Past Seminars

Spring 2020

Polynomial time guarantees for the Burer-Monteiro method

• Diego Cifuentes, Mathematics, MIT
• Monday, February 24, 3-4 p.m., Location: Olney 430

The Burer-Monteiro method is one of the most widely used techniques for solving large-scale semidefinite programs (SDP). The basic idea is to solve a nonconvex program in Y, where Y is an n×p matrix such that X = YYT. We show that this method can solve SDPs in polynomial time in an smoothed analysis setting. More precisely, we consider an SDP whose domain satisfies some compactness and smoothness assumptions, and slightly perturb the cost matrix and the constraints. We show that if $p\geq\sqrt{(2+2\eta)m}}$, where $m$ is the number of constraints and $\eta>0$ is any fixed constant, then the Burer-Monteiro method can solve SDPs to any desired accuracy in polynomial time, in the setting of smooth analysis. Our bound on $p$ approaches the celebrated Barvinok-Pataki bound in the limit as $\eta$ goes to zero, beneath which it is known that the nonconvex program can be suboptimal.

Spectral graph theory in quantum communication

• Gabor Lippner, Northeastern University
• Monday, March 2, 4-5 p.m., Location: Olney 430

Physically transmitting quantum information is an important building block of any quantum computer. A possible method to accomplish this is via a "quantum wire", that is, a network of interconnected (coupled) quantum particles. Finding network structures that propagate quantum information efficiently turns out to be very challenging. In this talk I will explain the relevance of spectral graph theory to this problem, and outline some recent results as well as some open problems. Joint work with Mark Kempton, and in part with Shing-Tung Yau, Or Eisenberg, and Whitney Drazen.

The following seminars have been canceled:

• Mark Lyon, Department of Mathematics and Statistics, University of New Hampshire
• Monday, March 23, 4-5 p.m., Location: Olney 430
• Lam Pham, Brandeis University
• Monday, March 30, 4-5 p.m., Location: Olney 430
• Rubén Campoy, Mathematics, UMass Lowell
• Monday, April 6, 4-5 p.m., Location: Olney 430
• Belleh Fontem, Manning School of Business, UMass Lowell
• Monday, April 13, 4-5 p.m., Location: Olney 430
• Victor Churchill, Dartmouth College
• Monday, April 27, 4-5 p.m., Location: Olney 430

Fall 2019

Stochastic Superparameterization Through Local Data Generation

• Yoonsang Lee, Department of Mathematics, Dartmouth College
• Wednesday, September 11, 3:30 p.m., Location: Olney 430

Stochastic superparameterization is a class of multiscale methods that approximate large-scale dynamics of complex dynamical systems such as turbulent flows. Unresolved sub-grid scales are modeled by a cheap but robust stochastic system that mimics the true dynamics of the sub-grid scales, which is crucial to model non-trivial and non-equilibrium dynamics. In this talk, we propose a numerical procedure to estimate the modeling parameters, which avoids the use of climatological data.

Hardness Results for Sampling Connected Graph Partitions with Applications to Redistricting

• Daryl Deford, MIT
• Wednesday, September 18, 4 p.m., Location: Olney 430

The problem of constructing ”fair'' political districts and the related problem of detecting intentional gerrymandering has received a significant amount of attention in recent years. A key problem in this area is determining the expected properties of a representative districting plan as a function of the input geographic and demographic data. A natural approach is to generate a comparison ensemble of plans using MCMC and I will present successful applications of this approach in both court cases and legislative reform efforts. However, our recent work has demonstrated that the commonly used boundary-node flip proposal can mix poorly on real-world examples. In this talk, I will present some new proposal distributions for this setting and discuss some related open problems concerning mixing times and spanning trees. I will also discuss some generic hardness results for sampling problems on partitions of planar graphs.

Multiscale Convergence Properties for Spectral Approximations of a Model Kinetic Equation

• Zheng Chen, Department of Mathematics, UMass Dartmouth
• Thursday, October 3, 2 p.m., Location: Olney 430

We prove some convergence properties for a semi-discrete, moment-based approximation of a model kinetic equation in one dimension. This approximation is equivalent to a standard spectral method in the velocity variable of the kinetic distribution and, as such, is accompanied by standard algebraic estimates of the form $N^{-q}$, where $N$ is the number of modes and $q$ depends on the regularity of the solution. However, in the multiscale setting, we show that the error estimate can be expressed in terms of the scaling parameter $\epsilon$, which measures the ratio of the mean-free-path to the domain in the system. In particular we show that the error in the spectral approximation is $\mathcal{O}(\epsilon^{N+1})$. More surprisingly, the coefficients of the expansion satisfy some super convergence properties. In particular, the error of the $\ell^{th}$ coefficient of the expansion scales like $\mathcal{O}(\epsilon^{2N})$ when $\ell =0$ and $\mathcal{O}(\epsilon^{2N+2-\ell})$ for all $1\leq \ell \leq N$. This result is significant, because the low-order coefficients correspond to physically relevant quantities of the underlying system. Numerical tests will also be presented to support the theoretical results.

