstract: Self-similar 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 Lq-spectrum.  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.

09-21-16 Prof. L. Mahadevan, Harvard SEAS

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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.

09-28-16 Hong Liu, MIT

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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 anti-commuting variables and the theory exhibits an emergent supersymmetry.

10-05-16

Alexander LogunovTel-Aviv University

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Title: Zeroes of harmonic functions and Laplace eigenfunctions

 Abs: Nadirashvili conjectured that for any non-constant 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 real-valued 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.

10-12-16  Conan Nai Chung Leung, CUHK

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Title:  Coisotropic A-branes and their SYZ transform

Abstract: “Kapustin introduced coisotropic A-branes as the natural boundary condition for strings in A-model, 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 Yang-Mills holomorphic bundles to coisotropic A-branes. This explains SYZ mirror symmetry away from the large complex structure limit.”

10-19-16 Vaughan Jones, UC Berkeley

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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
diffeomorphisms of the circle. A result of Ghys-Sergiescu says that a Thompson group can
be conjugated to a group of smooth diffeomorphisms. That’s the good news.
The bad news is that there is an important central extension of Diff(S^1) which requires a certain amount of smoothness for its definition. And Ghys-Sergiescu show that, no matter how the Thompson groups are embedded in Diff(S^1), the restriction of the central extension splits. Is it possible to obtain central extensions of the Thompson groups by any
procedure analogous to the constructions of the central extension of Diff(S^1)?
I will define all the players in this game, explain this question in detail,and present some failed attempts to answer it.

 10-26-16

Henry Cohn, Microsoft

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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.

11-02-16

Christian Borgs, Microsoft

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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 so-called 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 sigma-finite 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.

11-09-16

TIME CHANGE: 4PM

Norden E. HuangNational Central University, (Taiwan)

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Title: On Holo-Hilbert 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 intra-wave and inter-wave 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 intra-wave nonlinearity, the inter-wave nonlinear multiplicative mechanisms that include cross-scale coupling and phase lock modulations are left untreated. To resolve the multiplicative processes, we propose a full informational spectral representation: The Holo-Hilbert Spectral Analysis (HHSA), which would accommodate all the processes: additive and multiplicative, intra-mode and inter-mode, stationary and non-stationary, 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 wave-turbulence interactions and other data will be presented to demonstrate the usefulness of this new spectral representation.

11-16-16 Tristan Collins, Harvard University

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TIME CHANGE: 3:30PM

Title: Restricted volumes and finite time singularities of the Kahler-Ricci flow

Abstract:  I will discuss the relationship between restricted volumes, as defined algebraically or analytically, and the finite time singularities of the Kahler-Ricci flow.  This is joint work with Valentino Tosatti.

11-22-16 TUESDAY

TIME CHANGE: 4-5PM

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.

11-30-16

TIME CHANGE: 4:20PM

Sharad Ramanathan, Harvard MCB & SEAS

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Title: Finding co-ordinate systems to monitor the development of mammalian embryos
 12-07-16

Valentino Tosatti, Northwestern

Title: Metric limits of hyperkahler manifolds

Abstract: I will discuss a proof of a conjecture of Kontsevich-Soibelman and Gross-Wilson about the behavior of unit-diameter Ricci-flat Kahler metrics on hyperkahler manifolds (fibered by holomorphic Lagrangian tori) near a large complex structure limit. The collapsed Gromov-Hausdorff limit is a special Kahler metric on a half-dimensional complex projective space, away from a singular set of Hausdorff codimension at least 2. The resulting picture is also compatible with the Strominger-Yau-Zaslow mirror symmetry. This is joint work with Yuguang Zhang.

 12-14-16

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