All Seminars

Title: Fast and stable algorithms for large-scale computation
Colloquium: Computational Mathematics
Speaker: Yuanzhe Xi of University of Minnesota
Contact: James Nagy, jnagy@emory.edu
Date: 2018-02-08 at 4:00PM
Venue: MSC W301
Download Flyer
Abstract:
Scientific computing and data analytics have become the third and fourth pillars of scientific discovery. Their success is tightly linked to a rapid increase in the size and complexity of problems and datasets of interest. In this talk, I will discuss our recent efforts in the development of novel numerical algorithms for tackling these challenges. In the first part, I will present a stochastic Lanczos algorithm for estimating the spectrum of Hermitian matrix pencils. The proposed algorithm only accesses the matrices through matrix-vector products and is suitable for large-scale computations. This algorithm is one of the key ingredients in the new breed of “spectrum slicing”-type eigensolvers for electronic structure calculations. In the second part, I will present our newly developed fast structured direct solvers for kernel systems and its applications in accelerating the learning process. By exploiting intrinsic low-rank property associated with the coefficient matrix, these structured solvers could overcome the cubic solution cost and quadratic storage cost of standard dense direct solvers and provide a new framework for performing various matrix operations in linear complexity.
Title: The Riemann Hypothesis
Seminar: Algebra
Speaker: Ken Ono of Emory University
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2018-02-06 at 4:00PM
Venue: W304
Download Flyer
Abstract:
Title: Optimization for scalable graph analytics
Colloquium: Computational Mathematics
Speaker: Kimon Fountoulakis of University of California, Berkeley
Contact: James Nagy, jnagy@emory.edu
Date: 2018-02-05 at 4:00PM
Venue: MSC W301
Download Flyer
Abstract:
Graphs, long popular in computer science and discrete mathematics, have received renewed interest because they provide a useful way to model many types of relational data. In biology, e.g., graphs are routinely used to generate hypotheses for experimental validation; in neuroscience, they are used to study the networks and circuits in the brain; and in social networks, they are used to find common behaviors of users. These modern graph applications require the analysis of large graphs, and this can be computationally expensive. Graph algorithms have been developed to identify and interpret small-scale local structure in large-scale data without the requirement to access all the data. These algorithms have been mainly studied in the field of theoretical computer science in which algorithms are viewed as approximation methods to combinatorial problems.\\ \\In our work, we take a step back and we analyze scalable graph clustering methods from data-driven and variational perspectives. These perspectives offer complementary points of view to the theoretical computer science perspective. In particular, we study implicit regularization properties of certain methods, we solve data-driven issues of existing methods, we explicitly show what optimization problems certain graph clustering procedures are solving, we prove that existing optimization methods have better performance and generalize to unweighted graphs, and finally we demonstrate how state-of-the-art methods can be efficiently parallelized for modern multi-core hardware.
Title: New Era in Distributed Computing with Blockchains and Databases
Seminar: Computer Science
Speaker: Dr. C. Mohan of IBM Fellow and Distinguished Visiting Professor - Tsinghua University
Contact: Li Xiong, lxiong@emory.edu
Date: 2018-02-02 at 3:00PM
Venue: MSC E208
Download Flyer
Abstract:
A new era is emerging in the world of distributed computing with the growing popularity of blockchains (shared, replicated and distributed ledgers) and the associated databases as a way of integrating inter-organizational work. Originally, the concept of a distributed ledger was invented as the underlying technology of the cryptocurrency Bitcoin. But the adoption and further adaptation of it for use in the commercial or permissioned environments is what is of utmost interest to me and hence will be the focus of this keynote. Computer companies like IBM and Microsoft, and many key players in different vertical industry segments have recognized the applicability of blockchains in environments other than cryptocurrencies. IBM did some pioneering work by architecting and implementing Fabric, and then open sourcing it. Now Fabric is being enhanced via the Hyperledger Consortium as part of The Linux Foundation. A few of the other efforts include Enterprise Ethereum, R3 Corda and BigchainDB. While there is no standard in the blockchain space currently, all the ongoing efforts involve some combination of database, transaction, encryption, consensus and other distributed systems technologies. Some of the application areas in which blockchain pilots are being carried out are: smart contracts, supply chain management, know your customer, derivatives processing and provenance management. In this talk, I will survey some of the ongoing blockchain projects with respect to their architectures in general and their approaches to some specific technical areas. I will focus on how the functionality of traditional and modern data stores are being utilized or not utilized in the different blockchain projects. I will also distinguish how traditional distributed database management systems have handled replication and how blockchain systems do it. Since most of the blockchain efforts are still in a nascent state, the time is right for database and other distributed systems researchers and practitioners to get more deeply involved to focus on the numerous open problems.