Jump Process Approximation of Particle-Based Stochastic Reaction-Diffusion Models

• Samuel Isaacson, Department of Mathematics and Statistics, Boston University
• Wednesday, November 6, 4 p.m., Location: Olney 430

High resolution images of cells demonstrate the highly heterogeneous nature of the nuclear and cytosolic spaces. We are interested in understanding how this complex environment influences the dynamics of cellular processes. To investigate this question we have developed the convergent reaction-diffusion master equation (CRDME), a lattice particle-based stochastic reaction-diffusion method that can model the spatial transport and reactions of molecules within domains derived from imaging data. In this talk I will introduce the CRDME, and explain how it is similar in spirit to the popular reaction-diffusion master equation (RDME) model. The CRDME allows for the reuse of the many extensions of the RDME developed to facilitate modeling within biologically realistic domains, while eliminating one of the major challenges in using the RDME model.

Geometric Structure in Dependence Models and Applications

• Elisa Perrone, Department of Mathematical Sciences, UMass Lowell
• Wednesday, November 20, 4 p.m., Location: Olney 430

The growing availability of data makes it challenging yet crucial to model complex dependence traits. For example, hydrological and financial data typically display tail dependences, non- exchangeability, or stochastic monotonicity. Copulas serve as tools for capturing these complex traits and constructing accurate dependence models which resemble the underlying distributions of data. This talk inquires into the geometric properties of dependence models and copulas to address statistical challenges in several applications, such as hydrology and weather forecasting. In particular, we study the class of discrete copulas, i.e., restrictions of copulas to uniform grid domains, which admits representations as convex polytopes. In the first part of this talk, we give a geometric characterization of discrete copulas with desirable stochastic constraints in terms of the properties of their associated convex polytopes. In doing so, we draw connections to the popular Birkhoff polytopes, thereby unifying and extending results from both the statistics and the discrete geometry literature. We further consolidate the statistics/discrete geometry bridge by showing the significance of our geometric findings to construct entropy-copula models useful in hydrology. In the second part of this talk, we focus on weather forecasting problems. We show that discrete copulas are powerful tools for empirical modeling in applications. We discuss their use in the context of statistical postprocessing of ensemble weather forecasts, and present a case study for temperature forecasts in Austria.

Dimension of Sumsets of Restricted Digit Cantor Sets in the Integers

• Daniel Glasscock, Department of Mathematical Sciences, UMass Lowell
• Wednesday, December 4, 4 p.m., Location: Olney 430

Harry Furstenberg made a number of conjectures in the 60's and 70’s seeking to make precise the heuristic that there is no common structure between digit expansions of real numbers in different bases. Recent solutions to conjectures of his concerning the dimension of sumsets and intersections of p- and q- invariant sets now shed new light on old problems. In this talk, I will explain how to use tools from fractal geometry and uniform distribution to determine the dimension of sumsets of restricted digit Cantor sets with respect to different bases in the integers. This talk is based on joint work with Joel Moreira and Florian Richter.

Spring 2019

Computational Plasma Physics in the Solar System and Beyond

• Ofer Cohen, Department of Physics, UMass Lowell
• February 13, 3-4 p.m. Room: Olney 430

Applications of Statistical Modeling in Cognitive Neuroscience

• Kensuke Arai, Department of Mathematics and Statistics, Boston University
• February 19, 3:30-4:30 p.m. Room: Olney 430

Undergraduate Special Seminar: Cost Estimator Career

• Ryan Porter, Hanscom Air Force Base
• March 19, 2-2:30 p.m. Room: Olney 430

The Barycenter Method for Direct Optimization: an Overview, with Applications to Estimation of Switched Linear Models

• Felipe Pait, Electrical Engineering, Universidade de Sao Paulo
• March 25, 4-5 p.m. Room: Olney 430

Hardy Spaces of Fuchsian Groups

• Alexander Kheifets, Mathematical Sciences, UMass Lowell
• April 17, 4-5 p.m. Room: Olney 430

Evaluation of Far-field Gravitational-Wave Signals From Near-field Data

• Scott Field,Mathematics, UMass Dartmouth
• April 24, 4-5 p.m. Room: Olney 430

Master Thesis Defense: Accurate Numerical Solutions of Helmholtz Equation using Layered Media Green's Function

• Djeneba Kassambara, Mathematical Sciences, UMass Lowell
• April 25, 2-3 p.m. Room: Olney 430

Fall 2018

Improved Nystrom Kernel Matrix Approximation for Large-Scale Learning: Practical and Theoretical Aspects

• Farhad Pourkamali, Computer Science, UMass Lowell
• September 20, 2-3 p.m. Room: Olney 430

Computational methods for approaching slow manifolds, tracking extreme events, and understanding multi-scale dynamics

• Jeffrey Oishi, Bates College
• October 4, 2-3 p.m. Room: Olney 430

Inverse problem for generalized de Branges matrices

• Volodymyr Derkach, UMass Lowell
• October 11, 2-3 p.m. Room: Olney 430

Grocery stores and coffee shops: using random choices to make good decisions

• Amanda Redlich, Mathematical Sciences, UMass Lowell
• October 18, 2-3 p.m. Room: Olney 430

Hidden Physics Models: Machine Learning of Non-Linear Partial Differential Equations

• Maziar Raissi, Brown University
• November 8, 2-3 p.m. Room: Olney 430

Equilibrium and near-equilibrium dynamics of plasma in magnetic confinement devices

• Wrick Sengupta, Courant Institute of Mathematical Sciences, NYU
• November 15, 2-3 p.m. Room: Olney 430

Fast direct high-order methods for electromagnetic scattering from bodies of revolution

• Mike O'Neil, Courant Institute of Mathematical Sciences, NYU
• December 6, 2-3 p.m. Room: Olney 430

Spring 2018

Multi-marginal extensions of monotone operator theory and convex analysis

• Sedi Bartz, Department of Mathematical Sciences, UMass Lowell
• February 26, 3:30 - 4:30 p.m. Room: Olney 430

Quantile graphical model: a Bayesian approach

• Nilabja Guha, Department of Mathematical Sciences, UMass Lowell
• March 19, 3:30 - 4:30 p.m. Room: Olney 430

A hybridizable discontinuous Galerkin solver for axisymmetric plasma equilibrium

• Tonatiuh Sanchez-Vizuet, New York University
• April 9, 3:30 - 4:30 p.m. Room: Olney 430

Time reversibility of stationary processes

• Issa Zakeri, Drexel University
• April 24, 3:30 - 4:30 p.m. Room: Olney 430

Gromov's method for particle flow filters

• Fred Daum, Raytheon Company
• April 30, 3:30 - 4:30 p.m. Room: Olney 430

Fall 2017

On the behavior of the Douglas-Rachford algorithm in possibly non convex settings

• Minh N. Dao, CARMA, University of Newcastle, Australia
• September 14, 4:30 - 5:30 p.m. Room: Olney 430

Some recent results in Geometry and 2nd order ODEs

• Dimitris Christodoulou, Department of Mathematical Sciences, UMass Lowell
• September 21, 4:30 - 5:30 p.m. Room: Olney 430

Analysis of statistical tables with applications to transit networks

• Lee Jones, Department of Mathematical Sciences, UMass Lowell
• October 5, 4:30 - 5:30 p.m. Room: Olney 430

Windowed Green Function Method for problems of scattering by metasurfaces

• Carlos Perez-Arancibia, Department of Mathematics, MIT
• October 13, 4-5 p.m. Room: Olney 430

Hybridizable discontinuous Galerkin methods for Korteweg-de Vries type equations

• Bo Dong, Department of Mathematics, UMass Dartmouth
• October 26, 4:30 - 5:30 p.m. Room: Olney 430

Large gaps for Steklov eigenvalues under fixed boundary geometry

• Donato Cianci, Department of Mathematics, University of Michigan
• November 9, 4:30 - 5:30 p.m. Room: Olney 430

On local minimax learning risk bounds for pattern classification

• Lee Jones, Department of Mathematical Sciences, UMass Lowell
• November 17, 4:00 - 5:00 p.m. Room: Olney 430

Parametrized Homeomorphic Measures Theorems

• Vidhu Prasad, Department of Mathematical Sciences, UMass Lowell
• November 30, 4:30 - 5:30 p.m. Room: Olney 430

Numerical collocation method for simulating 1-D PDE model of human tear film dynamics

• Alfa Heryudono, Department of Mathematics, UMass Dartmouth
• December 7, 4:30 - 5:30 p.m. Room: Olney 430

Spring 2017

High resolution solution of inverse scattering problems

• Carlos Borges, University of Texas at Austin
• February 2, 4-5 p.m. Room: Olney 430

A scalable Bayesian Method for Integrating Functional Information in Genome-wide Association Studies

• Jingjing Yang, Biostatistics Department, University of Michigan
• February 21, 4-5 p.m. Room: Olney 212

Constructions of c-splitting potentials

• Sedi Bartz, University of British Columbia Okanagan
• February 27, 4-5 p.m. Room: Olney 212

A Frame Theoretic Approach of Non-uniform Fourier Data Processing

• Guohui Song, Clarkson University
• March 6, 4-5 p.m. Room: Olney 212

Bayesian approaches in inverse problems and uncertainty quantification

• Nilabja Guha, Texas A&M
• March 21, 4-5 p.m. Room: Olney 212

A stochastic methodology for the design of random meta-materials

• Ivi Tsantili, Beijing Computational Science Research Center
• April 6, 4-5 p.m. Room: Olney 430