Title: Computational mathematics meets medicine: Formulations, numerics, and parallel computing
Colloquium: Computational Mathematics
Speaker: Andreas Mang of University of Houston
Contact: James Nagy, jnagy@emory.edu
Date: 2018-02-01 at 4:00PM
Venue: MSC W301
Download Flyer
Abstract:
We will discuss computational methods that integrate imaging data with (bio)physics simulations and optimization in an attempt to aid decision-making in challenging clinical applications. In particular, we will focus on PDE-constrained formulations for diffeomorphic image registration, a classical inverse problem, which seeks to find pointwise correspondences between two or more images of the same scene. In its simplest form, the PDE constraints are the transport equations for the image intensities. We will augment these equations with a model of brain cancer progression to enable data assimilation in brain tumor imaging. We will see that our formulation yields strongly coupled, nonlinear, multiphysics systems that are challenging to solve in an efficient way. We will discuss the formulation, discretization, numerical solution, and the deployment of our methods in high-performance computing platforms. Our code is implemented in C/C++ and uses the message passing interface (MPI) library for parallelism.\\ \\We will showcase results for clinically relevant problems, study numerical accuracy, rate of convergence, time-to-solution, inversion quality, and scalability of our solver. We will see that we can solve clinically relevant problems (50 million unknowns) in less than two minutes on a standard workstation. If we use 512 MPI tasks we can reduce the runtime to under 2 seconds, paving the way to tackle real-time applications. We will also showcase results for the solution of registration problems of unprecedented scale, with up to 200 billion unknowns.
Title: Irrational points on random hyperelliptic curves
Seminar: Algebra
Speaker: Jackson Morrow of Emory University
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2018-01-30 at 4:00PM
Venue: W304
Download Flyer
Abstract:
We consider genus $g$ hyperelliptic curves over $\mathbb{Q}$ with a rational Weierstrass point, ordered by height. If $d
Title: On strong Sidon sets of integers
Seminar: Combinatorics
Speaker: Sang June Lee of Duksung Women's University
Contact: Dwight Duffus, dwight@mathcs.emory.edu
Date: 2018-01-29 at 4:00PM
Venue: MSC W303
Download Flyer
Abstract:
FOR FULL ABSTRACT SEE PDF ATTACHMENT. The motivation of strong Sidon sets is that a strong Sidon set generates many Sidon sets by altering each element a bit. This implies that a dense strong Sidon set will guarantee a dense Sidon set contained in a sparse random subset of N. In this talk, we are interested in how dense a strong Sidon set can be. This is joint work with Yoshiharu Kohayakawa, Carlos Gustavo Moreira and Vojtech Rodl.
Title: New methods in EEG/MEG source analysis
Seminar: Numerical Analysis and Scientific Computing
Speaker: Johannes Vorwerk of Scientific Computing and Imaging (SCI) Institute, University of Utah
Contact: Lars Ruthotto, lruthotto@emory.edu
Date: 2018-01-26 at 2:00PM
Venue: MSC W301
Download Flyer
Abstract:
Electro- and magnetoencephalography (EEG and MEG) have become important tools for non-invasive functional neuroimaging due to their unique time resolution. In many applications of EEG/MEG, the goal is to reconstruct the sources inside the brain volume that evoke the measured signal, which leads to a related ill-posed inverse problem (EEG/MEG inverse problem). To solve this inverse problem accurately, it is necessary to precisely simulate the electric/magnetic field caused by a point-like source inside the brain volume: the so-called forward problem of EEG/MEG. When aiming to take the individual head shape and conductivity distribution of the subject’s head into account, the EEG/MEG forward problem has to be solved numerically, e.g., using finite element methods (FEM). In this talk, we present examples showing how the use of novel mathematical methods can increase the accuracy of and help to better understand the uncertainties inherent to EEG/MEG forward solutions. We further analyze the influence of these uncertainties on EEG/MEG inverse solutions.
Title: Cohomology of hyperkahler manifolds
Seminar: Algebra
Speaker: Nikon Kurnosov of University of Georgia
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2018-01-23 at 4:00PM
Venue: W304
Download Flyer
Abstract:
Hyperkahler manifolds are Riemannian manifolds with three complex structures satisfying quaternionic relations and kahler. There are known just few of them with maximal holonomy and being compact starting from K3. But existence of new examples and explicit structure of cohomology remain open. In this talk I will speak about cohomology of hyperkahler manifolds, Verbitsky, Loojenga and Lunts have proved that Lie algebra $so(4,b_2-2)$ acts on cohomology. Using it we can prove that the second Betti number is bounded and that all cohomology of hyperkahler manifold $X$ can be embedded into the cohomology of the product of several copies of abelian variety A, what generalize classical Kuga-Satake construction.
Title: Building Energy - Modeling, Optimization and Optimal Control
Seminar: Numerical Analysis and Scientific Computing
Speaker: Raya Horesh of IBM Research AI, TJ Watson Research Center
Contact: Lars Ruthotto, lruthotto@emory.edu
Date: 2018-01-19 at 2:00PM
Venue: MSC W301
Download Flyer
Abstract:
Buildings consume about 40\% of the total energy in most countries, contributing to a significant amount of greenhouse gas (GHG) emissions and global warming. Therefore, reducing energy consumption in buildings, making buildings more energy efficient and operating buildings in more energy efficient manner are important tasks. Analytics can play an important role in identifying energy saving opportunities in buildings by modeling and analyzing how energy is consumed in buildings and optimizing energy consuming operations of buildings. In this talk I will cover areas ranging from physics based (ODE/PDE models) and data driven modeling to inverse problem for parameter estimation and model predictive control (MPC) framework that optimally determines control profiles of HVAC system given dynamic demand response signal, on-site energy storage system and energy generation system while satisfying thermal comfort of building occupants within the physical limitation of HVAC and other equipment.